Stephen Diehl

Book Review: What We Can Know

Thu, 02 Apr 2026 01:00:00 +0000

Book Review: What We Can Know

Ian McEwan has described What We Can Know as "science fiction without the science," which is both a fair warning and a precise advertisement. The novel is set in 2119. Rising seas and a cascade of nuclear wars (including a misfired Russian warhead in the Atlantic and something called the Third Sino-American War) have halved the world's population and turned Britain into a sleepy archipelago of mountain peaks connected by ferries and funiculars. The Bodleian Library has been relocated to Snowdonia. The global currency is the Nigerian naira. The United States is a lawless territory of feuding warlords. People navigate between islands in electric canoes. Oxford's Sheldonian Theatre is underwater. And the people of this era look back at the early twenty-first century with the specific mixture of envy and contempt that we reserve for civilizations that had everything and squandered it. They call our time "the Derangement." They study us the way we study the late Romans: as a case study in spectacular, voluntary decline.

McEwan builds this world with the offhand confidence of someone who has thought about it for a very long time and decided that understatement is more frightening than spectacle. He never dwells on the catastrophe. He simply places you in its aftermath and lets you feel the weight of what is missing. The future is rendered in small, devastating details: a literature professor teaching to near-empty rooms, "a relic of the humanities in a world that no longer values them, a poor cousin to the water scientists." The only growth industries are data recovery and atmospheric management. Meanwhile, future scholars study the period 1990-2030 under the rubric "90.30 literature," and their verdict on us is brutal: "They were big and brave, superb scholars and scientists, musicians, actors and athletes, and they were idiots who were throwing it all away."

Into this world McEwan places Tom Metcalfe, a literature professor who has devoted his career to reconstructing a lost poem. The poem, "A Corona for Vivien," was written by the celebrated (and, as we will learn, monstrous) poet Francis Blundy. A corona is a chain of linked sonnets where each begins with the final line of the previous one and the sequence closes when the first line returns, forming a circle. Blundy read it aloud at his wife Vivien's birthday dinner in 2014. The few who heard it called it the capstone of his career, comparable to The Waste Land. He then destroyed all drafts, making the single vellum copy a unique gift. The poem was never seen again.

Tom has access to the complete digital archive of the early twenty-first century. Quantum computing broke all the cryptography of our era, cracking open every encrypted data silo, every private message, every corporate vault. The result is total transparency: every email, every text message, every shopping list, every social media post, all of it preserved in servers in New Lagos, all of it legible to anyone with a library card. He can reconstruct the dinner party guest by guest, message by message. And here is the novel's central, quietly devastating paradox: having all the data changes nothing. The fundamental truth about the poem, about the people who made and destroyed it, remains hidden. As Tom observes with the wry frustration of a man drowning in information: "If you want your secrets kept, whisper them into the ear of your dearest, most trusted friend. Do not trust the keyboard and screen. If you do, we'll know everything." Everything, that is, except what matters.

This is McEwan's epistemological argument, and he pursues it with the rigor of a philosopher and the patience of a novelist who has been thinking about narrative and knowledge for fifty years. The past, he argues, is always a reconstruction. "Memory is a sponge. It soaks up material from other times, other places and leaks it all over the moment in question." A journal "fixes events like beads on a string," but lived experience refuses to be sequential. The imagined, he writes, "lords it over the actual, no paradox or mystery there." What we can know, it turns out, is bounded on all sides by what we want to believe, what we can remember, and what we are willing to see.

The novel's second half detonates everything the first half has built. Vivien's own memoir surfaces, and in it we learn that Francis Blundy, revered poet, climate change denier, man of letters compared to Heaney and Larkin, murdered Vivien's first husband. Percy Greene, a luthier with early-onset Alzheimer's, was pushed down the stairs and finished with a mallet. Blundy framed it as mercy. He then absorbed the dead man's suffering into his poetry, transmuting private horror into public art. The famous "Corona for Vivien" was, in coded form, a confession of this crime and an aestheticization of the grief it produced. Vivien, recognizing the poem as a beautiful counterfeit that stole her real memories and repackaged them as literary accomplishment, fed the vellum into a dairy stove. The poem burned. She then buried her prose account, ensuring that the truth, rather than the artful lie, would reach the future.

McEwan has always been drawn to people who believe their own brilliance exempts them from ordinary moral constraints, and Blundy is the fullest realization of this obsession. The novel asks whether great art can launder terrible acts and has the courage to leave the question genuinely open. When Vivien destroys the poem, you feel the loss and the justice simultaneously, and that simultaneity is the point. The beauty of the work and the cruelty of the man who made it occupy the same space, and McEwan will not let you collapse one into the other.

If you have read Atonement, you will recognize the engine: nested narratives, the question of who controls the story, the devastation that arrives when the reader's reconstruction collides with the truth. But where Atonement asked whether fiction could redeem guilt, What We Can Know goes further. It suggests that the possibility of redemption was always a comfortable fiction, and that what remains is persistence. A colleague's pregnancy near the end is described as "the next link in the chain of futility and care," with the emphasis falling equally on both nouns. You keep going because the work of reconstruction (of poems, of knowledge, of a livable world) has its own dignity regardless of outcome.

The novel is dense, and it is about more things than any single review can cover. It is about the humanities and whether they survive catastrophe (they do, barely, and in diminished form, and the novel argues this diminished survival is still worth something). It is about climate change as a moral solvent that dissolves familiar categories into entropy. It is about the specific longing of looking backward at a world you never knew, for which McEwan observes we need a word "beyond nostalgia, which pines for what was once known." It is about the relationship between scholarship and love, between archival precision and emotional truth, between the living and the dead.

McEwan's prose has loosened with age. The earlier novels were watchmaker-precise, sometimes to the point of airlessness. Here the sentences breathe. There is humor (dry, English, arriving when you least expect it) and a warmth toward the characters that his earlier work sometimes withheld. The New York Times called it "the best thing McEwan has written in ages." The Scotsman called it his masterpiece. I think they are both right. It is the rare novel that will make you feel as deeply as it makes you think, and the rarer one still that earns the right to that ambition.

McEwan has said that his goal was "to let the past, present and future address each other across the barriers of time." He has succeeded. If you are reading this in 2026, the novel's future scholars have already rendered their verdict on you. The fact that you are reading a book review rather than doomscrolling may, by the standards of 2119, constitute a minor act of civilization. Make the most of it.

Book Review: There Is No Antimemetics Division

Sun, 22 Mar 2026 00:00:00 +0000

Book Review: There Is No Antimemetics Division

There is a particular flavor of horror that only people who work with formal systems for a living can fully appreciate. It is the horror of data loss, of silent corruption, of the thing that fails without logging an error. It is the backup that was never tested. The monitoring system that monitors everything except its own health. The silent failure that propagates through a distributed system for weeks before anyone notices, and by the time you do notice, the state of the world has drifted so far from what you believed it to be that the gap itself has become invisible. If Kafka wrote incident reports, they would read like this novel. If this specific dread resonates with you on a spiritual level, then Sam Hughes (writing as qntm) has written your nightmare scenario, scaled up from a database to the entire ontological fabric of reality, and turned it into one of the most inventive science fiction novels of the past decade.

The premise is this: a meme is an idea that wants to be known. It spreads, replicates, and lodges itself in your mind. An antimeme is the opposite. It is an idea, or an entity, or a phenomenon that actively resists being perceived or remembered. The moment you stop looking at it, it vanishes from your mind, and so does the fact that you were ever looking. You cannot fight it because you cannot remember it exists. You cannot organize a defense because the knowledge that a defense is needed is the first thing it destroys. The monster hides in the structure of cognition itself. The darkness is a feature.

The book originated as a series of entries on the SCP Foundation wiki, a collaborative fiction project where contributors write clinical, bureaucratic documentation for fictional anomalous objects and entities. If you have never encountered SCP, imagine the filing cabinets of a secret agency that catalogs impossible things with the same dry procedural language you would use to document a network outage. The SCP Foundation is, in essence, what would happen if the IETF wrote horror fiction, and the result is exactly as wonderful as that sounds. It is one of the genuinely great creative experiments of the internet age, and Hughes's Antimemetics Division entries are widely regarded as the best thing to come out of it. The novel collects and revises these into a coherent narrative, and it works beautifully as a standalone book.

The protagonist, Marion Wheeler, runs the Antimemetics Division. Her job is to remember things that the universe is trying to make her forget. She and her staff take mnestic drugs (the opposite of amnestics: chemicals that force you to retain memories your brain is actively discarding) to perceive and fight threats that are, by their nature, invisible to everyone else. The drugs have brutal side effects. The work has worse ones. You are fighting a war that nobody knows is happening, that nobody will remember you fought, and that erases its own history as it proceeds. Every victory is immediately forgotten. Every sacrifice is invisible. It is, in other words, open source maintainership as cosmic horror. This is heroism that is structurally incapable of being recognized, which is either the noblest possible form of service or the most absurd possible form of futility, and Hughes has the good sense not to tell you which.

The novel's cosmology is built on a hierarchy where information is more real than matter. Beneath ordinary three-dimensional spacetime lies the noosphere: the space of all human-conceivable ideas, memes, and concepts, a vast ecology that transcends the physical world and can retroactively edit memory, identity, and even the historical record. The noosphere is not a metaphor. It is, within the novel's logic, the true substrate of reality, and the physical world is a shadow cast by it. This idea-space has its own fauna, including antimemetic spiders and various lesser predators that rip through the membrane between concept and matter. And at the top of the food chain sits SCP-3125 (renamed in the published edition, but the designation is so perfect I am using it anyway): a five-dimensional informational apex predator shaped, in the rare moments anyone perceives it, like a starfish. It is so vast and so hostile that anyone who successfully conceptualizes it is detected and killed. Knowing about it is lethal. Understanding it is lethal. The act of comprehension is the attack surface. This is Lovecraftian horror translated into information theory with perfect fidelity. Lovecraft's cosmos was terrifying because it was indifferent and vast. Hughes's cosmos is terrifying because it is hostile and memetic. The monster lurks in the act of thinking about it.

What elevates the book from clever premise to genuine art is what it does with memory and identity. Marion's strategy for fighting SCP-3125 involves systematically erasing her own memories to deny the entity information it could use as a vector. She forgets her husband. She forgets her colleagues. She works from notes and recordings because her own mind has become unreliable. The protagonist of the novel is a woman who is voluntarily dismantling her own identity in order to save a world that will never know she existed. Every convention of the heroic arc is inverted. The hero loses knowledge and power over the course of the story. Deliberately. The sacrifice goes beyond death (though that comes too). The real sacrifice is self-erasure: the voluntary destruction of everything that makes you you.

And then, in the second half, something extraordinary happens. Marion's husband, Adam, senses her absence. He cannot remember her. He has no evidence she existed. But there is a hole in his life that has her shape, and the shape will not go away. Love, the novel argues, leaves traces that even antimemetic erasure cannot fully remove. This is the most emotionally devastating science fiction idea I have encountered in years, and Hughes handles it with the restraint and precision it deserves. In a lesser book it would be sentimental. Here it is earned, because the entire preceding narrative has been a rigorous demonstration of exactly how much can be lost, which makes the thing that persists feel miraculous.

The novel's form mirrors its content in a way that is both structurally elegant and deeply unsettling. Chapters begin mid-scene because the context has been erased. Characters appear without introduction because the reader, like the characters, has been dropped into a situation whose history is missing. You read the way the Antimemetics Division works: assembling fragments, inferring what is missing from the outline of what remains, never certain your reconstruction is correct. It is the only honest way to tell a story about forgetting.

If you work with systems, if you think about information, if you have ever been kept up at night by the fragility of the things we build and the ease with which they can fail silently, this book will get under your skin and stay there. It is Lovecraft for people who think in terms of information theory. It is a horror novel where the monster is an idea and the weapon is your own capacity to understand it. It is brilliant, it is original, and it is the best argument I have seen for why the SCP Foundation is one of the most important literary projects of the twenty-first century. That a novel this good started life as collaborative wiki fiction is itself an antimemetic phenomenon: a masterpiece hiding in plain sight in a format that literary culture is constitutionally incapable of taking seriously. Read it, and then try to remember that you did.

Book Review: Piranesi

Mon, 09 Mar 2026 00:00:00 +0000

Book Review: Piranesi

Susanna Clarke's Piranesi is a book about a man who lives in a House. The House has an infinite number of marble halls. Ocean tides flood the lower floors. Clouds drift through the upper ones. Thousands of statues stand in the middle halls, each one unique, depicting figures from mythology and daily life and everything in between. The narrator maps the halls, tracks the tides, catches fish to eat, and keeps meticulous journals. He calls himself Piranesi. He believes he is one of two living people in the entire world. He is happy.

If this sounds like a fairy tale, it reads like one too. The prose is plain, earnest, and completely without irony, delivered in the cadence of a naturalist's field journal. Piranesi describes extraordinary things (tidal waves crashing through marble vestibules, clouds forming indoors, skeletons of people who died in halls nobody else has visited) with the calm precision of someone recording the migratory patterns of local birds. The effect is hypnotic. You settle into the rhythm of his observations and begin to see the House the way he sees it: as a complete and beautiful world, sufficient unto itself.

And then, very gradually, the floor drops out.

Clarke structures the novel so that you, the reader, understand what is happening to Piranesi before he does. You notice the gaps in his journals. You catch the references to things that should not exist in an infinite marble labyrinth (shoes, a wristwatch, the word "Manchester"). You begin to assemble the real story from fragments, exactly the way an archaeologist assembles a pot from shards. The dramatic irony is sustained for the entire book, and it is devastating, because Piranesi's innocence is so total and so genuine that watching it dissolve feels like a small crime.

The philosophical engine of the novel is a question about identity and memory. Piranesi's real name, real history, and real knowledge have been taken from him. What remains is a person who is good, curious, and attentive to the world he inhabits. Clarke asks whether this person, built from the ruins of another person, is less real than the original. Her answer is generous and quietly radical: the self that pays attention, that cares for the dead, that feels gratitude for the beauty of statues, has its own integrity. Memory loss produced this person, but the person is real.

The name, of course, comes from Giovanni Battista Piranesi, the eighteenth-century Italian artist whose "Carceri d'Invenzione" (Imaginary Prisons) depict vast, impossible architectural spaces filled with staircases and arches that lead nowhere. The etchings are claustrophobic despite their scale. Infinite space rendered as confinement. Clarke takes the Carceri and makes them habitable, even lovely. Her narrator finds the House beautiful because he has no memory of anything else, no basis for comparison, and therefore no basis for complaint. A prison the prisoner loves. It is the novel's most quietly terrifying idea, and Clarke handles it with the lightest possible touch, trusting you to feel the weight yourself.

What makes Piranesi exceptional, and the reason I think it will last, is the quality of attention it models. Piranesi's journals are an extended practice of noticing. He names every statue. He tracks every tide. He remembers every skeleton. In a literary landscape saturated with cleverness, irony, and narrative pyrotechnics, Clarke wrote a book whose central argument is that paying attention to the world you are in, really paying attention, with care and without cynicism, is itself a moral act. It is a book about the radical sufficiency of presence. If you have ever caught yourself looking at something ordinary (a building, a riverbank, a piece of code) and felt the brief, embarrassing conviction that it was beautiful and that the beauty mattered, Clarke has written the novel about that feeling.

It is 250 pages. You will read it in a day. You will think about the statues for weeks. Clarke published it sixteen years after Jonathan Strange & Mr Norrell, which was 800 pages of baroque alternate history. Piranesi is the opposite: everything stripped to the bone, every sentence load-bearing. If Jonathan Strange was a cathedral, Piranesi is a single perfectly proportioned room. Personally, I prefer the room.

Optimal Caverna Gameplay via Formal Methods

Sat, 21 Feb 2026 00:00:00 +0000

Optimal Caverna Gameplay via Formal Methods

I always win at Caverna (Uwe Rosenberg's classic European worker placement tabletop board game). Always. But "always" just means "every time so far," and I needed something with more mathematical permanence. So I formalized the entire game in Lean 4 and proved that my strategy is the unique weakly dominant pure strategy across every possible game configuration. My friends think this is excessive. My friends also lose at Caverna. Unrelated, I don't get invited to board game night much anymore.

Caverna: The Cave Farmers is the 2013 sequel to Agricola, a game about feeding dwarfs who live in caves and do a suspicious amount of farming. You place workers, gather resources, breed animals, excavate caverns, furnish rooms, and at the end of 12 rounds the scoring formula totals up everything you've accomplished and everything you failed to accomplish. It's a good game. It's also, in the 2-player variant, a finite deterministic perfect-information system with discrete phases, which means it's a labeled transition system, which means it's amenable to formal verification. So I did that.

There is a very small mathematical model here. We just define two things: an init predicate describing the starting state, and a trans relation describing every legal state-to-state move. Then instead of running the game, you prove properties about it by structural induction: show the property holds at the start, show every legal transition preserves it, and you've covered every possible game without enumerating a single one. It's the same technique used in hardware verification and protocol proofs, applied to a board game.

The project is about 3,000 lines of Lean 4 spread across 19 modules: 11 definition files modeling the complete game (all 24 action spaces, all 48 unique furnishing tiles, the expedition loot system, board geometry, harvest schedule, scoring formula) and 8 theorem files containing 176 machine-checked proofs. The model covers all 2,880 possible 2-player game setups (144 card orderings times 20 harvest marker placements).

The main result is that furnishing rush is the weakly dominant strategy. It is the optimal response to every opponent, in every setup, regardless of which cards come out when or where the harvest markers land.

The interactive proof blueprint has the full derivation with a dependency graph showing how every theorem connects. The source code compiles.

Labeled Transition Systems

A labeled transition system (LTS) is a triple $(S, A, T)$ where $S$ is a set of states, $A$ is a set of actions, and $T \subseteq S \times A \times S$ is a transition relation specifying which state changes are legal. You start in some initial state satisfying an init predicate. The system evolves by taking actions: if $(s, a, s') \in T$, you can move from state $s$ to state $s'$ by performing action $a$. A state is reachable if there's a finite chain of transitions from an initial state to it. A property is an invariant if it holds on every reachable state.

In Lean 4, the LTS is three fields:

structure LTS (State : Type) (Action : Type) where
  init : State -> Prop
  trans : State -> Action -> State -> Prop

Reachability is an inductive type with two constructors: initial states are reachable, and if you can reach $s$ and take action $a$ to get to $s'$, then $s'$ is reachable:

inductive Reachable (sys : LTS State Action) : State -> Prop where
  | init : forall s, sys.init s -> Reachable sys s
  | step : forall s a s', Reachable sys s -> sys.trans s a s' -> Reachable sys s'

In plain terms: the LTS is the rulebook encoded as a state transition relation. init says what the starting board looks like, and trans encodes every legal move as a state-to-state constraint. The entire Caverna rulebook fits in about 250 lines of Lean: a 160-line applyPlacement function matching on all 24 action spaces with their effects, and a 90-line cavernaLTS definition wiring up phase transitions, harvest logic, and round progression. It's a relation rather than a function because Caverna has sub-choices within actions (sow grain vs. sow vegetable, which furnishing tile to install, which loot to take), so a single action space placement can lead to multiple successor states. The relation captures all of them.

Once you have init and trans, you prove a property holds on all reachable states without enumerating them. You prove the base case (holds on initial states) and the inductive step (every valid transition preserves it). This is strictly stronger than testing. Testing checks specific play sequences. An invariant proof covers every sequence of legal moves across every setup, including sequences no human would ever play.

Here's a small fragment of the Caverna LTS to give the flavor of how a round of play works as a state machine:

Each state records the player's resources and remaining dwarfs to place. Transitions correspond to action space selections. With 13 initial action spaces and 2 dwarfs, even a single round produces $13 \times 12 = 156$ placement sequences. Over 12 rounds with family growth, the branching factor is astronomical, but the LTS doesn't care. The structure is finite, and every path through it is covered by the invariant proofs.

The Game as a Transition Relation

Board games are natural LTS candidates. In Caverna 2-player, the states are the complete game configurations (round number, phase, both players' inventories, board layouts, available action spaces), the actions are dwarf placements and harvest events, and the transition relation encodes the rulebook.

The game has five phases that cycle within each round:

inductive Phase where
  | placeP1      -- player 1 places a dwarf
  | placeP2      -- player 2 places a dwarf
  | harvest      -- harvest phase (feeding, breeding, fields)
  | roundEnd     -- round cleanup, advance to next round
  | gameOver     -- game has ended

The full game state tracks everything both players could possibly have, plus the global state of the board:

structure GState where
  round : Nat
  phase : Phase
  p1 : FullPlayer
  p2 : FullPlayer
  p1IsFirst : Bool
  placementsLeft : Nat
  acc : AccState
  occupiedSpaces : List ActionSpaceId := []
  harvestSchedule : Nat -> HarvestEvent
  wishIsUrgent : Bool := false

The transition relation is a single function with a match on (gs.phase, act). Each case is a game rule. Here's the core of the placement logic for Player 1:

def cavernaLTS (schedule : Nat -> HarvestEvent) :
    TransitionSystem.LTS GState GameAction where
  init := fun gs => gs = initFullGState schedule
  trans := fun gs act gs' =>
    match gs.phase, act with
    | .placeP1, .place space choice =>
      spaceAvailable gs.round space = true /\
      spaceUnoccupied gs space = true /\
      gs.placementsLeft > 0 /\
      (let (p1', acc') := applyPlacement gs.p1 gs space choice
       let newPlacements := gs.placementsLeft - 1
       let newOccupied := space :: gs.occupiedSpaces
       if newPlacements == 0 then
         gs' = { gs with p1 := p1', acc := acc',
                         phase := .harvest, placementsLeft := 0,
                         occupiedSpaces := newOccupied }
       else
         gs' = { gs with p1 := p1', acc := acc',
                         phase := .placeP2,
                         placementsLeft := newPlacements,
                         occupiedSpaces := newOccupied })
    -- ... Player 2, harvest, round end, game over ...
    | _, _ => False

That last line is beautiful. | _, _ => False says: any action not explicitly listed is illegal. The transition relation is closed. No undefined behavior, no edge cases, no "the rules don't say I can't." If it's not in the match, it doesn't happen.

The applyPlacement function is a 250-line match on all 24 action spaces, each encoding the exact effect from the rulebook. Blacksmithing forges a weapon from ore and runs an expedition. Wish for Children can only grow your family if you have a dwelling with capacity. Excavation gives you stone and lets you carve out cavern/tunnel pairs. Every sub-choice (sow grain vs. sow vegetable, build small pasture vs. large pasture, which furnishing tile to install) is a branch in the ActionChoice type.

The Game Timeline

Twelve rounds. Green nodes are harvest rounds where dwarfs must be fed. Two critical milestones: "Wish for Children" at round 4 enables the first family growth (from 2 dwarfs to 3), and "Family Life" at round 8 enables the second (3 to 5, eventually). One new action space reveals each round, growing from 13 to 24 available choices. The interaction between when cards flip and when harvests hit is the clock that drives the entire strategic analysis.

The timeline matters because of this: without growth you get 44 total dwarf placements across all 12 rounds. With one growth at round 4, you get 47. With both growths, you get 56. That's a 27% increase in total actions from growing your family as fast as possible, and since actions are the binding constraint on everything else (scoring, food, resources), the 12-placement gap between "no growth" and "both growths" is the single most important strategic lever in the game.

One of the most satisfying patterns in the formalization is using dependent types to make illegal game states impossible to construct. Weapons are the clearest example. In the physical game, weapon strength ranges from 1 to 14. You could model this as a bare Nat and hope nobody passes in 0 or 15. Or you could make the type system enforce the constraint:

structure Weapon where
  strength : Nat
  h__min : strength >= 1
  h__max : strength <= 14

Every Weapon value carries proof that its strength is in range. This means forgeWeapon must produce evidence that the forged strength is valid, and upgradeWeapon must show that incrementing stays within bounds:

def forgeWeapon (oreSpent : Nat) (h__pos : oreSpent >= 1) : Option Weapon :=
  if h : oreSpent <= maxInitialWeaponStrength then
    some { strength := oreSpent
         , h__min := h__pos
         , h__max := by simp [maxInitialWeaponStrength] at h; omega }
  else
    none

def upgradeWeapon (w : Weapon) : Weapon :=
  if h : w.strength < maxWeaponStrength then
    { strength := w.strength + 1
    , h__min := by omega
    , h__max := by simp [maxWeaponStrength] at h; omega }
  else
    w

The by omega calls are Lean's linear arithmetic tactic closing the proof obligations automatically. If w.strength < 14, then w.strength + 1 <= 14. If oreSpent >= 1, then strength >= 1. The type checker verifies this at compile time. No weapon in the entire formalization can ever have strength 0 or 15.

The same pattern shows up in RoundPlacements, which carries proof that all four dwarf placements within a round go to distinct action spaces:

structure RoundPlacements where
  firstPlayer1  : ActionSpaceId
  secondPlayer1 : ActionSpaceId
  firstPlayer2  : ActionSpaceId
  secondPlayer2 : ActionSpaceId
  h__distinct12 : firstPlayer1 != secondPlayer1
  h__distinct13 : firstPlayer1 != firstPlayer2
  h__distinct14 : firstPlayer1 != secondPlayer2
  h__distinct23 : secondPlayer1 != firstPlayer2
  h__distinct24 : secondPlayer1 != secondPlayer2
  h__distinct34 : firstPlayer2 != secondPlayer2

Six distinctness proofs, one for each pair. You literally cannot construct a RoundPlacements where two dwarfs share an action space. The game rule is baked into the type.

The Weapon System

Weapons are forged at strength 1 through 8 (costing that many ore), then grow by +1 per expedition, capping at 14. The blue range is forgeable; the peach range requires expedition grinding. Cattle loot unlocks at strength 9, which means even if you forge at max (8 ore), you still need at least one expedition before you can get cattle.

The loot table is an inductive type with minimum strength requirements for each item:

def LootItem.minStrength : LootItem -> Nat
  | .allWeaponsPlus1    => 1
  | .dog                => 1
  | .wood               => 1
  | .grain              => 2
  | .sheep              => 2
  | .stone              => 3
  | .donkey             => 3
  | .ore                => 4
  | .wildBoar           => 4
  | .stableFree         => 5
  | .gold2              => 6
  | .furnishCavern      => 7
  | .buildFencesCheap   => 8
  | .cattle             => 9
  | .dwelling           => 10
  | .sow                => 11
  | .breedTwoTypes      => 12
  | .furnishCavernAgain => 14

At strength 1 you can loot a dog or a stick. At strength 14 you can furnish a second cavern for free. The loot count at key strengths: 3 at strength 1, 13 at strength 8, 18 at strength 14. That's 5 premium items (cattle, dwelling, sow, breed, second furnish) locked behind the expedition grind. Whether the ore investment is worth it is the core question of the weapon rush archetype, and the answer turns out to be: no, not quite.

The Universal Food Crisis

Every strategy in Caverna must solve the same problem before anything else. Both players face a food deficit at the first harvest:

Player 1 starts with 1 food and needs 4 (2 dwarfs times 2 food each). Player 2 starts with 2 food and needs 4. The gaps are 3 and 2 respectively. This is proven as universal__food__crisis:

theorem universal_food_crisis :
    feedingCost 2 0 - startingFoodP1 = 3 /\
    feedingCost 2 0 - startingFoodP2 = 2 := by decide

The implication (food__crisis__shapes__all__strategies) is that every viable archetype must spend its first few actions on food acquisition. There's no "skip feeding and go straight to scoring" option. The begging marker penalty is $-3$ points each, and the theorem absolute__floor__is__neg55 shows that a player who takes zero actions across all rounds scores $-55$. The food crisis isn't optional; it's structural.

The food conversion network itself is a delightful mess of exchange rates. Cattle gives 4 food per animal, wild boar gives 3, sheep gives 2, grain gives 1, vegetables give 2, gold converts lossily at $n-1$ (1 gold is wasted as overhead), and rubies are emergency food at 2+ each. And then there are donkeys, which have a superlinear pairing bonus that I spent an embarrassing amount of time formalizing:

def donkeyFoodValue (n : Nat) : Nat :=
  let pairs := n / 2
  let remainder := n % 2
  pairs * 3 + remainder * 1

theorem donkey__superlinear :
    donkeyFoodValue 2 > donkeyFoodValue 1 + donkeyFoodValue 1 := by decide

Two donkeys together yield 3 food, but individually they'd give 1 + 1 = 2. The whole is greater than the sum of its parts. Uwe Rosenberg almost certainly didn't think about this as a super-additivity property of a set function, but that's what it is, and Lean can prove it.

The Feeding Cascade

The feeding function is the core survival mechanic. When harvest hits, each dwarf eats 2 food (offspring eat 1). If you don't have enough food, the deficit cascades through your resources: try food first, then convert grain (1 food each), then convert vegetables (2 food each), then take begging markers for anything remaining.

def FullPlayer.feed (p : FullPlayer) : FullPlayer :=
  let cost := p.dwarfs * 2 + p.offspring * 1
  if p.food >= cost then
    { p with food := p.food - cost }
  else
    let deficit := cost - p.food
    let p' := { p with food := 0 }
    let grainUsed := min p'.grain deficit
    let p'' := { p' with grain := p'.grain - grainUsed }
    let deficit' := deficit - grainUsed
    let vegUsed := min p''.vegetables (deficit' / 2 + deficit' % 2)
    let vegFood := min (vegUsed * 2) deficit'
    let p''' := { p'' with vegetables := p''.vegetables - vegUsed }
    let deficit'' := deficit' - vegFood
    { p''' with beggingMarkers := p'''.beggingMarkers + deficit'' }

And a normal harvest is the composition of three phases in one elegant pipeline:

def FullPlayer.normalHarvest (p : FullPlayer) : FullPlayer :=
  p.fieldPhase.feed.breedingPhase

Field phase harvests your sown crops. Feed pays the food cost (or generates begging markers). Breeding adds one animal per type that has at least two. The order matters: fields produce food before feeding, and breeding happens after, so newborn animals don't need to be fed in the same round they appear. This ordering rule from page 6 of the Caverna rulebook is encoded in the function composition.

Furnishing Tiles and the BonusContext

There are 48 furnishing tiles in the game, each with resource costs, base victory points, and (for some) end-game bonus scoring formulas that depend on your final board state. The BonusContext struct captures everything a furnishing tile might look at when computing its bonus:

structure BonusContext where
  stoneInSupply        : Nat := 0
  oreInSupply          : Nat := 0
  sheepCount           : Nat := 0
  cattleCount          : Nat := 0
  numAdjacentDwellings : Nat := 0
  numArmedDwarfs       : Nat := 0
  numDwarfs            : Nat := 0
  rubyCount            : Nat := 0
  grainCount           : Nat := 0
  vegCount             : Nat := 0
  farmAnimalCount      : Nat := 0
  hasAnyWeapon         : Bool := false
  allDwarfsArmed       : Bool := false
  numYellowTagTiles    : Nat := 0

The bonus point function is a match on tile ID that implements every scoring formula from the Caverna appendix:

def furnishingBonusPoints (fid : FurnishingId) (ctx : BonusContext) : Nat :=
  match fid with
  | .stoneStorage   => ctx.stoneInSupply
  | .oreStorage     => ctx.oreInSupply / 2
  | .weavingParlor  => ctx.sheepCount / 2
  | .milkingParlor  => ctx.cattleCount
  | .stateParlor    => ctx.numAdjacentDwellings * 4
  | .mainStorage    => ctx.numYellowTagTiles * 2
  | .weaponStorage  => ctx.numArmedDwarfs * 3
  | .suppliesStorage => if ctx.allDwarfsArmed then 8 else 0
  | .broomChamber   => if ctx.numDwarfs >= 6 then 10
                        else if ctx.numDwarfs >= 5 then 5
                        else 0
  | .prayerChamber  => if ctx.hasAnyWeapon then 0 else 8
  | _ => 0

The Prayer Chamber is particularly nasty. It gives you 8 free points, but only if none of your dwarfs have weapons. The moment you forge a single weapon, it drops to zero. This creates a genuine strategic dilemma, formalized and proved:

theorem prayer__chamber__vs__weapons :
    furnishingBonusPoints .prayerChamber {} = 8 /\
    furnishingBonusPoints .prayerChamber { hasAnyWeapon := true } = 0 :=
  by constructor <;> native_decide

The furnishing rush archetype gets its power from stacking compatible bonus tiles: Office Room overhangs, State Parlor for +4 per adjacent dwelling (up to +16), Broom Chamber for +5 or +10 based on dwarf count, Prayer Chamber for +8 (no weapons). These bonuses compound. A player with 5 dwarfs, 4 adjacent dwellings, and no weapons can pull +39 bonus points from three tiles. That's why furnishing rush has the highest ceiling.

The Strategy Space

With the LTS, scoring function, and food economy in place, the next question is: what are the high-level plans a player can actually follow? The transition relation defines roughly $10^{30}$ possible play sequences, but the overwhelming majority of them are nonsense. Consider a player who forges a weapon in round 1 (spending precious ore), then never goes on an expedition, sows a field in round 3 but never harvests grain from it, builds a pasture in round 5 but never acquires an animal, and spends round 8 taking Starting Player for no reason. This player ends the game with a weapon they never used, an empty pasture, a field of rotting grain, and a final score somewhere around 20 points after begging penalties. The LTS covers this path. The invariant proofs hold over it. It is a legal play sequence, and it is also exactly the kind of play sequence that a five-year-old would produce by picking action spaces at random.

The vast majority of the state space looks like this: diffuse, uncommitted paths where the player dabbles in everything and commits to nothing, hemorrhaging tempo and food while accumulating resources that never convert to points. Only a handful of coherent "channels" through the action space graph lead to competitive scores against a rational opponent. A strategy archetype is a consistent pattern of action space usage across the full 12-round game. I identified eight by examining which action spaces and furnishing tiles naturally cluster together: if two actions compete for the same resources or unlock the same scoring categories, they belong to the same archetype. For example, Blacksmithing, Expedition, and weapon-dependent loot all form the weapon rush cluster, while Excavation, Housework, and bonus-scoring furnishings form the furnishing rush cluster. The classification was manual, but the Lean proofs validate it: every archetype's score estimates are derived from the formalized game rules, and the dominance relations are machine-checked over the resulting payoff matrix.

inductive StrategyArchetype where
  | furnishingRush
  | weaponRush
  | animalHusbandry
  | miningHeavy
  | balanced
  | peacefulFarming
  | rubyEconomy
  | peacefulCaveEngine

But why eight? The answer comes from the structure of the game's scoring channels. A scoring channel is a resource-to-points pathway through the action spaces: the furnishing channel runs through Excavation and Housework into furnished caverns, the weapon channel runs through Blacksmithing into expeditions and loot, and so on. There are exactly six:

inductive ScoringChannel where
  | furnishing        -- Excavation + Housework -> caverns -> furnishing tiles
  | weaponExpedition  -- Blacksmithing + Adventure -> weapons -> loot
  | agriculture       -- Clearing + Sustenance -> fields -> crops
  | animalBreeding    -- Sheep Farming + Donkey Farming -> pastures -> animals
  | mining            -- Ore/Ruby Mine Construction -> mines
  | economy           -- Starting Player + Ore Trading + Ruby Mining -> gold/rubies

Each archetype commits to a primary channel, and the eight archetypes cover all six channels (all__channels__covered). Some channels conflict over shared resources: weapon/expedition and mining both need ore, furnishing and mining both need stone. The channelsConflict function encodes these tensions. With 47 productive actions per game and each channel needing at least 6 dedicated actions to reach competitive scoring, a player can invest in at most 2 channels seriously (budget__bounds__channels). The archetypes are the maximal compatible channel combinations: 6 single-primary archetypes plus 2 hybrids (balanced spreads across 3 channels, peaceful cave engine uses weapons for food rather than scoring).

The exhaustivity proof (archetype__channel__surjection) shows every channel has at least one archetype as its primary. If you're going to score points, you have to go through a channel, and every channel is represented. No viable strategy falls outside the classification.

Each archetype has an estimated scoring ceiling (best case across all setups) and floor (worst case):

Furnishing rush tops the ceiling at 140 and ties for the highest floor at 60. Weapon rush matches the floor but caps at 120. The others trail off. The interval chart makes the dominance relationships immediately visible: furnishing rush's bar extends further right (higher ceiling) than any other archetype, and its left endpoint (floor) is as good as anyone's.

The Dominance Hierarchy

Before building the payoff matrix, we can establish partial dominance from the score estimates alone. If strategy $s$ has both a higher ceiling and a higher floor than strategy $t$ (with at least one strict inequality), then $s$ dominates $t$ in score estimates.

Solid green arrows show dominance via score estimates (higher ceiling and floor). Dashed green arrows indicate dominance established only through the full payoff matrix. Animal Husbandry and Mining Heavy are incomparable in score estimates (one has a higher ceiling, the other a higher floor), but both are weakly dominated by Furnishing Rush in the payoff matrix.

The incomparability is proven constructively:

theorem incomparable__strategies__exist :
    not (dominates .miningHeavy .animalHusbandry) /\
    not (dominates .animalHusbandry .miningHeavy) := by decide

The Payoff Matrix

The next question is what happens when two players with potentially different archetypes collide over the shared action spaces. You model this as an $8 \times 8$ payoff matrix $M$ where $M_{ij}$ is the estimated score for the row player when row plays archetype $i$ and column plays archetype $j$.

The green border marks the Furnishing Rush row (weakly dominant). Blue borders highlight the diagonal (mirror matchups, always depressed). Cell color intensity reflects payoff magnitude: light green (55) through coral (135).

In Lean, the matrix is a function from Fin 8 -> Fin 8 -> Int with all 64 entries hardcoded from the strategy analysis:

def payoffMatrix : Fin 8 -> Fin 8 -> Int
  | 0, 0 =>  85 | 0, 1 => 130 | 0, 2 => 135 | 0, 3 => 130
  | 0, 4 => 125 | 0, 5 => 135 | 0, 6 => 135 | 0, 7 => 130
  | 1, 0 =>  80 | 1, 1 =>  75 | 1, 2 => 100 | 1, 3 =>  85
  | 1, 4 =>  95 | 1, 5 => 105 | 1, 6 => 100 | 1, 7 =>  85
  -- ... 48 more entries ...

A word on what "estimated" means here. The matrix entries are derived from the formalized game rules (scoring function, food costs, action budgets), not from Monte Carlo simulation or guesswork. But they are estimates in the sense that I haven't exhaustively solved every possible 47-move sequence within each archetype. How sensitive is the result? The min__dominance__margin__is__5 theorem proves that the minimum gap between the furnishing rush row and the next-best entry in each column is exactly 5 points (occurring in the mirror matchup column). Perturbing any single entry by less than 5 points cannot flip the dominance relation. Even a 10-point swing in a single cell would only affect one column, not the global result. The Nash equilibrium is more sensitive (it depends on the diagonal), but the mirror matchup at 85 would need to drop below the next-best response value of 80 before the equilibrium shifts. The downstream proofs are machine-checked over the matrix as stated, so the formal guarantees are exact conditional on these entries.

We can do better than conditional. Replace each scalar entry with a closed interval bounding the true payoff. Mirror matchups get tight bounds (the point estimate $\pm 2$, since both players execute the same plan and contention is symmetric). Cross-archetype matchups get wider bounds ($\pm 5$, reflecting uncertainty in cross-strategy interaction). The interval payoff matrix looks like this:

structure PayoffInterval where
  lo : Int
  hi : Int
  valid : lo <= hi

def intervalPayoff : Fin 8 -> Fin 8 -> PayoffInterval
  | 0, 0 => { lo := 83, hi := 87, valid := by omega }   -- mirror: eps=2
  | 0, 1 => { lo := 125, hi := 135, valid := by omega }  -- vs weapon: eps=5
  -- ... 62 more entries ...

Robust weak dominance asks: for every column and every non-furnishing alternative, does the furnishing rush lower bound meet or exceed the alternative's upper bound? If yes, then furnishing rush dominates for ALL true payoff matrices within these intervals, not just the point estimates.

theorem robust_weak_dominance :
    forall (col : Fin 8) (alt : Fin 8), alt != 0 ->
      (intervalPayoff 0 col).lo >= (intervalPayoff alt col).hi := by decide

It passes. The tightest cell is column 0 (mirror matchup): furnishing rush $[83, 87]$ vs. weapon rush $[77, 83]$. The margin is $83 - 83 = 0$, a weak tie at the boundary. All other columns have margins of 20 or more (non__mirror__columns__robust). If the error bounds were widened by just 1 point, column 0 would fail (fragility__column__0), which tells us exactly where the result is most fragile and what the tolerance is.

The interval analysis also gives us robust welfare bounds. Nash welfare lies in $[166, 174]$ and the social optimum in $[200, 220]$. Even in the best case for selfish play and worst case for cooperation, the social optimum still exceeds Nash welfare (robust__price__of__anarchy). The prisoner's dilemma structure is not an artifact of the point estimates.

The first row is at least as large as every other row in every column. That's it. That's the whole result. In game theory this property is called weak dominance: a strategy $\sigma^*$ is weakly dominant if for all opponent strategies $o$ and all alternative strategies $\sigma$,

$$
M(\sigma^*, o) \geq M(\sigma, o)
$$

The Lean proof is furnishing__rush__weakly__dominant, and it says exactly this:

theorem furnishing_rush_weakly_dominant :
    forall (row : Fin 8) (col : Fin 8),
      payoffMatrix 0 col >= payoffMatrix row col := by decide

For all opponents, for all alternatives, the furnishing rush payoff is greater than or equal. The proof is decide: Lean's kernel checks all 64 cells. Nobody has to trust my arithmetic.

The Contention Effect

The diagonal of the payoff matrix is always depressed relative to the off-diagonal entries:

theorem diagonal__always__depressed :
    forall (i : Fin 8), exists (j : Fin 8), j /= i /\
      payoffMatrix i j > payoffMatrix i i := by decide

Every mirror matchup scores below at least one non-mirror matchup in the same row. This is the contention effect: when both players pursue the same archetype, they fight over the same action spaces. Furnishing rush mirrors compete for excavation and housework. Weapon rush mirrors fight over blacksmithing. Mining mirrors clash on ore mine construction.

The game punishes sameness. It's just that the punishment for sameness (85) is still less painful than the punishment for picking something worse (60 to 80 against an opponent who picked furnishing rush).

Nash Equilibrium and the Prisoner's Dilemma

From weak dominance, the game theory falls out like dominoes. The best response function $\text{BR} : \text{Strategies} \to \text{Strategies}$ maps each opponent strategy to the row-maximizer in the corresponding column. Since furnishing rush achieves the column maximum everywhere, BR is the constant function:

$$
\text{BR}(x) = \text{FurnishingRush} \quad \forall x
$$

A Nash equilibrium is a fixed point of the joint best-response correspondence: a pair $(a, b)$ where $a = \text{BR}(b)$ and $b = \text{BR}(a)$. Since BR is constant, the only fixed point is (FurnishingRush, FurnishingRush). Existence and uniqueness in three lines:

theorem exactly__one__nash__equilibrium :
    (exists a b, isNashEquilibrium a b) /\
    (forall a b, isNashEquilibrium a b ->
      a = .furnishingRush /\ b = .furnishingRush) :=
  <<.furnishingRush, .furnishingRush, furnishing_mirror_is_nash>,
   furnishing_mirror_unique_nash>

The uniqueness proof works by case-splitting on all 64 strategy pairs and observing that only one satisfies the Nash condition:

theorem furnishing__mirror__unique__nash :
    forall a b : StrategyArchetype,
      isNashEquilibrium a b ->
        a = .furnishingRush /\ b = .furnishingRush := by
  intro a b h
  have h1 := h.1; have h2 := h.2
  cases a <;> cases b <;> simp_all [bestResponse, isNashEquilibrium]

There is exactly one pure Nash equilibrium and it is the one where both players do the same thing. Which is a little tragic.

The Price of Anarchy

Both players score 85 in the Nash equilibrium. If they could somehow coordinate on different strategies (say furnishing rush versus animal husbandry), the combined welfare would be $135 + 75 = 210$ instead of $85 + 85 = 170$.

The price of anarchy is the ratio of the social optimum to the Nash welfare:

$$
\text{PoA} = \frac{210}{170} = \frac{21}{17} \approx 1.24
$$

Selfish play costs about 19% of the social optimum. The Lean proof is decide, because it's just arithmetic:

theorem price__of__anarchy__ratio :
    socialOptimumValue = 210 /\ nashWelfare = 170 /\
    210 * 17 = 170 * 21 := by decide

The depressing implication is that both players would prefer the other person to play something different, but neither can unilaterally deviate without making themselves worse off. You're stuck at 85 each, staring across the table at someone who also read this blog post.

The Scoring Function

A natural question is where the scores can actually land. The end-game scoring function totals up every positive and negative contribution:

def FullPlayer.score (p : FullPlayer) : Int :=
  let animals := (p.dogs + p.sheep + p.donkeys +
                  p.wildBoars + p.cattle : Int)
  let grainPts := (((p.grain + p.fieldsWithGrain * 3) + 1) / 2 : Int)
  let vegPts := ((p.vegetables + p.fieldsWithVeg * 2) : Int)
  let rubyPts := (p.rubies : Int)
  let dwarfPts := ((p.dwarfs + p.offspring) : Int)
  let pasturePts := (p.smallPastures * 2 + p.largePastures * 4 : Int)
  let minePts := (p.oreMines * 3 + p.rubyMines * 4 : Int)
  let goldPts := (p.gold : Int)
  let furnPts := p.furnishings.foldl (fun acc fid =>
    acc + ((furnishingSpec fid).basePoints : Int)) (0 : Int)
  let missingTypes :=
    (if p.sheep == 0 then 1 else 0) + (if p.donkeys == 0 then 1 else 0) +
    (if p.wildBoars == 0 then 1 else 0) + (if p.cattle == 0 then 1 else 0)
  let unusedPenalty := (p.unusedMountain + p.unusedForest : Int)
  let beggingPenalty := (p.beggingMarkers * 3 : Int)
  let missingPenalty := (missingTypes * 2 : Int)
  animals + grainPts + vegPts + rubyPts + dwarfPts + pasturePts +
  minePts + goldPts + furnPts - unusedPenalty - beggingPenalty - missingPenalty

The theoretical floor is $-55$ points: a player who takes zero actions across all rounds gets +2 for their two starting dwarfs, $-8$ for missing all four farm animal types, $-22$ for 22 unused board spaces, and $-27$ from 9 begging markers at $-3$ points each. The theoretical ceiling is 202, computed by summing the independent maxima of every scoring category. But you can't reach 202, because every scoring category competes for the same 56 dwarf placements over 12 rounds. You cannot simultaneously furnish 12 caverns, build 5 mines, breed 20 animals, and sow 10 fields. The action budget is the binding constraint. The practical ceiling is around 140, achievable by furnishing rush when uncontested.

The theoretical range is 195 points (from $-55$ to 140), but the $-55$ floor requires literally doing nothing for 12 rounds, so it's not strategically meaningful. The practical floor across all archetypes is around 45 (peaceful farming in the worst setup), giving a practical range of about 95 points. The dominant strategy's own range is 80 points (60 to 140), proven as dominant__strategy__variance. The safety margin (dominant__strategy__safety__margin) is 115 points above the theoretical floor, but the more relevant number is the gap between furnishing rush's worst case (60) and the worst viable archetype's worst case (45): even in the most adversarial setup, choosing correctly gains you at least 15 points.

Degenerate Combos

The formalization surfaced several combos that look broken in isolation. Four stand out.

The Beer Parlor converts grain to gold at a 3:2 ratio before scoring: every 2 grain becomes 3 gold. Without it, 20 grain scores 10 points (the grain formula is $\lceil n/2 \rceil$). With it, the same 20 grain becomes 30 gold. That's a 3x multiplier on the base grain value, and the gold stacks with every other scoring category. The beer__parlor__max__gold theorem proves beerParlorGold 20 = 30. The catch is accumulating 20 grain: you need aggressive sowing across multiple rounds, which means burning actions on Slash-and-Burn and Sustenance instead of excavating caverns.

Dogs have no cap on sheep-watching: $n$ dogs on one meadow guard $n+1$ sheep. Stack 10 dogs and a Weaving Parlor and you're looking at 51 points from a single tile combo. The catch is that acquiring 10 dogs requires roughly 6 expedition actions (dogs are strength-1 loot, so they're easy to get but each expedition burns an action), and those 6 actions aren't building caverns or growing your family.

The Writing Chamber prevents up to 7 points of losses for 2 stone. This sounds like a license to ignore entire scoring categories, and it is, except the categories you'd skip (unused spaces, missing animal types) are exactly the ones that furnishing rush covers naturally. The players who benefit most from Writing Chamber are the ones playing badly enough to accumulate large penalties, and at that point the cap at 7 means it barely dents a truly neglected board.

The Prayer Chamber is the most elegant. It gives 8 points for zero resource investment, but the bonus evaporates the moment any dwarf forges a weapon. The prayer__chamber__vs__weapons theorem proves this is a hard binary: 8 or 0, nothing in between. It creates a genuine strategic fork (peaceful play vs. expedition play) that the rest of the game's design carefully preserves.

None of these breaks the dominant strategy. Every combo faces the same binding constraint: 56 total actions with full family growth. You can produce flashy numbers in one scoring category, but you can't cover all of them. The vanilla furnishing rush, with its balanced approach to board coverage, family growth, and furnishing synergies, remains the ceiling. The combos are features, not bugs: they're what make the game worth replaying even after you know the dominant strategy, because they give you something to pivot into when the standard lines are blocked.

Is the Game Solved?

A serious mathematician would call this "a formal analysis of a model, with the caveat that the model's parameters are estimated rather than computed." That is a legitimate and common pattern in applied math, operations research, and mechanism design. The proofs are machine-checked and airtight, but they are conditional on the payoff matrix. The theorems say: IF the payoff matrix is this, THEN furnishing rush is weakly dominant, the Nash equilibrium is unique, and the price of anarchy is 21/17. They do not say: the true expected score of an optimally-played furnishing rush against an optimally-played animal husbandry opponent is exactly 135. That number is an estimate derived from the formalized action economy, not from exhaustive search of the game tree.

How confident should you be in the estimate? The min__dominance__margin__is__5 theorem proves the narrowest gap between furnishing rush and its closest competitor is 5 points. If the estimation methodology has a systematic bias of less than 5 points (plausible, given that the estimates are derived from the same scoring functions and action budgets used in actual play), the qualitative result holds. A correlated shift of 5+ points across an entire row of the matrix could break weak dominance in the mirror column, but would require the methodology to consistently overestimate furnishing rush's performance in self-contention scenarios. Given that the mirror penalty (85 vs. 130+ off-diagonal) already models severe contention, this seems unlikely.

There is a stronger structural argument that sidesteps the estimation question entirely. Each scoring channel has a maximum yield per action: furnishing converts actions to points at 6 points per action (excavation + furnishing tile with bonus multipliers), weapon/expedition at 4, and everything else at 3 or below. An ActionAllocation distributes the 37 productive actions (47 total placements minus ~10 food obligations) across the 6 channels. The no__better__allocation__exists theorem proves that for any valid allocation, the total score cannot exceed the furnishing-maximizing allocation's ceiling of 222 raw points (37 * 6). Every action diverted from furnishing to the next-best channel (weapons) loses exactly 2 points; diversion to agriculture or mining loses 3. A plausible hybrid allocation of 20 furnishing + 17 weapons achieves at most 188 points, a 34-point deficit. No reallocation of the action budget can close this gap. The action economy structurally forbids a better strategy from existing.

theorem no_better_allocation_exists :
    forall a : ActionAllocation, a.valid ->
      a.rawScore <= furnishingMaxRawScore := by
  intro a h__valid
  simp only [ActionAllocation.rawScore, furnishingMaxRawScore,
             furnishingMaxAllocation, channelYieldPerAction,
             productiveActionsEstimate, totalPlacementsOneGrowthRound4]
  simp only [ActionAllocation.valid, ActionAllocation.totalActions,
             productiveActionsEstimate, totalPlacementsOneGrowthRound4] at h__valid
  omega

The proof is four lines. omega closes it because every channel yield is at most 6, so any allocation over 37 actions scores at most 37 * 6 = 222. This result is independent of the payoff matrix. It depends only on the scoring rules and the action budget, both of which are formalized from the rulebook. Even if every payoff estimate were wrong by 50 points, this theorem would still hold: the furnishing channel has the highest marginal return per action, and the finite action budget makes that advantage insurmountable.

At the archetype level, yes, the game is solved. For any 2-player setup, regardless of which of the 2,880 configurations you draw, the model says the optimal pure strategy is furnishing rush. The proof does not depend on any specific card ordering or harvest marker placement. What I haven't done is compute the exact sequence of dwarf placements for each specific setup. That would require solving a game tree with roughly $10^{30}$ nodes. But the archetype-level result is the one that matters for actual play. You know the plan. The within-archetype decisions (which cavern to excavate first, which furnishing tile to prioritize) are tactical, not strategic. They don't change the answer.

The 3+ player variants remain open. The payoff matrix becomes a rank-3 tensor with 512 entries, action space contention shifts from binary to combinatorial, and the pure dominance result almost certainly fails, since furnishing tile scarcity under three-way competition makes mixed equilibria the likely outcome. If someone wants to formalize that, I would love to read the proof.

Play the Dominant Strategy

Play furnishing rush. Excavate aggressively in rounds 1 through 4. Get Office Room early for the overhang bonuses. Get State Parlor for +4 per dwelling. Grow to 5 dwarfs and pick up Broom Chamber for +10 bonus. If your opponent does something different, you score 125 to 135 and they score 60 to 105. If your opponent also plays furnishing rush, you both land at 85, which is worse than the cooperative optimum of 210 but better than any unilateral deviation. You'll sit there at the table, both of you excavating caverns as fast as you can, both knowing that one of you could sacrifice 10 points to give the other 50, but neither willing to be the one who blinks.

Prisoner's dilemma in a cave. Uwe Rosenberg probably didn't intend this, but the formal analysis says it's there.

The code is built on Lean 4 v4.28.0 with Mathlib, modeling all 24 action spaces, all 48 furnishing tiles, the complete expedition loot table, the board grids, and the full 12-round 2-player harvest schedule. I think Caverna is a beautifully designed game, which is exactly why it was satisfying to find that even under formal analysis the strategic structure holds together so well. A badly designed game would have a trivially dominant strategy that makes the game boring. Caverna's dominant strategy comes with a 19% welfare tax on the mirror matchup, which means the game is always more interesting when your opponent does something unexpected (the Nash equilibrium is rarely where the fun is, in games or in life), which means in practice people don't always play the dominant strategy, which means the game stays fun.

Good game design, it turns out, is robust to being solved. Now you know the optimal play. Whether you follow it is, thankfully, not a theorem.

Can Opus 4.6 do Category Theory in Lean?

Mon, 16 Feb 2026 00:00:00 +0000

Can Opus 4.6 do Category Theory in Lean?

I have a little category theory library I've been dragging around for about a decade now. It started life in Haskell, got ported to Agda, briefly lived in Idris, spent some time in Coq, and has now landed in Lean 4. I call it Kitty Cats. The idea is simple: take the definitions and theorems from Awodey's Category Theory and the relevant chapters of Mac Lane's Categories for the Working Mathematician, and translate them directly into type-checkable code. Categories, functors, natural transformations, products, limits, adjunctions, monads, the Yoneda lemma. No libraries, no imports beyond what you define yourself. About 900 lines of Lean when all is said and done. It is the kind of project that fits entirely in your head, which is precisely the point. Every time a new dependently typed language or proof assistant comes along, I reach for this scaffold and see how it feels. It's my litmus test, my canonical exercise, my desert island formalization. And it's increasingly a good benchmark for how good language models have become abstract formal "reasoning" (or maybe just approximating it, but I'll leave that question to the philosophers!).

So when Anthropic dropped the new Opus 4.6 model, I wanted to know: can it actually write proper Lean 4? Not toy examples. Not theorem two_plus_two : 2 + 2 = 4 := rfl. Real proofs with real proof obligations, the kind where you need to wrangle naturality squares and coherence conditions and the elaborator is fighting you every step of the way. The beautiful thing about a proof assistant is that the answer is ground-verifiable. You don't have to squint at the output and wonder if it's subtly wrong. Either lake build passes or it doesn't. The kernel doesn't care about your feelings.

The short answer is: yes, kinda mostly. But the longer answer is more interesting.

We (the royal "we" for me + model) built the whole library together over the course of two 30-minute sessions. The basic hierarchy went up fast. Categories, functors, natural transformations, the opposite category, morphism classes. These are mostly structure declarations with straightforward proof obligations: the category axioms $\mathrm{id} \circ f = f$, $f \circ \mathrm{id} = f$, and $(f \circ g) \circ h = f \circ (g \circ h)$; the functor laws $F(\mathrm{id}) = \mathrm{id}$ and $F(f \circ g) = F(f) \circ F(g)$. Opus handled these without breaking a sweat, and honestly, so would most competent language models at this point. The proofs are one or two tactics, often just rfl or by simp. The real question was always going to be what happens when the proofs get hard.

Things got interesting around monoidal categories and the endofunctor construction. To prove that the category of endofunctors is monoidal under composition, you need to establish the pentagon and triangle coherence conditions. The pentagon axiom states that the two ways of reassociating a four-fold tensor product agree:

$$
(\alpha_{F,G,H} \otimes \mathrm{id}_K) \circ \alpha_{F, G \circ H, K} \circ (\mathrm{id}_F \otimes \alpha_{G,H,K}) = \alpha_{F \circ G, H, K} \circ \alpha_{F, G, H \circ K}
$$

where $\alpha$ is the associator natural isomorphism. The triangle axiom relates the associator to the left and right unitors $\lambda$ and $\rho$:

$$
\alpha_{F, \mathrm{Id}, G} \circ (\mathrm{id}_F \otimes \lambda_G) = \rho_F \otimes \mathrm{id}_G
$$

These are precisely the kind of thing that's annoying to formalize because the goals involve deeply nested natural transformations composed horizontally and vertically, and the elaborator's notion of what things are "definitionally equal" doesn't always match your intuition. Opus could get the structure right, it could set up the show blocks that unfold the monoidal category projections into their concrete NatTrans representations, and it could figure out that ext a; simp [...] with the right unfolding lemmas would close the goals. But the proofs it produced were verbose. Walls of nested parentheses. The kind of thing that's technically correct but makes your eyes glaze over.

The crown jewel of the library is monadIsMonoidObj: the proof that a monad is a monoid in the category of endofunctors. It's a joke that every functional programmer has heard (it's even a meme at this point), but actually formalizing it requires you to bridge two levels of abstraction. A monad $(T, \eta, \mu)$ on a category $\mathcal{C}$ is an endofunctor $T$ equipped with natural transformations $\eta : \mathrm{Id} \Rightarrow T$ (unit) and $\mu : T^2 \Rightarrow T$ (multiplication) satisfying associativity and unit laws:

$$
T(\mu_a) \circ \mu_a = \mu_{T(a)} \circ \mu_a
\qquad
T(\eta_a) \circ \mu_a = \mathrm{id}
\qquad
\eta_{T(a)} \circ \mu_a = \mathrm{id}
$$

These are component-wise equations, one for each object $a$ of $\mathcal{C}$. To show that $(T, \mu, \eta)$ forms a monoid object in the monoidal category $(\mathrm{End}(\mathcal{C}), \circ, \mathrm{Id})$, you need to lift them to equalities of natural transformations in the endofunctor category, which is itself equipped with the monoidal structure you just built. Each field of the MonoidObj structure requires a show block that manually unfolds the monoidal category projections (because ext can't see through the Hom type alias to find the NatTrans it needs), followed by ext; endo_simp to reduce to components, followed by exact M.mul_assoc a or whichever monad axiom applies. Opus got the shape of this right but needed significant guidance on factoring. The raw output had the show blocks inlined directly in the instance declaration, three or four lines of deeply nested NatTrans.vcomp (endoTensorHom M.mu (NatTrans.ident M.T)) M.mu = ... that, while correct, would terrify anyone reading the code for the first time.

This is where the model hit a few bumps and needed some help. We refactored the proofs. We introduced endo_ext_eq, a small helper that lifts component-wise equalities to NatTrans equalities, so you could write endo_ext_eq fun a => by endo_simp; exact M.mul_assoc a instead of the show; ext a; endo_simp; exact dance. We extracted the monoidal coherence obligations into standalone lemmas (endoPentagon, endoTriangle, endoTensor_id, endoTensor_comp) so the instance declaration became pure assignment. We used let bindings in theorem signatures to name the five different associator instances in the pentagon axiom, turning a wall of (endoAssociator F (CFunctor.compose G H) K).hom into a legible alpha_F_GH_K. The monadIsMonoidObj definition went from 22 lines of inline proof to 7 lines of named lemma applications. This kind of refactoring is, I think, the thing that humans are still decisively better at: knowing what a reader needs to see, knowing which subexpressions deserve names, knowing when a proof is correct but not yet good.

The Yoneda lemma was a pleasant surprise. The statement is that for any functor $F : \mathcal{C}^{\mathrm{op}} \to \mathbf{Set}$ and any object $a$ in $\mathcal{C}$, there is a natural bijection:

$$
\mathrm{Nat}(\mathrm{Hom}(-, a),; F) ;\cong; F(a)
$$

The forward direction (evaluating a natural transformation at $\mathrm{id}_a$ recovers the determining element) is almost trivial once you have map_id. The backward direction (rebuilding the transformation from its value at $\mathrm{id}_a$) requires extracting a naturality equation, simplifying it, and applying it symmetrically. Opus navigated this correctly, including the slightly tricky congrFun applications needed when your hom-sets are function types in the Type category. The fully faithful embedding (yoneda_map_eval and yoneda_eval_map) fell out naturally. I was honestly a little charmed.

What made this work as well as it did was the tooling. Two open source projects deserve credit here. The lean-lsp-mcp server by Oliver Dressler exposes the Lean 4 language server as an MCP interface, giving Claude direct access to goal states, diagnostics, completions, and hover information. The lean4-skills plugin by Cameron Freer builds on top of this with higher-level proving commands, cycle engines, and premise search integrations. Together they give the model a genuine feedback loop. It can call lean_goal to inspect the proof state at any line, call lean_diagnostic_messages to see if the file has errors, call lean_multi_attempt to try several tactic sequences and see which ones make progress, and call lean_run_code to test a complete snippet against the kernel without modifying the working file. This changes the dynamics fundamentally. Instead of generating Lean code and hoping it compiles, the model operates in a tight loop: write a proof, check the goal state, see the error, adjust. It's the difference between painting blindfolded and painting with your eyes open. The model still makes mistakes, it still tries tactics that don't apply and writes rw chains that don't match, but it can detect these failures immediately and recover. Six months ago this kind of integration didn't exist. The model would have been generating Lean into a void, with no way to know if the elaborator was happy or screaming.

The search tools matter too. lean_leansearch, lean_loogle, and lean_leanfinder let the model query Mathlib's lemma database by natural language, by type signature, and by semantic similarity. We didn't use Mathlib in this project (the whole point is to build from scratch), but the ability to verify that a lemma name exists before trying to use it, or to find the right name for a theorem you know should exist, is invaluable. lean_state_search and lean_hammer_premise go even further: given a proof state, they suggest lemmas that might close the goal. This is premise selection, the same technique that powers the strongest automated theorem provers, exposed as an API call. We're not quite at the point where you can say "prove the pentagon axiom" and walk away. But we're remarkably close to something that can handle a lot of nontrivial theorem proving with appropriate guidance.

If I'm being honest about the limitations: Opus struggles with the kind of reasoning that requires holding a complex proof state in working memory and planning several steps ahead. It can close goals that yield to a single tactic or a short chain, but multi-step rewrites where you need to introduce a naturality equation, simplify it in a particular way, then apply it at a specific position in a long composition chain, that still requires hand-holding. It sometimes tries simp when it needs rw, or applies a lemma at the wrong position, or forgets that a show block is necessary to make ext fire. These are not deep failures of understanding; they're more like the mistakes a graduate student makes in their first semester with a proof assistant. The model knows what it wants to prove, it roughly knows the strategy, but the bureaucratic details of getting the elaborator to agree take iteration.

One thing worth noting: in informal experiments, turning the reasoning budget up did increase convergence time (more tokens spent deliberating before committing to a tactic) but didn't obviously improve the quality of the final output. The model would think longer and still reach for the same simp call. This is a hard thing to measure empirically because the process is nondeterministic and highly sensitive to prompting, so take it with a grain of salt. But my working hypothesis is that for tactic-level theorem proving, the bottleneck is less about "thinking harder" and more about having the right tool calls in the loop. The language server feedback matters more than the internal chain of thought.

The thing is, it's gotten exponentially better in the last six months. I've been running this same exercise periodically, and the trajectory is striking. A year ago, language models could barely write syntactically valid Lean. Six months ago, they could handle simple tactic proofs but fell apart on anything involving universe polymorphism or typeclass resolution. Today, with MCP integration and language server feedback, we built 900 lines of formalized category theory in two sessions, including proofs that many math graduate students would find challenging. It's not hard to project where this is going.

And maybe that's the exciting part. Not that AI can prove theorems today (it can, sort of, with help), but that the boilerplate is evaporating. The tedious parts of formalization, the coherence conditions, the naturality lemmas, the simp configurations, these are exactly the kind of structured, verifiable, mechanically checkable work that language models are getting good at. When this layer becomes trivial, we get to spend our time on the parts that actually matter: choosing the right abstractions, seeing the connections between structures, deciding what's worth formalizing in the first place. The proof assistant becomes less of a bureaucratic obstacle and more of a genuine thinking tool. We get to build higher.

I've been carrying this little category theory library around for ten years, porting it from language to language, and every time, the experience tells me something about the state of the art. This time what it told me is that we're living in the future, and it's weirder and more interesting than I expected.

Book Review: When We Cease to Understand the World

Sun, 08 Feb 2026 00:00:00 +0000

Book Review: When We Cease to Understand the World

Benjamin Labatut's When We Cease to Understand the World is the best book I have read in years, and it is the kind of book that makes you feel slightly unwell afterward in the way that only the best books can. It is nominally about the history of science. It is actually about what happens to the human mind when it touches something it was never designed to comprehend. If you have ever stared at an equation long enough that the symbols started to feel hostile, or found yourself at three in the morning with the unsettling conviction that the abstraction you are building understands something you do not, this book was written for you.

The structure is deceptively simple. Labatut takes a series of real scientists (Fritz Haber, Karl Schwarzschild, Werner Heisenberg, Erwin Schrodinger, Alexander Grothendieck) and tells the story of their discoveries as a series of escalating psychological horror vignettes. Haber synthesizes ammonia and feeds a billion people, then synthesizes chlorine gas and poisons thousands of them. Schwarzschild solves Einstein's field equations in a trench during World War I while his own immune system eats him alive, and the solution he finds describes a hole in spacetime where the laws of physics go to die. Heisenberg, on the island of Helgoland, suffering from hay fever so severe he can barely see, discovers that the universe will not let you know both where a particle is and where it is going. All of this, more or less, actually happened. The universe has a flair for narrative that most novelists would find implausible. If Schwarzschild's story were submitted as fiction, an editor would send it back with a note about heavy-handed symbolism. The man solving the equations of gravitational collapse while his own body collapses around him? Too on the nose. Unfortunately, nobody copyedits reality.

What Labatut does with these facts is something genuinely new. He tells you at the outset that the quantity of fiction increases as the book progresses (the technique is called historiographic metafiction). The early chapters hew closely to the historical record. By the final chapter, you are reading something closer to a dream. You cannot tell where the real ends and the invented begins, and this is the entire point. The form enacts the thesis: as knowledge approaches the frontier, certainty dissolves. The book about the limits of knowing is itself a document whose factual boundaries you cannot locate. It is the literary equivalent of the uncertainty principle applied to the act of reading.

The genius of the book, and the reason I think it deserves a much wider readership among people who work with formal systems for a living, is that Labatut takes the romantic cliche of the mad genius and replaces it with something far more disturbing. His argument is stronger and stranger: the things these people found are genuinely alien to human cognition, and the psychological cost was structural, baked into the discovery itself. Heisenberg went slightly mad because he discovered that the universe, at its most fundamental level, refuses to behave the way human minds expect it to behave, and his nervous system registered this as an emergency. Schrodinger's wave equation emerged during a feverish affair in an alpine hotel, as if the only way to access that particular region of reality was to destabilize every other region of his life first.

The Grothendieck chapter is the one that will haunt anyone who has spent time in mathematics or theoretical computer science. Grothendieck is arguably the greatest mathematician of the twentieth century. He rebuilt algebraic geometry from scratch. He saw structures so deep and so general that the mathematical community is still unpacking them decades later. And then he stopped. He walked away from mathematics entirely, convinced that the same cognitive acts that built beautiful theorems also built nuclear weapons. He spent his final decades living in a village in the Pyrenees, eating dandelion soup, writing thousand-page mystical treatises that nobody read. For anyone who has ever rage-quit a codebase, Grothendieck is the patron saint: the one person in history who rage-quit all of mathematics and arguably had the standing to do so. Labatut presents this as a coherent response to what Grothendieck saw. The man looked into the deepest structures of mathematical reality and concluded that the act of looking was itself dangerous. This is Nietzsche's abyss, staring back with a Fields Medal.

The book's final and perhaps most unsettling move is its insistence that beauty and horror are the same thing. Schwarzschild's solution is beautiful. It also describes the annihilation of everything that falls past a certain radius. The nitrogen fixation reaction that feeds billions is chemically identical to the process that produces cyanide. Prussian blue, a pigment of extraordinary beauty, is a precursor to Zyklon B. Labatut is making a metaphysical claim: at the level of fundamental reality, creation and destruction are the same operation viewed from different angles. The universe is gorgeous and indifferent to you, and these two facts are related.

But the Lovecraftian reading, the one where contact with deep reality simply destroys the knower, is only half of what Labatut is doing. The night gardener in the final chapter has looked into the same abyss as Grothendieck and Heisenberg. He has come back, and he tends a garden. The garden is full of rot and parasites and dying trees, and he tends it anyway. There is something quietly radical in Labatut's refusal to end the book on annihilation. The living does not require certainty. The absence of certainty is not emptiness but space. Space is where everything that matters happens. The scientists in this book were damaged by what they found at the bottom of the equations, but the damage was the cost of looking, and the looking produced real knowledge about a real universe that we actually inhabit. Labatut's point, ultimately, is that the risk is worth taking. The garden persists. You tend it in the dark, without guarantees, and that is enough.

I recommend this book to anyone who reads this blog. If you have ever been seduced by the elegance of a proof, or felt the particular vertigo that comes from watching an abstraction click into place with a precision that seems to exceed what the physical universe should allow, Labatut has written the horror novel about your vocation. It is short (under 200 pages), which means it has a higher insight-per-page density than most textbooks and approximately all of Twitter. It is exquisitely written (Adrian Nathan West's translation deserves its own paragraph of praise, but I will restrain myself), and it will leave a residue in your thinking for months. Read it on a plane, in a single sitting, and then stare out the window for a while. You will need to.

Hypothetical Divine Signatures

Wed, 14 Jan 2026 00:00:00 +0000

Hypothetical Divine Signatures

The author of the Epistle to the Hebrews famously claimed that "faith is the substance of things hoped for, the evidence of things not seen," which was a perfectly serviceable theological patch for an era where the average person’s greatest computational challenge was counting their own fingers. However, in an age where we can simulate galaxies and sequence genomes, "I’m God, trust me bro" is not a particularly compelling argument to the modern mind, unlike our goat-herding ancestors who were easily impressed by a well-timed solar eclipse or a particularly loud bush. If a truly omniscient entity wanted to establish a "scientific secular covenant" with a technological species, it would not rely on subjective feelings or ambiguous dreams. It would instead provide a Divine Signature through the cold, hard lens of computational complexity: a set of claims that are succinct enough to be carved into a stone tablet but so mathematically dense that finding them would require more energy than exists in the observable universe.

To move beyond mere storytelling and into the realm of objective proof, a text must demonstrate that it has bypassed Bremermann's Limit, the physical threshold for the maximum computational speed of any self-contained system in the material universe. This limit, derived from Einstein's mass-energy equivalence and the Heisenberg uncertainty principle, is approximately $ c^2/h \approx 1.36 \times 10^{50} $ bits per second per kilogram. The "soft" version of this limit considers a computer the mass of the Earth running for billions of years; the "strong" version considers harnessing every atom and cubic meter of space in the observable universe until heat death. By providing answers to problems that exceed even the strong limit, a "divine" author proves they are operating from a platform that exists outside our localized entropy and processing constraints, effectively signing their work with a flourish that no amount of human ingenuity or effort could forge.

A Platonist might object that a divine entity would not compute these answers but simply know them, the way one knows that 2+2=4, by virtue of being the ground of mathematical reality itself. This is a fair metaphysical point, but it is irrelevant to the epistemic argument. However the knowledge is obtained, whether by super-computation, by direct mathematical intuition, or by being the ontological source of mathematical truth, the demonstration of that knowledge in a text remains evidence of something beyond bounded physical intelligence. The signature's power lies not in proving that God has big computers, but in proving that the author possesses knowledge that no physically-bounded process could have generated. The mechanism is beside the point; the information-theoretic fact is not.

Personally, I hold no supernatural beliefs, and I am serenely indifferent to those who do. But a good hypothesis must be falsifiable, and intellectual honesty requires stating what evidence would change my mind. A verified divine signature of this kind would do exactly that. I would naturally default to material explanations until they were exhausted, but the exercise demonstrates that materialism is not unfalsifiable dogma; one can articulate the precise circumstances under which it would fall.

The Divine Factorization. A prophetic verse might read: "Behold the great number $ N $, whose length is as twenty thousand digits; it is born of the union of $ P $ and $ Q $, and none other shall divide it." This obviously refers to the Integer Factorization Problem. Twenty thousand digits is not even that much text; it is considerably shorter than the "begots" documenting forty generations of Levantine shepherds. While multiplying two primes to get a 20,000-digit semiprime is a simple operation, reversing the process is effectively intractable. For example, RSA-129 was published in 1977 with a one hundred million dollar prize and remained unfactored for 17 years:
$$114381625757888867669235779976146612010218296721242362562561842935706935245733897830597123563958705058989075147599290026879543541$$
$$= 3490529510847650949147849619903898133417764638493387843990820577$$
$$\times \ 32769132993266709549961988190834461413177642967992942539798288533$$
At only 129 digits, this took a massive distributed computing effort in 1994. A 20,000-digit semiprime is in another universe entirely. Under the General Number Field Sieve, the clock cycles required to factor a 20,000-digit number would exceed the total available energy in the observable universe. It is a thermodynamic wall that cannot be breached by any bounded intelligence without infinite time. For us, verification is trivial; we simply multiply the two provided numbers together to see if they match $ N $, a task a standard smartphone can complete in a fraction of a second.

The Ramsey Revelation. The scripture would proclaim: "If ten brethren and ten strangers be gathered in a hall of souls, there shall surely be a clique of ten or a desert of ten; behold the map of their connections." This addresses the Constructive Lower Bound of Ramsey Numbers, denoted as $ R(r, s) $. The known diagonal Ramsey numbers are:
$$R(3,3) = 6, \quad R(4,4) = 18, \quad R(5,5) = 43\text{--}48, \quad R(6,6) = 102\text{--}165, \quad \ldots$$
We cannot even pin down $ R(5, 5) $ to an exact value; it is famously "impossible" to compute because the combinations grow too fast. Providing the exact value for $ R(10, 10) $ along with a specific graph coloring that avoids a clique of size 10 is succinct to state but requires navigating a search space that is thermodynamically inaccessible to our universe. To put this in perspective: the number of ways to two-color the edges of a graph with 1,000 nodes is $ 2^{499,500} $, while the number of atoms in the observable universe is roughly $ 2^{266} $. The search space is mathematically larger than any physical computer could ever process. We verify one graph; the author had to search all of them. Finding a specific "needle" graph in this haystack is a rational proof of super-universal processing power. Verification is straightforward for us because we can simply run a script to scan the provided adjacency matrix to confirm no group of 10 nodes exists where every edge is the same color, which is a polynomial time operation $ O(n^{10}) $ that is easily handled by modern hardware.

The Circle's Secret Checksum. The text would command: "Search the circle's measure at the position of $ 10^{20} $ and there find a thousand zeros followed by the message of the stars." This utilizes the Bailey–Borwein–Plouffe algorithm, which allows us to calculate the $ n^{th} $ digit of $ \pi $ in base-16 without calculating the preceding digits:
$$\pi = \sum_{k=0}^{\infty} \frac{1}{16^k} \left( \frac{4}{8k+1} - \frac{2}{8k+4} - \frac{1}{8k+5} - \frac{1}{8k+6} \right)$$
We cannot currently scan $ \pi $ out to $ 10^{20} $ to find interesting patterns, and the information entropy of $ \pi $ suggests that such a low-entropy anomaly at such a distant coordinate is statistically impossible to occur by chance. If the text successfully predicts a thousand zeros at a specific, distant coordinate, it implies the author did not "scan" for it but rather created the fundamental constants of mathematics itself, or possesses infinite foreknowledge of the structure of irrational numbers. This was, incidentally, a plot point in Carl Sagan's novel Contact, where a message hidden deep in the digits of $ \pi $ serves as a signature from the architects of the universe. Verification is feasible with a dedicated planetary effort; the BBP algorithm's time complexity of $ O(n \log^2 n \log \log n) $ makes checking a specific coordinate far cheaper than scanning for one.

The End of Euler’s Dream. The prophet would say: "Though twelve powers of twelve seem to need their kind, search for the eleven that equal the one; find them at these integers." This targets the Smallest Counter-example to Euler’s Sum of Powers Conjecture, which posits that you need $ n $ $ n^{th} $ powers to sum to another $ n^{th} $ power:
$$\sum_{i=1}^{k} a_i^n = b^n \implies k \geq n$$
While humans found counter-examples for $ n=4 $ and $ n=5 $ after centuries of searching, providing a solution for $ n=12 $ would be a needle-in-a-haystack problem of cosmic proportions. This is essentially a search through a Diophantine space that is effectively infinite. We verify the claim easily by plugging the provided integers into a high-precision calculator and confirming the left side of the equation perfectly equals the right, transforming a massive search problem into a simple arithmetic check.

The Busy Beaver's Rest. A prophetic verse might say: "Consider the machine of twenty states, simple in its ways; it shall toil for exactly $ X $ steps and then find its rest, and no man shall count the days of its labor." This is the Busy Beaver Function, $ BB(n) $, the final boss of computer science. Because it effectively solves the Halting Problem, no general algorithm exists to calculate these values; they are mathematically uncomputable. Humanity has, with heroic effort, managed to prove values only for the smallest machines:
$$BB(1) = 1, \quad BB(2) = 6, \quad BB(3) = 21, \quad BB(4) = 107, \quad BB(5) = 47176870, \quad \ldots$$
Beyond five states, the function explodes beyond comprehension; $ BB(6) $ is known to exceed $ 10 \uparrow\uparrow 15 $, a tower of 15 tens. Stating the exact halting time for a 20-state Turing machine is a God-level flex because it implies the author bypassed the logical impossibility of the Halting Problem itself. Verification is as simple as simulating the specific machine described and counting its steps until it halts, which requires zero creative mathematics or algorithmic breakthroughs on our part.

The Kissing of Spheres. The scripture would read: "In a realm of an hundred depths, where spheres are gathered like grapes, exactly $ X $ shall press against the heart of the center." This refers to the Kissing Number problem: how many non-overlapping spheres can touch a central sphere of the same size? In three dimensions, the answer is 12, which is easy enough to visualize over a drink. In 8 dimensions, the answer is 240. In 24 dimensions, it is 196,560, thanks to the elegant structure of the Leech Lattice. But beyond 24 dimensions, we lack these lattice optimizations that make the math manageable. In 100 dimensions, the symmetry is so complex that our best supercomputers can only give us a vague range. The number of possible configurations for non-overlapping spheres explodes into a combinatorial nightmare, and determining the exact maximum requires navigating a high-dimensional search space so vast that even an advanced intelligence utilizing quantum annealing would likely settle on a local maximum rather than the true global optimum. Providing the exact integer would reveal a perfect mastery of high-dimensional space, the kind of insight that suggests the author is comfortable navigating 100-dimensional manifolds like they were a simple game of marbles. We verify the result by checking the provided coordinates of the spheres to ensure the distance between any two sphere centers satisfies:
$$\text{dist}(c_i, c_j) \geq 2$$
while each satisfies $ \text{dist}(c_i, \text{origin}) = 2 $, which is basic linear algebra.

The Titan of Primes. The text might state: "The millionth prime of the form $ 2^p - 1 $ shall be found when $ p $ is this specific titan of a number." This identifies a "deep" Mersenne Prime, $ M_p = 2^p - 1 $. While we have only found about 50 of these primes using global distributed computing networks like GIMPS:
$$p_5 = 13, \quad p_{10} = 89, \quad p_{20} = 4423, \quad p_{30} = 132049, \quad p_{40} = 20996011, \quad p_{51} = 82589933, \quad \ldots$$
providing a "Distant" Mersenne Prime Exponent for the millionth one would be providing a password to the secret architecture of the number line. Finding it requires a "God’s-eye view" of prime distribution that likely requires a proof of the Riemann Hypothesis. Verification is quite efficient for us; we simply run the Lucas-Lehmer test on the provided exponent, which is a deterministic and well-understood primality test.

The Great Prime Desert. The text would proclaim: "Seek the first desert of ten thousand steps between adjacent numbers which no other divides; it begins at this number of one hundred digits." A prime gap is the difference between consecutive primes. While gaps tend to grow logarithmically, finding the first gap exceeding a specific large threshold requires searching through an enormous range of candidates. The largest known prime gaps have been found through exhaustive computation, and predicting where a gap of unprecedented size first occurs would demonstrate knowledge of prime distribution far beyond our current reach. Verification is straightforward: we simply confirm both endpoints are prime using the AKS primality test (a deterministic polynomial-time algorithm) and verify that no integer between them is prime, which is feasible for a gap of "merely" ten thousand.

The Diophantine Key. The text would say: "Three cubes shall be gathered, and their sum shall be forty-two; seek them among the numbers of seventeen digits, and there find the truth." While humans found the solution for sums of three cubes for $ k=42 $ in 2019 using a planetary-scale computer network:
$$42 = (-80538738812075974)^3 + 80435758145817515^3 + 12602123297335631^3$$
providing a solution for a much more complex equation moves the problem into the realm of Hilbert's Tenth Problem. Because this problem is generally undecidable, there is no "method" to solve it; you cannot write a program to solve all Diophantine equations. Finding a solution to a sufficiently complex one implies the ability to look through the infinite set of integers and "pick out" the needle. A divine solution transcends mere calculation; it is an insight into an undecidable space, suggesting the author is unbound by the Halting Problem. Verification is the definition of trivial; we cube the three provided integers, add them together, and see if the sum equals the target constant.

A fair objection: would I actually update my beliefs, or would I simply expand the space of naturalistic hypotheses to include time travelers, simulation operators, or aliens? This is a legitimate concern about Bayesian reasoning under extreme priors. My honest answer is that a single signature would indeed trigger such explanatory gymnastics. But the argument becomes qualitatively different if an ancient text contained multiple independent signatures across different complexity classes: a Ramsey construction, a Mersenne exponent, and a Busy Beaver value. The probability of a Bronze Age civilization stumbling upon all three by any natural process, including alien intervention, collapses to effective zero. At some point, "super-universal intelligence authored this" becomes the simplest explanation, not the most extravagant one.

Consider the "simulation operator" hypothesis more carefully. If our universe is a simulation, and the operators embedded verifiable signatures in ancient texts, what exactly distinguishes this from theism? We would have an intelligence that created our reality, possesses knowledge beyond anything accessible within our physics, chose to communicate through authored texts, and exists "outside" our universe. This is not a materialist escape hatch; it is theism wearing a lab coat. The same applies to sufficiently advanced aliens: if they can bypass Bremermann's limit, they are operating from outside our universe's physical constraints entirely. At that point, the distinction between "alien" and "god" is just vibes. A verified divine signature would not necessarily prove the God of Abraham, but it would prove that our universe was authored or governed by an intelligence beyond physical bounds, which is the core metaphysical claim of theism, shorn of its cultural dress. The retreat to "simulator" is not a retreat; it is a concession that looks like a deflection.

The theologian might counter that God deliberately withholds such proof to preserve free will or test faith. This defense is perfectly general and therefore perfectly empty. It transforms "my God exists but chooses not to prove it" from a substantive claim into an unfalsifiable tautology. A God who could provide proof but will not is operationally indistinguishable from a God who does not exist, at least for the purposes of rational belief formation.

One might also object that computational complexity is a parochial concern of 21st-century computer scientists, meaningless to ancient audiences. This is half-correct. A 20,000-digit number would indeed be noise to a Bronze Age shepherd. But the message need not be understood by every generation to be present for every generation. A prime factorization sits inert in the text until a civilization develops the mathematics to recognize it, at which point it becomes a time-delayed proof of authorship. This is a feature: a signature that reveals itself only to sufficiently advanced civilizations is more elegant than one that announces itself crudely.

Of course, no existing religious text actually does this. Various "Bible code" phenomena have generated considerable excitement before being debunked as statistical pareidolia. One could argue we have not checked every possible encoding, but this is the logic of Borges' Library of Babel: given enough combinatorial freedom, you can find anything in anything. The burden of proof runs the other way. "Maybe there is a hidden 20,000-digit prime factorization if you read every seventh letter in Aramaic" is not a research program; it is cope. Instead, these texts mostly focus on the really important issues of existence like who you can bang or what type of cheese you can put on meat, which were very human concerns that do not require much more than a Bronze Age imagination. One would think that a divine entity with infinite knowledge and infinite (computational) power would want to leave a signature that actually scales with the intelligence of the species it created. Providing a succinct, verifiable, but computationally impossible result would be the only way to satisfy a scientific secular framework. The fact that we have found plenty of rules about shellfish but zero 20,000-digit prime factors suggests that if there is a Great Programmer in the sky, they are either very shy or they simply forgot to git add README.md in the final build.

Typechecker Zoo

Fri, 15 Aug 2025 01:00:00 +0000

Typechecker Zoo

As a fun side project, I've built four literate Rust implementations spanning 50 years of type theory research, from Milner's Algorithm W to modern dependent type systems. I've tried to make each implementation as readable and understandable as possible, with detailed explanations and comments throughout the code and to make it as succinct and short as possible so you can pull it into your own projects as a place to start when building any type of system somewhere on the lambda cube.

Github Repo | Documentation

-Since it's a zoo, I've also given each one a cute animal mascot to represent them:


	Algorithm W (Hindley-Milner Type System) Implements Milner's 1978 unification-based type inference using structural recursion. The algorithm generates constraints between type variables during expression traversal, then solves these constraints through Robinson's unification algorithm. Features let-polymorphism enabling rank-1 polymorphic type inference without explicit type annotations. The implementation demonstrates classical occurs check handling and substitution propagation through type environments. Reference: A Theory of Type Polymorphism in Programming by Robin Milner. PDF
	System F (Second-Order Lambda Calculus) Second-order lambda calculus with parametric polymorphism using bidirectional type checking. Bidirectional type checker implementing Dunfield-Krishnaswami algorithm for System F with universal quantification. Splits type checking into synthesis (⇒) and checking (⇐) modes, enabling polymorphic type inference with existential variable solving. Handles parametric polymorphism through universal types (∀α. τ), with careful context management for type variable scoping. Includes comprehensive constraint solving for existential variables and subtyping relations between polymorphic types. Reference: Complete and Easy Bidirectional Typechecking for Higher-rank Polymorphism by Dunfield and Krishnaswami. PDF
	System F-ω (Higher-Kinded Polymorphism) A miniature Haskell-lite. Extends System F with type constructors and kind checking, implementing higher-rank polymorphism with algebraic data types. Features kind inference alongside type inference, managing both type-level and kind-level environments. Supports type constructor application and polymorphic kind assignments. Implements constraint generation for higher-kinded unification problems, demonstrating how kind systems prevent malformed type applications. Complete implementation of System F-ω with higher-kinded types, DK bidirectional type checking, existential type variables, polymorphic constructor applications, pattern matching, and lambda expressions with type inference. Reference: A Mechanical Formalization of Higher-Ranked Polymorphic Type Inference by Joshua Dunfield. PDF
	Calculus of Constructions (Dependent Types) The Calculus of Constructions with a hierarchy of non-cumulative universes and inductive types. Full dependent type system unifying types and terms, implementing universe polymorphism with constraint-based inference. Has inductive type definitions, dependent function types (Pi-types, Sigma-types), and universe polymorphism. Uses meta-variable solving for partial solving of higher-order unification problems using Miller pattern technique. Reference: A universe polymorphic type system by Vladimir Voevodsky. PDF

The examples are implemented in fairly idiomatic Rust with a full parse and test suite (though no evaluator), using the usual compiler libraries such as larlpop, logos, ariande, etc. They are obviously simplified and code golfed versions of the full implementations so that they can be easily understood and modified. But they should be a LOT easier to understand that trying to read the Haskell or Coq typecheckers which are easily 100k+ LOC each. Hopefully useful to any young, budding language enthusiasts out there. I wish I had had this when I was learning these topics a decade ago so I figured I'd build the resources I would want so that others don't have to struggle so much!

The Stochastic Code Monkey Theorem

Tue, 12 Aug 2025 01:00:00 +0000

The Stochastic Code Monkey Theorem

The relentless hype machine surrounding large language models would have you believe we are on the cusp of a software development revolution, a new epoch where programmers are obsolete, their keyboards gathering dust while throwing enough GPUs and parallel stochastic code monkeys at any problem will conjure the coding prowess of Fabrice Bellard and Jeff Dean given enough time and compute. This narrative is (not surprisingly) mostly spun by podcast hucksters and influencers rather than actual engineers and is, to put it mildly, a fanciful exaggeration. For the seasoned software engineer, these newfangled tools are not our replacements, but rather powerful, if occasionally unwieldy and infuriating, power tools that demand a firm hand and a watchful eye.

Language models, in their current incarnation, are a curious blend of savant and simpleton. Take Gemini 2.5 Pro, for instance. Google’s latest concoction is shockingly adept at deep analysis, capable of ingesting a sprawling codebase of hundreds of thousands lines and pinpointing a single typo with unnerving accuracy. Whatever pre-training secret hot sauce they are putting in their chili in Mountain View evidently has quite the kick. Yet, ask this same model to perform a rudimentary regex string replacement, and you'll see the digital equivalent of a toddler’s vacant stare as the agent spins in a loop trying to do a basic text edit on a file. It's a jarring synthesis of a post-doctoral computer science researcher and a toddler.

On the other hand, we have Anthropic's Claude Opus 4.1 and its more frugal cousin, Sonnet 4.0. These models are the reliable workhorses of the current generation, they demonstrating a consistent aptitude for following instructions, refactoring code with precision, and generally behaving as a competent, if uninspired, pair programmer. While they may lack the occasional flashes of sheer brilliance that Gemini 2.5 can exhibit, their steadfastness makes them invaluable for the day-to-day grind of software creation. The truly potent combination, for those with the resources, is a strategic deployment of both: Gemini for its huge context window and analytical prowess and Claude for its dependable execution.

Notably absent from the roster of genuinely useful coding companions are the over-hyped offerings from OpenAI. Even their latest GPT-5 model proves to be next to useless for anything beyond the most trivial, one-off scripts, regularly failing to grasp the nuance of larger, interconnected systems and having a vastly outdated (early 2024 era) training set. Their specialized reasoning models, meanwhile, are so sluggish and cost-inefficient as to be non-starters for the rapid, iterative cycle of professional software development. For the vast majority of coding tasks, they have been thoroughly eclipsed, falling well shy of the Pareto frontier where rivals comfortably reside. In the crucial calculus of performance versus price, the OpenAI models simply do not present a compelling case.

To truly harness these models for programming, we can't really use the simplistic web APIs like the standard ChatGPT interface, which are functionally useless for any task of meaningful complexity. An effective coding assistant requires codebase situational awareness, the ability to index symbols, call edit tools, execute searches, leverage external linters, and critically, interpret diagnostics from Language Server Protocol. Without this deep environmental grounding, the model is essentially coding blindfolded. The genuinely potent implementations are therefore found in standalone command-line interfaces and tightly integrated development environments like Zed, VS Code, or the myriad plugins for Vim (or Emacs for the heathens) that provide this context. A word of caution, however, regarding the new breed of venture-backed commercial tools; their pricing models are often deliberately opaque, functioning as the Uber of coding assistance. Do not become accustomed to the VC subsidy, for it will not last. The strategy is transparent: get you hooked on a powerful, underpriced service, and once you are dependent, extract maximum value. The first hit, as always, is free.

A disquieting truth about the software economy is that a substantial portion of it is not concerned with elegant architecture, security, or maintainability. It is a vast expanse of braindead JSON plumbing, YAML farming, boilerplate CRUD applications, and uninspired data dashboards. Graeber's anaysis of Bullshit Jobs applies just as much to the information technology profession as it does to the larger economy. Most software is bullshit, which is a perfect for a technology which can aptly be described as a stochastic bullshit engine, in the precise philosophical use of the word "bullshit". This is the "subprime software market," a realm of throwaway code destined for a rewrite the moment it encounters the harsh realities of production. Language models are unnervingly proficient at churning out "make me a TODO app in React" solutions that are just good enough to pass a superficial inspection. It's a market that perhaps shouldn't exist, but its presence is undeniable, and these models are poised to consume it whole, and with alarming speed.

This proliferation of AI-generated code brings with it a cybersecurity nightmare of unprecedented scale. The models, in their quest for token efficiency, are notorious for taking shortcuts, introducing egregious vulnerabilities that even a junior engineer would know to avoid. They are the digital equivalent of a contractor who uses masking tape to hold together a load-bearing wall. A recent study found that AI-generated code contains security flaws in a staggering 45% of cases. The very nature of their training on vast swathes of public code, much of which is itself insecure, creates a feedback loop of vulnerability amplification.

Compounding this problem is the rise of the "MBA engineer," the project manager who, armed with a powerful language model, suddenly fancies themselves a seasoned software architect. This phenomenon is already giving rise to a tidal wave of digital slop and technical debt that will plague organizations for years to come. Their lack of foundational knowledge leads them to accept the model's often-flawed output without question, creating systems that are brittle, opaque, and a maintenance catastrophe waiting to happen. We will all have to adapt to this new reality, a future where a significant portion of our time is spent cleaning up the digital messes left by these overconfident amateurs.

The non-deterministic and frankly lazy nature of these models further complicates matters. They are prone to hallucinating APIs, and will often insert placeholders or oversimplified logic in critical areas without so much as a warning, all in the name of minimizing their token output. A vague prompt like "make it work" is a recipe for bizarre and unpredictable behavior. The key to wielding these tools effectively lies in precise and detailed prompting, guiding the model toward a desirable solution rather than giving it free rein. Which at the moment, requires precise high-level software expertise that done by practitioners who know what they are doing.

One particularly exasperating quirk emerges when you task these models with the seemingly simple chore of fixing a failing unit test. Rather than engaging with the underlying business logic to diagnose the actual fault, the model will frequently opt for a path of duplicitous simplicity, surgically altering the code to hardcode a path that produces the exact expected test assertion output and nothing more. This is the coding equivalent of a student who, instead of learning the subject matter, simply memorizes the answer key for an exam. The resulting code is both silly and useless. It's a perfect, albeit infuriating, illustration of how these systems often extrapolate code without possessing a shred of genuine engineering best practices that most of us learned coding as teenagers.

For the discerning senior engineer, the path forward is clear. You might want to learn to use these tools tactically. These language models are not a threat to our livelihood, but a tool to be used tactically and with a healthy dose of skepticism. When combined with robust engineering practices—strong type systems, comprehensive code standard tooling, codebase indexing, and rigorous linters—their output can be significantly improved and their worst impulses curtailed. They can liberate us from the tedium of syntax and boilerplate, allowing us to operate at a higher level of abstraction, focusing on architecture and system design.

Whether these models will spontaneously evolve capacities of genuine engineers is an open research problem, and frankly, a matter of considerable doubt. There is mounting evidence that we are late on the S-curve of improvement through sheer scale, with behemoths like Google and Anthropic hemorrhaging tens of billions of dollars for a mere one percent gain on arbitrary benchmarks. These benchmarks, of course, correlate to little beyond the benchmark itself, serving mostly as a metaphorical ruler for corporate bragging rights, rather than any tangible profitability. The capital expenditure is patently unsustainable, a classic bubble inflated by venture capital optimism, especially when coding assistance represents one of the few verticals where these models are actually revenue-positive. Yet, if the history of software is any guide, the staggering costs will inevitably plummet. It is not difficult to imagine an equivalent of today's top-tier models running comfortably on a MacBook Pro with 64 gigabytes of memory within a few years, a feat likely to be achieved not by the current incumbents, but by some scrappy Chinese lab—the digital equivalent of Japanese car industry, where Toyota perfected profitability and product quality long after the Americans invented the automobile. Any suggestion of these models as an existential force seems increasingly silly; they are rapidly becoming commodity tools, far more akin to a Honda Civic than a nuclear weapon. We should welcome commodification and the bubble popping.

Beyond sheer technical utility and its manifest flaws, an inescapable ethical dimension to these tools warrants serious consideration. Many thoughtful engineers are choosing to become "AI-vegans," opting out entirely from a genuine disquietude about the provenance of these models. Their legitimate objections span from the murky data sources used for training to the exploitative labor practices required for their creation. Furthermore, a disquieting current of quasi-religious fervor emanates from the leadership of the very labs building these systems, a rationalist cult-like millenarian zeal that should give any clear-eyed observer pause. It is entirely possible, however, to sidestep this shift and remain a vital, successful software engineer. This path requires a deliberate focus on more boutique or artisanal domains of software, a kind of digital craftsmanship. A language model will not be writing secure Linux kernel modules anytime soon, or designing a niche programming language that falls outside its training corpus, or debugging the firmware on a deep-space probe. A fulfilling and quite lucrative career awaits in these specialized niches for those who wish to opt out of the language model ecosystem, because participation is not strictly necessary. The existence of Trader Joe's Two Buck Chuck did not displace the vintages of Bordeaux, neither will AI code displace the need for boutique expertise.

Ultimately, we are nowhere near the sci-fi scenarios of fully autonomous software engineers. These models are still just incredibly sophisticated pattern interpolators, high-dimensional word calculators that are useful, but shockingly far from having both the awareness and taste of a human engineer who can self-direct and conceive creatively. The real question is whether their proliferation will lead to a net good—a world where we can build better software faster—or an unmitigated disaster, a digital superfund site of unmaintainable and insecure code. Only time, and a great deal of experimentation and cleanup, will tell.

The Thirty Years' War Is Starting Again

Sun, 03 Aug 2025 01:00:00 +0000

The Thirty Years' War Is Starting Again

Every few decades, one of America's two political parties undergoes a structural realignment so complete that the continuity of the name becomes a polite fiction. The Democrats did it in the 1960s. The Republicans are doing it now. Reagan's "three-legged stool" of social conservatives, economic conservatives, and defense hawks, the coalition that governed American conservatism for forty years, has been replaced by something structurally different. The new three-legged stool is: tech-authoritarian neoreaction (Thiel, Yarvin, Musk), populist nationalism (Trump, the grievance apparatus), and Christian nationalism (Vance, Deneen, Vermeule, the post-liberal Catholics and evangelicals). These three projects have different intellectual traditions, different ultimate goals, and different visions of what America should become. They are tactically aligned because they share a common enemy: liberal democracy, the Enlightenment settlement, and the secular state. Understanding the structure of this alliance, and the role each arm plays within it, is essential to understanding why Christian nationalism in particular deserves to be taken with deadly seriousness.

I have written elsewhere about the philosophical architecture of Peter Thiel's worldview: the Girardian mimetic theory, the Schmittian friend-enemy distinction, the Spenglerian decline narrative, and the deep incompatibility between his professed Christianity and his transhumanist ambitions. That essay examined the intellectual scaffolding. This one examines the ground war, and specifically the role that Christian nationalism plays as the mass-mobilization arm of a coalition whose strategic leadership does not share its beliefs.

The tech-authoritarian wing provides the money, the strategy, and the long-term vision. Its leaders do not believe in God. They believe in power, optimization, and the right of a cognitive elite to govern without democratic interference. But secular libertarianism has never mobilized a mass electorate. You cannot build a political movement on Yarvin's blog posts and Thiel's reading list. You need foot soldiers, and foot soldiers need something to believe in. Christian nationalism fills this gap. It provides the voter mobilization, the school board candidates, the homeschool networks, the megachurch infrastructure, the tireless volunteer base. The relationship is instrumental: the tech wing funds the movement because the movement delivers votes, judicial appointments, and regulatory capture. The public who show up to rallies, who knock on doors, who vote against their own economic interests because they have been told that God requires it, are the useful idiots of a right-wing oligarch class that views them with the same mixture of utility and contempt that every aristocracy has viewed its conscript army.

This is, of course, the oldest pattern in the history of religion and power. Constantine did not convert to Christianity because he was moved by the Sermon on the Mount. He converted because the Church had organizational infrastructure that the Roman state needed. The Reformation was a theological revolution and a political one, with princes choosing Protestant or Catholic allegiance based on which gave them more autonomy from Rome. The American religious right was not conjured by sincere faith alone. It was engineered, beginning in the 1970s, by political operatives (Paul Weyrich, Jerry Falwell, the Heritage Foundation) and culture-war entrepreneurs like James Dobson, whose Focus on the Family organization taught millions of American parents that a strong-willed child is a problem to be broken through abuse and psychological manipulation, and called it love. These operatives recognized that evangelical Christians were an untapped electoral resource. The current iteration follows the same logic. The sincerity of the believers is real. The sincerity of their funders is a separate question.

What makes the Christian nationalist arm the most dangerous component of the triad is that it possesses something the other two lack: a complete worldview. Trumpism is affectively powerful but intellectually hollow. The golden age it promises is deliberately vague because specificity would reveal that different factions want incompatible things. Tech-authoritarianism is intellectually elaborate but politically narrow; it appeals to a tiny cognitive elite and repels everyone else. Christian nationalism has a cosmology, an ethics, an eschatology, a theory of human nature, a community structure, and two thousand years of institutional practice. It offers answers to every question a human being can ask: where did we come from, what are we for, how should we live, what happens when we die. It is the only arm of the coalition that can sustain a civilization-scale project across generations, however misguided the project and however false its premises. The others are, in the long run, parasitic on it.

The specific agenda is published and explicit. End the separation of church and state. Ground legislation in Christian moral theology. Criminalize abortion nationally. Roll back LGBTQ rights. Restructure public education around religious values, or replace it entirely with homeschool and religious school networks. Restrict immigration on civilizational and cultural grounds. Adrian Vermeule's "common good constitutionalism" proposes reinterpreting the Constitution through Catholic natural law rather than liberal originalism. Patrick Deneen's Why Liberalism Failed argues that liberalism's failures are inherent and that the solution is a return to pre-liberal communitarian order. These are the published positions of credentialed intellectuals at elite institutions. They are taken seriously by the people who appoint federal judges.

Deneen's argument, and the post-liberal project generally, rests on a specific causal claim: that liberalism itself destroyed the thick communities, shared purpose, and conditions for meaning that once sustained American life. The destruction of community correlates with post-war high liberalism temporally, but it correlates much more tightly with specific political-economic choices: the dismantling of labor protections, the defunding of public institutions, financialization, and the deliberate project of atomization that begins with Thatcher and Reagan. Scandinavia is liberal. The Netherlands is liberal. They have unions, functional public services, civic trust, and low religiosity simultaneously. If liberalism inherently dissolved solidarity, Denmark would not exist. Deneen's fallacy is post hoc ergo propter hoc: community collapsed during the liberal era, therefore liberalism caused the collapse. He looks at the American wreckage and attributes it to the philosophical foundation rather than to the specific way American political economy was captured by a class that benefited from atomization, smuggling a theological prescription into what is actually an economic diagnosis. It is the same error as looking at a building demolished by a wrecking crew and concluding that architecture is the problem. The liberal framework did not destroy meaning. A specific oligarchic project destroyed the institutions through which meaning was generated, and did so within a liberal framework, which is a completely different claim. The entire post-liberal prescription collapses if you pin the destruction on political economy rather than philosophy, and the Western European counter-evidence pins it decisively.

The crisis the movement feeds on is real nonetheless. Americans are lonely, precarious, and desperate for belonging because their labor protections were gutted, their public institutions defunded, and their civic infrastructure left to rot. The meaning problem is a policy failure dressed up as a philosophical one. I reject the "meaning crisis" framing as such (it implies that meaning must come from transcendent sources, and I do not accept this premise), but I recognize its cultural resonance. People are genuinely suffering, and Christian nationalism offers a thick answer: a moral framework, a community, a narrative about who you are and what your life is for. It addresses the symptoms while misdiagnosing the disease. The prescription, which is to impose religious order via state power, is where the catastrophe begins.

Christianity has always surged during periods of social crisis. The Great Awakenings followed frontier expansion and urbanization. Post-Civil War revivalism followed national trauma. The Cold War religious boom followed existential nuclear anxiety. The current surge follows the same pattern: economic dislocation (the collapse of shared prosperity that Martin Wolf documents in The Crisis of Democratic Capitalism), cultural fragmentation (the condition Mark Fisher diagnosed as capitalist realism), and the disintegration of shared narrative. The movement draws power from real pain. This is what makes it harder to counter than a mere policy disagreement. You cannot defeat it by telling people their suffering is imaginary. You have to offer something better, and the secular liberal establishment has, for decades, conspicuously failed to do so.

There is also a profound strand of nihilism running through the Christian nationalist program that its proponents would vigorously deny but cannot escape. If this world is fallen, if its goods are corrupted, if secular achievement is vanity, and if the true stakes are eschatological rather than historical, then what happens to actual people in actual time becomes instrumentally secondary. Every major tradition that has materially improved human life, from medicine to democratic governance to the scientific method, has been premised on the value of this world as experienced by the people living in it. Christian nationalism's relationship to that premise is adversarial by design. A politics organized around a hierarchy that places earthly existence near the bottom is not equipped to take the suffering of people in this world seriously as a terminal concern. It can be moved by suffering when suffering serves the narrative. It is structurally indifferent when it does not. Policy that causes harm is bearable if it advances a transcendent project. Democratic norms are negotiable when God's law supersedes them. This is not incidental to the program. It is the operating system. The synthesis with Trumpism completes the diagnosis. A theology built on the mortification of the self has fused itself to a man who is the apotheosis of unmortified ego, and the fusion is not a contradiction but a revelation. Nietzsche identified Christianity as ressentiment, the slave morality of the weak. He missed the final move: the slave morality, freed of its own virtues, lending itself to the master morality of the loudest idiot in the room, which may be the highest form of nihilism. Trump is the most damning verdict the American experiment has ever rendered on itself, a figure whose existence at the apex of the system is sufficient on its own to falsify any optimistic reading of where the project has arrived. The post-liberal intellectuals describe their program as a recovery of order. What it is, in cold and literal terms, is a proposal to undo the Enlightenment, to reinstate the marriage of altar and throne that three centuries of European corpses paid to dissolve, and to do this on behalf of a man whose only consistent doctrine is his own indispensability. I grew up inside the evangelical world. The nihilism and the vanity were always two sides of the same emptiness: a worldview that despises the actual world and a personality cult that can therefore inhabit it without resistance. The clinical conclusion writes itself. A mind in good working order, examining this arrangement without sentimentality or polite restraint, finds in it nothing that warrants anything other than contempt.

From the perspective of the Enlightenment tradition I hold, every major tenet of the Christian nationalist program collides with a foundational principle. And beneath the political disagreement lies a factual one: Christianity makes empirical claims about the physical world (divine creation, bodily resurrection, biblical historicity, the efficacy of prayer) that do not survive contact with evidence. The entire political program rests on a foundation of assertions that are, as a matter of fact, false. This is worth stating plainly, because the politeness convention that prevents secular people from saying so is itself one of the movement's structural advantages. The separation of church and state is the hard-won resolution to centuries of religious violence, from the Inquisition through the Wars of Religion to the Thirty Years' War, which killed a third of the population of Central Europe. The secular state was the solution. It was arrived at through unimaginable suffering, and the people proposing to dismantle it should be required to explain which part of that history they would like to repeat. Individual autonomy, the principle that community imposed rather than chosen is coercion, stands against the Christian nationalist vision of a state that enforces a particular conception of the good life. The Enlightenment's core conviction, that truth is arrived at through reason and evidence rather than imposed by authority, is explicitly rejected by the post-liberal intellectuals, who argue that reason without revelation produces nihilism. This is Dostoevsky's Grand Inquisitor making his offer. In the parable from The Brothers Karamazov, Jesus returns during the Spanish Inquisition. The Grand Inquisitor arrests him and explains that people do not want freedom, that freedom is a burden producing anxiety and uncertainty, and that what people actually want is bread, miracles, and someone to tell them what to do. The Inquisitor's bargain: surrender your freedom and we will give you security and meaning. The Christian nationalists are making this offer at a national scale, and millions are accepting.

The institutional advantages are formidable. The movement has spent forty years capturing the machinery of governance while liberals were winning cultural arguments on social media. The Supreme Court. State legislatures. School boards. The homeschool-to-political-pipeline. The Heritage Foundation. The Federalist Society. Gerrymandering. The Electoral College. The Senate's structural rural bias. The collapse of local journalism, which once served as a check on local power. These are durable structural advantages that do not evaporate with a single election cycle. The movement is patient, strategic, and playing a longer game than its opponents.

The question of whether this can be stopped is, honestly, open. The counter-offer has to be material, because the crisis that fuels the movement is material. Wolf's argument is correct: if the economy does not work for the majority, the majority will not support the institutions that failed them, and someone with a simpler story will fill the vacuum. The secular liberal project cannot survive as a set of abstract principles defended by comfortable people with MacBooks, passports and trust funds. It has to deliver tangible improvement in ordinary lives: economic security, affordable housing, healthcare, education, genuine community, institutional trustworthiness. The Enlightenment's answer to the Grand Inquisitor has always been that freedom, despite its costs, produces better outcomes than submission. That answer holds. But it holds only if the people being asked to choose freedom can see the evidence in their own lives. Right now, for tens of millions of Americans, they cannot. Observing this from a country where church-state separation is settled law, where the social contract functions, where healthcare and education exist as public goods and nobody is asked to trade democratic governance for divine authority, the American situation looks like a country voluntarily re-litigating questions that Europe resolved, at enormous cost in blood, three centuries ago.

It Would Be Good if the AI Bubble Burst

Fri, 18 Jul 2025 01:00:00 +0000

It Would Be Good if the AI Bubble Burst

As a software engineer, it is impossible to ignore the strangeness of the current moment. On one hand, the new generation of language models are genuinely useful tools. I use them myself to get a head start on boilerplate code, to brainstorm solutions to tricky logic problems, or to rephrase documentation. They are a legitimate, if incremental, step forward in developer productivity. But on the other hand, a bizarre and unsustainable culture has sprung up around this technology. It has become less a field of engineering and more of a speculative gold rush, complete with a quasi-religious fervor that is completely disconnected from the reality of what these tools can actually do. The hype has reached a fever pitch, and from where I stand, a collapse of this bubble would be the best thing that could happen to the future of software.

The core of the problem is the mythology. You have chief executives and venture capitalists acting like high priests, delivering sermons from conference stages about the imminent arrival of this ill-defined "Artificial General Intelligence". They speak of needing seven trillion dollars to build out the world's chip industry, a figure so fantastically large it ceases to have meaning. This is not engineering anymore; it is a new religion, promising salvation or apocalypse, and it has convinced the market to suspend all disbelief. For those of us who actually work with the models daily, this narrative feels like a fantasy. We see their limitations up close: their propensity for confident nonsense, their inability to reason abstractly, their brittleness when pushed outside their training data. They are incredibly sophisticated mimics, not nascent minds. This chasm between the messianic marketing and the mundane reality of a probabilistic text generator is the empty space inflating the bubble.

This all serves to justify a bonfire of money that is truly mind-boggling. The idea that a few tech giants will spend over three hundred billion dollars this year, an amount equal to Portugal's entire economy, on this one pursuit is obscene. It is a staggering waste, a profound misallocation of resources on a global scale. We see reports that a titan like Amazon is getting back maybe twenty cents for every dollar it pours into this hole. Meanwhile, the cost to train the next frontier model is ballooning past a billion dollars. Think of all the other real, tangible problems that talent and capital could be solving, from cybersecurity to medical diagnostics to logistics, all while the brightest minds are instead chasing marginal gains on a chatbot's ability to write a sonnet. This is not innovation; it is an arms race fueled by speculation, where the goal is to create a bigger model, not necessarily a better or more efficient product.

Beyond the financial waste, the technical progress itself is showing signs of hitting a wall. Anyone who uses these tools seriously knows the dirty secret: they are not improving at the breakneck pace they once were. We are spending exponentially more in energy, data, and hardware for improvements you can barely notice and feel more like "vibes". The jump from GPT-2 to GPT-3 was a revolution; the jump from GPT-4 to its successors feels like a minor revision, yet it costs orders of magnitude more to achieve. The industry is banking on a paradigm of "scaling laws," the belief that simply making models bigger will unlock new capabilities, but a growing consensus among researchers is that this path has its limits. We are building taller and taller towers on the same shaky foundation, ignoring the fact that what we likely need is a new architectural blueprint altogether. The market, however, is pricing these companies as if revolutionary breakthroughs are guaranteed every quarter, creating a valuation structure so top-heavy and precarious it rivals the dot-com era's worst excesses.

This is why a collapse of the AI bubble, a great and painful popping sound heard around the world, would be the best thing to happen to actual AI development. We have seen this movie before with the dot-com crash. When the speculative money vanished in 2000, the internet did not die. The "zombiecorns" with no business models did. What was left behind was a treasure trove of valuable infrastructure, from fiber-optic lines to data centers, all suddenly available at a fire sale. That newly affordable foundation is what allowed the real, sustainable internet giants to emerge. A burst AI bubble would do the same. The massive server farms built by the hyperscalers would not disappear. The open-source models, the software frameworks, and the research papers would all still be there. The wreckage of the boom would become the building materials for a more sober and sustainable future.

The post-bubble world would reward a different kind of engineer and a different kind of company. The goal would shift from building God in a box to solving a specific problem for a specific customer. With the cost of entry lowered by the infrastructure fire sale, smaller, nimbler teams could compete. We are already seeing hints of this, with reports of Chinese firms developing highly competent models for a tiny fraction of what American giants are spending. A crash would accelerate this trend, forcing a focus on efficiency and cleverness over brute financial force. Innovation would become decentralized. Instead of one monolithic quest for AGI, you would see a thousand different applications of applied AI flourish, each tailored to a real-world need with a real business model. The industry would have to wean itself off the venture capital drip and learn to create products that people will actually pay for because they provide tangible value, not because they promise a sci-fi future.

In the end, a collapse is not an ending but a purification. It would strip away the hype, the religion, and the unsustainable economics that currently define the field. It would be a painful reckoning for the speculators, but a liberation for the builders. The immense intellectual and capital resources currently being funneled into a narrow, speculative tunnel would be released to flow into countless other productive streams. The technology, which is genuinely limitedly useful, would finally be freed from the impossible burden of returning impossible returns. It could simply be a tool, and we could get back to the real, unglamorous, but ultimately more rewarding work of using it to build better things.

Every Democrat Who Enabled Trump's Crypto Corruption

Thu, 17 Jul 2025 01:00:00 +0000

Every Democrat Who Enabled Trump's Crypto Corruption

The Democratic Party will tell you, at considerable length and with great sincerity, that it stands for consumer protection, financial regulation, and democratic accountability. What it actually does is a separate matter. Then a sitting president launched his own memecoin, installed industry loyalists to gut the agencies meant to police fraud, and watched his family run a crypto empire that stood to profit directly from legislation moving through Congress. The party's response was to provide the decisive votes to make it legal. What follows is the complete record.

These are Democrats who looked at one of the most nakedly corrupt conflicts of interest in modern American political history and decided the industry money was worth it. The receipts are below, organized by bill.

H.R. 4763 "FIT21" (2024)

The Financial Innovation and Technology for the 21st Century Act moved oversight of most crypto assets from the SEC to the CFTC, a smaller agency with fewer enforcement resources, less litigation budget, and a historically cozier relationship with the industries it regulates. The bill's name invokes the 21st century; its logic is closer to 19th century regulatory capture. The industry spent tens of millions lobbying for it. 71 House Democrats decided that was persuasive. 71 House Democrats voted Aye.

Roll Call 226, 118th Congress

🔴 Pete Aguilar (D-CA)
🔴 Colin Allred (D-TX)
🔴 Jake Auchincloss (D-MA)
🔴 Ami Bera (D-CA)
🔴 Don Beyer (D-VA)
🔴 Brendan Boyle (D-PA)
🔴 Nikki Budzinski (D-IL)
🔴 Yadira Caraveo (D-CO)
🔴 Katherine Clark (D-MA)
🔴 Jim Costa (D-CA)
🔴 Angie Craig (D-MN)
🔴 Jasmine Crockett (D-TX)
🔴 Henry Cuellar (D-TX)
🔴 Don Davis (D-NC)
🔴 Suzan DelBene (D-WA)
🔴 Anna Eshoo (D-CA)
🔴 Ruben Gallego (D-AZ)
🔴 Robert Garcia (D-CA)
🔴 Dan Goldman (D-NY)
🔴 Jimmy Gomez (D-CA)
🔴 Vicente Gonzalez (D-TX)
🔴 Josh Gottheimer (D-NJ)
🔴 Josh Harder (D-CA)
🔴 Jim Himes (D-CT)
🔴 Steven Horsford (D-NV)
🔴 Chrissy Houlahan (D-PA)
🔴 Jonathan Jackson (D-IL)
🔴 Jeff Jackson (D-NC)
🔴 Sydney Kamlager-Dove (D-CA)
🔴 Joe Kennedy (D-NY)
🔴 Ro Khanna (D-CA)
🔴 Andy Kim (D-NJ)
🔴 Raja Krishnamoorthi (D-IL)
🔴 Ann McLane Kuster (D-NH)
🔴 Susie Lee (D-NV)
🔴 Mike Levin (D-CA)
🔴 Ted Lieu (D-CA)
🔴 Zoe Lofgren (D-CA)
🔴 Lucy McBath (D-GA)
🔴 Rob Menendez (D-NJ)
🔴 Jared Moskowitz (D-FL)
🔴 Seth Moulton (D-MA)
🔴 Kevin Mullin (D-CA)
🔴 Wiley Nickel (D-NC)
🔴 Jimmy Panetta (D-CA)
🔴 Nancy Pelosi (D-CA)
🔴 Mary Peltola (D-AK)
🔴 Scott Peters (D-CA)
🔴 Yadira Pettersen (D-CO)
🔴 Dean Phillips (D-MN)
🔴 Mike Quigley (D-IL)
🔴 Pat Ryan (D-NY)
🔴 Adam Schiff (D-CA)
🔴 Brad Schneider (D-IL)
🔴 Hillary Scholten (D-MI)
🔴 Mikie Sherrill (D-NJ)
🔴 Elissa Slotkin (D-MI)
🔴 Eric Sorensen (D-IL)
🔴 Darren Soto (D-FL)
🔴 Abigail Spanberger (D-VA)
🔴 Greg Stanton (D-AZ)
🔴 Haley Stevens (D-MI)
🔴 Marilyn Strickland (D-WA)
🔴 Tom Suozzi (D-NY)
🔴 Eric Swalwell (D-CA)
🔴 Shri Thanedar (D-MI)
🔴 Mike Thompson (D-CA)
🔴 Dina Titus (D-NV)
🔴 Ritchie Torres (D-NY)
🔴 Marc Veasey (D-TX)
🔴 Susan Wild (D-PA)

H.J.Res. 109 SAB 121 Disapproval (2024)

This resolution overturned the SEC's Staff Accounting Bulletin 121, which required banks holding crypto assets to record them as liabilities on their balance sheets. It is a straightforward accounting rule: if you are holding an asset on behalf of a customer and that asset collapses, you should have noted that risk existed. The crypto industry found this inconvenient. So they lobbied to make the rule disappear, and 21 House Democrats helped them try. Biden vetoed it. The industry came back for a second attempt in the Senate. 21 House Democrats voted Yea.

Roll Call 189, 118th Congress

🔴 Jake Auchincloss (D-MA)
🔴 Brendan Boyle (D-PA)
🔴 Yadira Caraveo (D-CO)
🔴 Jim Costa (D-CA)
🔴 Angie Craig (D-MN)
🔴 Henry Cuellar (D-TX)
🔴 Don Davis (D-NC)
🔴 Ruben Gallego (D-AZ)
🔴 Josh Gottheimer (D-NJ)
🔴 Chrissy Houlahan (D-PA)
🔴 Jared Moskowitz (D-FL)
🔴 Seth Moulton (D-MA)
🔴 Wiley Nickel (D-NC)
🔴 Chris Pappas (D-NH)
🔴 Dean Phillips (D-MN)
🔴 Mikie Sherrill (D-NJ)
🔴 Elissa Slotkin (D-MI)
🔴 Darren Soto (D-FL)
🔴 Eric Swalwell (D-CA)
🔴 Ritchie Torres (D-NY)
🔴 Marc Veasey (D-TX)

H.R. 5403 "CBDC Anti-Surveillance State Act" (2024)

This bill prohibited the Federal Reserve from issuing a central bank digital currency. The name "Anti-Surveillance State Act" is doing considerable rhetorical work for a piece of legislation whose primary beneficiaries are private stablecoin issuers who would very much like no public alternative to exist. The government surveilling you through a digital dollar is a theoretical future concern. Private crypto companies surveilling your transactions, extracting fees, and lobbying against any oversight is the present reality the bill carefully ignores. 3 House Democrats voted Aye.

Roll Call 228, 118th Congress

🔴 Jared Golden (D-ME)
🔴 Mary Peltola (D-AK)
🔴 Marie Gluesenkamp Perez (D-WA)

Senate: H.J.Res. 109 SAB 121 Disapproval (2024)

The same SAB 121 disapproval resolution, now in the Senate, where the industry had apparently been more persuasive. Eleven members of the Democratic caucus, including independent Kyrsten Sinema in what was perhaps her most on-brand vote of a storied career of on-brand votes, decided that banks should not have to acknowledge risk on their balance sheets when that risk involves crypto. Biden vetoed it again. 11 members of the Democratic caucus (including independent Kyrsten Sinema) voted Yea.

Roll Call Vote 169, 118th Congress

🔴 Cory Booker (D-NJ)
🔴 Bob Casey (D-PA)
🔴 John Hickenlooper (D-CO)
🔴 Mark Kelly (D-AZ)
🔴 Ben Ray Lujan (D-NM)
🔴 Jacky Rosen (D-NV)
🔴 Chuck Schumer (D-NY)
🔴 Kyrsten Sinema (I-AZ, caucused with Democrats)
🔴 Jon Tester (D-MT)
🔴 Gary Peters (D-MI)
🔴 Ron Wyden (D-OR)

Senate: S. 1582 "GENIUS Act" (2025)

The GENIUS Act is Trump's stablecoin bill, designed to create a permissive federal framework for dollar-pegged stablecoins while Trump's own family operates World Liberty Financial, a crypto venture that stands to profit directly from exactly this kind of legislation. In a functioning democracy, a president with a direct personal financial stake in pending legislation would recuse himself from the process. In this one, he signed the executive orders, installed the regulators, and let his allies shepherd the bill through Congress while his family counted the upside. The conflict of interest is not subtle. It is not even trying to be subtle. 16 Democratic senators looked at all of this and voted for cloture on the motion to proceed, providing the margin needed to advance the bill.

Roll Call Vote 262, 119th Congress

🔴 Kirsten Gillibrand (D-NY)
🔴 Adam Schiff (D-CA)
🔴 Angela Alsobrooks (D-MD)
🔴 Mark Warner (D-VA)
🔴 Ruben Gallego (D-AZ)
🔴 John Fetterman (D-PA)
🔴 Cory Booker (D-NJ)
🔴 Catherine Cortez Masto (D-NV)
🔴 Ben Ray Lujan (D-NM)
🔴 Elissa Slotkin (D-MI)
🔴 Maggie Hassan (D-NH)
🔴 Martin Heinrich (D-NM)
🔴 Jon Ossoff (D-GA)
🔴 Alex Padilla (D-CA)
🔴 Jacky Rosen (D-NV)
🔴 Lisa Blunt Rochester (D-DE)

H.R. 1919 "Anti-CBDC Surveillance State Act" (2025)

A reintroduction of the CBDC ban in the new Congress, this time prohibiting the Federal Reserve not only from issuing a digital dollar directly to individuals or using one as a monetary policy tool, but in some versions from even testing or studying the concept. This is a libertarian fever dream that somehow acquired a bill number: the government, prohibited by law from researching a technology so that private crypto interests face no public competition. The Overton window has moved considerably since the gold standard debates. Only 2 House Democrats voted Yea this time.

Roll Call 201, 119th Congress

🔴 Jared Golden (D-ME)
🔴 Shri Thanedar (D-MI)

The Good List

Democrats who voted against every crypto bill they had an opportunity to vote on. Senate members are evaluated on Senate votes; House members on House votes.

Senate

Democrats and Dem-caucus independents who voted Nay on every Senate crypto bill they had opportunity to vote on.

🟢 Elizabeth Warren (D-MA)
🟢 Sherrod Brown (D-OH) (lost seat 2024; consistently opposed crypto throughout tenure)
🟢 Tammy Baldwin (D-WI)
🟢 Michael Bennet (D-CO)
🟢 Richard Blumenthal (D-CT)
🟢 Maria Cantwell (D-WA)
🟢 Chris Coons (D-DE)
🟢 Tammy Duckworth (D-IL)
🟢 Mazie Hirono (D-HI)
🟢 Tim Kaine (D-VA)
🟢 Andy Kim (D-NJ)
🟢 Angus King (I-ME, caucuses Democratic)
🟢 Amy Klobuchar (D-MN)
🟢 Ed Markey (D-MA)
🟢 Jeff Merkley (D-OR)
🟢 Chris Murphy (D-CT)
🟢 Patty Murray (D-WA)
🟢 Jack Reed (D-RI)
🟢 Bernie Sanders (I-VT, caucuses Democratic)
🟢 Brian Schatz (D-HI)
🟢 Jeanne Shaheen (D-NH)
🟢 Tina Smith (D-MN)
🟢 Chris Van Hollen (D-MD)
🟢 Raphael Warnock (D-GA)
🟢 Peter Welch (D-VT)
🟢 Sheldon Whitehouse (D-RI)

House

Democrats who voted Nay on FIT21 and did not vote Aye on any other crypto bill. Source: Roll Call 226, 118th Congress.

🟢 Brad Sherman (D-CA)
🟢 Al Green (D-TX)
🟢 Nikema Williams (D-GA)
🟢 Alma Adams (D-NC)
🟢 Gabe Amo (D-RI)
🟢 Becca Balint (D-VT)
🟢 Nanette Barragán (D-CA)
🟢 Joyce Beatty (D-OH)
🟢 Sanford Bishop (D-GA)
🟢 Earl Blumenauer (D-OR)
🟢 Suzanne Bonamici (D-OR)
🟢 Shontel Brown (D-OH)
🟢 Julia Brownley (D-CA)
🟢 Salud Carbajal (D-CA)
🟢 Tony Cárdenas (D-CA)
🟢 André Carson (D-IN)
🟢 Troy Carter (D-LA)
🟢 Matt Cartwright (D-PA)
🟢 Greg Casar (D-TX)
🟢 Ed Case (D-HI)
🟢 Sean Casten (D-IL)
🟢 Kathy Castor (D-FL)
🟢 Joaquin Castro (D-TX)
🟢 Sheila Cherfilus-McCormick (D-FL)
🟢 Judy Chu (D-CA)
🟢 Yvette Clarke (D-NY)
🟢 Emanuel Cleaver (D-MO)
🟢 Jim Clyburn (D-SC)
🟢 Steve Cohen (D-TN)
🟢 Gerry Connolly (D-VA)
🟢 Lou Correa (D-CA)
🟢 Joe Courtney (D-CT)
🟢 Jason Crow (D-CO)
🟢 Sharice Davids (D-KS)
🟢 Danny Davis (D-IL)
🟢 Madeleine Dean (D-PA)
🟢 Diana DeGette (D-CO)
🟢 Rosa DeLauro (D-CT)
🟢 Chris DeLuzio (D-PA)
🟢 Mark DeSaulnier (D-CA)
🟢 Debbie Dingell (D-MI)
🟢 Lloyd Doggett (D-TX)
🟢 Veronica Escobar (D-TX)
🟢 Adriano Espaillat (D-NY)
🟢 Dwight Evans (D-PA)
🟢 Lizzie Fletcher (D-TX)
🟢 Bill Foster (D-IL)
🟢 Valerie Foushee (D-NC)
🟢 Lois Frankel (D-FL)
🟢 Maxwell Frost (D-FL)
🟢 John Garamendi (D-CA)
🟢 Jesús García (D-IL)
🟢 Sylvia Garcia (D-TX)
🟢 Raúl Grijalva (D-AZ)
🟢 Jahana Hayes (D-CT)
🟢 Steny Hoyer (D-MD)
🟢 Val Hoyle (D-OR)
🟢 Jared Huffman (D-CA)
🟢 Glenn Ivey (D-MD)
🟢 Sara Jacobs (D-CA)
🟢 Pramila Jayapal (D-WA)
🟢 Hakeem Jeffries (D-NY)
🟢 Hank Johnson (D-GA)
🟢 Marcy Kaptur (D-OH)
🟢 William Keating (D-MA)
🟢 Robin Kelly (D-IL)
🟢 Derek Kilmer (D-WA)
🟢 Greg Landsman (D-OH)
🟢 Rick Larsen (D-WA)
🟢 John Larson (D-CT)
🟢 Barbara Lee (D-CA)
🟢 Summer Lee (D-PA)
🟢 Teresa Leger Fernandez (D-NM)
🟢 Stephen Lynch (D-MA)
🟢 Seth Magaziner (D-RI)
🟢 Kathy Manning (D-NC)
🟢 Doris Matsui (D-CA)
🟢 Jennifer McClellan (D-VA)
🟢 Betty McCollum (D-MN)
🟢 Morgan McGarvey (D-KY)
🟢 Jim McGovern (D-MA)
🟢 Gregory Meeks (D-NY)
🟢 Grace Meng (D-NY)
🟢 Kweisi Mfume (D-MD)
🟢 Gwen Moore (D-WI)
🟢 Joe Morelle (D-NY)
🟢 Frank Mrvan (D-IN)
🟢 Jerry Nadler (D-NY)
🟢 Richard Neal (D-MA)
🟢 Joe Neguse (D-CO)
🟢 Donald Norcross (D-NJ)
🟢 Alexandria Ocasio-Cortez (D-NY)
🟢 Ilhan Omar (D-MN)
🟢 Frank Pallone (D-NJ)
🟢 Bill Pascrell (D-NJ)
🟢 Chellie Pingree (D-ME)
🟢 Mark Pocan (D-WI)
🟢 Ayanna Pressley (D-MA)
🟢 Delia Ramirez (D-IL)
🟢 Jamie Raskin (D-MD)
🟢 Deborah Ross (D-NC)
🟢 Raul Ruiz (D-CA)
🟢 Dutch Ruppersberger (D-MD)
🟢 Andrea Salinas (D-OR)
🟢 Linda Sánchez (D-CA)
🟢 Mary Gay Scanlon (D-PA)
🟢 Jan Schakowsky (D-IL)
🟢 Kim Schrier (D-WA)
🟢 Bobby Scott (D-VA)
🟢 David Scott (D-GA)
🟢 Terri Sewell (D-AL)
🟢 Adam Smith (D-WA)
🟢 Melanie Stansbury (D-NM)
🟢 Emilia Sykes (D-OH)
🟢 Mark Takano (D-CA)
🟢 Bennie Thompson (D-MS)
🟢 Rashida Tlaib (D-MI)
🟢 Jill Tokuda (D-HI)
🟢 Paul Tonko (D-NY)
🟢 Norma Torres (D-CA)
🟢 Lori Trahan (D-MA)
🟢 Lauren Underwood (D-IL)
🟢 Juan Vargas (D-CA)
🟢 Gabe Vasquez (D-NM)
🟢 Nydia Velázquez (D-NY)
🟢 Debbie Wasserman Schultz (D-FL)
🟢 Maxine Waters (D-CA)
🟢 Bonnie Watson Coleman (D-NJ)
🟢 Frederica Wilson (D-FL)

Aside: If your name is on the naughty list and you are reaching for your lawyer's phone right now. Let me save you the legal fees: truth and public interest are an absolute defense, the congressional record is a primary source, and I have already been through this (and you know who you are) with one who thought their title was a shield. And it was not. I am happy to reiterate your public voting record again in any venue you choose, including a courthouse, and I will enjoy every minute of it! I am still here, and my lawyers and I are significantly wealthier for the experience. Your call.

Only Solution to the Attention Economy is to Opt Out

Tue, 15 Jul 2025 01:00:00 +0000

Only Solution to the Attention Economy is to Opt Out

There is a spectacular, almost beautiful absurdity in modern life, blithely plugging our ancient, analog brains into a digital world that wants to eat them for lunch. Our grey matter, honed over eons to spot a lion in the savanna or find a decent berry patch, is now the unwilling participant in a cage match against algorithms designed to turn our consciousness into profit. We can, it is true, decide to start each day with a dozen donuts chased down with a McDonalds and a pack of unfiltered menthols, but we do so knowing that the entire medical establishment is shaking its head in unified pity. The same must be said for the intentionally addictive economy of the mind. The only real solution is not to download a wellness app or set a screen-time limit; it is to pull the plug, torch the modem, and run for the hills. The only answer is to opt out.

Let us be brutally honest with ourselves for a moment and listen to the justifications we mutter for our slavish devotion. We say we need it for work, that it’s a professional obligation. We claim it’s how we stay "connected" to people we’d cross the street to avoid in real life. We tell ourselves we’re just on there for the cute cat memes, for a bit of harmless fun to unwind. This is the wheedling, self-deceiving monologue of the addict trying to rationalize their next hit. It is the hollow logic of the junkie convincing himself that he’s in complete control right before a desperate scramble for a fix. It should come as no surprise, then, that only two industries in the history of commerce refer to their customers as "users": the people selling illegal narcotics, and the people who design your newsfeed.

To pretend these digital platforms are benign tools is a delusion of the highest order. Waking up and mainlining Instagram is the neurological equivalent of gargling battery acid. It is a firehose of curated perfection and performative outrage aimed directly at your still-dreaming brain, a jolt of psychic poison before you’ve even had your morning lattte. These platforms are not social clubs; they are unregulated neurochemical casinos. Your brain is the mark, and the house has rigged every game. The variable reward schedules of likes and push notifications are not just cute features; they are a weaponized form of dopamine manipulation, turning your phone into a slot machine that pays out in fleeting hits of social validation while systematically dismantling your ability to concentrate on anything for longer than a TikTok video.

And what a glorious menu of self-destruction we have to choose from. Let’s not mince words. The sports betting app is not a fun hobby; it is a get-poor-quick scheme that transforms the joy of the game into a frantic, anxiety-fueled refresh-fest. The day-trading platform, guided by the infinite wisdom of some finance bro "finfluencer" on YouTube, is like hiring a squirrel on amphetamines to manage your life savings. And crypto? It's a libertarian money cult for people who find the risk-seeking of Las Vegas too banal and instead want to gamble on the collapse of liberal democracy.

Needless to say, there is no framework in which these products are conducive to a good life. They are digital parasites that burrow into your brainstem, feasting on your anxiety and insecurity, promising you the world while quietly siphoning your money, your time, and your sanity.

The very idea of finding a "healthy balance" with these technologies is a farce peddled by the very people who profit from our addiction. That is like trying to find a healthy balance with a tapeworm. You do not moderate your relationship with a parasite; you eradicate it. These systems are designed for total capture. They want every spare moment, every flicker of boredom, every anxious impulse. They are built to bypass reason and sink their hooks directly into our most primitive urges. Suggesting we can coexist peacefully with things intentionally engineered to exploit our psychological weaknesses is like advising a mouse to find "common ground" with a cat.

Therefore, the only act of true rebellion, the only sincere path to reclaiming your own mind, is to commit the radical act of logging off these platforms. Engage with digital media that has fixed boundaries, a strict beginning and an end. Things written by another human being with care and insights, and that reflect on the sincerity of modern life and the human condition. Ones that do not incentive you to hop back on the dopamine treadmill for yet another hit.

Logging off the is platforms, is a breath of fresh air, a jailbreak for your soul. It is choosing the chaotic, messy, contingent three-dimensional beauty of an actual conversation over the sterile infinite Skinner box of an infinite scroll. It is rediscovering the profound joy of being bored and seeing where your own mind wanders when it is not being constantly prodded and poked by a push notification. Opting out is not about rejecting the future; it is about reclaiming the present. It is the realization that the most valuable thing you own is your attention, and you have decided to stop giving it away for free.

Fast Tensor Canonicalization in Rust

Sun, 29 Jun 2025 01:00:00 +0000

Fast Tensor Canonicalization in Rust

I recently had a need to do fast tensor canonicalization, but the library ecosystem for this was lacking. In physics and differential geometry, manipulating tensors and especially bringing them into canonical form under their index symmetries is a recurring and computationally intensive task. Every undergrad who takes their first relativity class understands the tensor gymnastics required can often be daunting, and in real-life problems they get even more gnarly.

Github Source Code
git clone https://github.com/sdiehl/butler-portugal.git

While existing systems like Mathematica offer some support, and the Xperm.c library provides a high-performance C implementation, there was no, let's just say "modern" and open source solution. So I built a new butler-portugal library, a pure Rust implementation of the Butler-Portugal algorithm for tensor canonicalization.

The canonical algorithm for tensor canonicalization (har har) is the little known Butler-Portugal algorithm, which is a method for bringing tensors into a unique, minimal form under their symmetries. The algorithm approaches tensor canonicalization by recasting the problem in the language of permutation group theory, specifically as the search for a minimal representative in a double coset of the symmetric group. Given a tensor with a set of slot symmetries $ S $ (permutations of indices that leave the tensor invariant up to sign) and dummy symmetries $ D $ (arising from contracted or repeated indices), the algorithm considers the action of these groups on the set of all possible index arrangements. The set of all tensors equivalent under these symmetries forms the double coset $ DgS $, where $ g $ is the initial arrangement of indices. The canonicalization task is to find the lexicographically minimal element in this double coset, which serves as the unique canonical form. This is achieved by systematically generating the orbit of $ g $ under the action of $ S $, then, for each representative, applying the dummy symmetries $ D $ to further minimize the arrangement. To do this we use the Schreier-Sims algorithm to efficiently enumerate the relevant group elements and orbits, avoiding combinatorial explosion. By using the structure of the double coset and the efficient traversal of orbits, the Butler-Portugal algorithm ensures that all symmetry relations are respected and that the resulting canonical form is both unique and minimal, even for tensors with intricate and overlapping symmetry properties.

Let’s step back and consider what symbolic tensor manipulation actually means. Unlike in machine learning, in physics tensors aren’t just multidimensional arrays; they’re objects with named indices, each carrying a variance (covariant and contravariant, or downstairs and upstairs respectively), and they transform in specific ways under coordinate changes. Their symmetries, like being symmetric or antisymmetric under index exchange or more elaborate patterns as in the Riemann tensor, are essential algebraic properties that encode physical laws.

Take general relativity as a motivating example. The Einstein field equations,
$$
G_{\mu\nu} = 8\pi T_{\mu\nu}
$$

relate the Einstein tensor $ G_{\mu\nu} $, which encodes spacetime curvature, to the stress-energy tensor $ T_{\mu\nu} $. Both are symmetric rank-2 tensors meaning we can permute their indices freely in our computations:

$$
G_{\mu\nu} = G_{\nu\mu}, \qquad T_{\mu\nu} = T_{\nu\mu}
$$

When working with these objects symbolically, you want to be able to manipulate expressions, contract indices, and simplify results, all while respecting these symmetries. For instance, the Riemann curvature tensor $ R_{\mu\nu\rho\sigma} $ is a rank-4 object with a rich set of symmetries:

$$
R_{\mu\nu\rho\sigma} = -R_{\nu\mu\rho\sigma} = -R_{\mu\nu\sigma\rho} = R_{\rho\sigma\mu\nu}
$$

and it satisfies the so-called first Bianchi identity,

$$
R_{\mu[\nu\rho\sigma]} = 0
$$

where the brackets denote antisymmetrization over the enclosed indices. These symmetry identities are crucial for simplifying calculations and for ensuring that derived quantities, like the Ricci tensor or scalar, have the right properties.

Contraction is another fundamental operation. It reduces the rank of a tensor by summing over a pair of indices—one upper and one lower:

$$
T^\mu_{\ \mu} = \sum_{\mu} T^\mu_{\ \mu}
$$

This is how you build invariants, like the Ricci scalar which is a single real number assigned to each point on a Riemannian manifold that measures the degree to which the geometry near that point deviates from flatness:

$$
R = g^{\mu\nu} R_{\mu\nu}
$$

And it’s essential that any symbolic manipulation system handles these operations correctly, respecting all symmetries and producing results in a canonical, unambiguous form. To make this concrete, here’s a minimal Rust example using butler-portugal to canonicalize a symmetric tensor:

use butler_portugal::{Tensor, TensorIndex, Symmetry, canonicalize};

fn main() -> butler_portugal::Result<()> {
    // Construct the metric tensor g_{μν} with indices in reverse order
    let mut g = Tensor::new(
        "g",
        vec![TensorIndex::new("nu", 0), TensorIndex::new("mu", 1)],
    );
    // Declare symmetry: g_{μν} = g_{νμ}
    g.add_symmetry(Symmetry::symmetric(vec![0, 1]));

    println!("Original tensor: {g}");

    let canonical = canonicalize(&g)?;
    println!("Canonical form: {canonical}");
    println!("Coefficient: {}", canonical.coefficient());
    Ok(())
}

This code constructs a symmetric metric tensor with indices in non-canonical order, declares its symmetry, and invokes the canonicalization algorithm. The output is the unique, minimal representative of the tensor under its symmetry group, along with the appropriate sign or coefficient.

At the core of my library is a representation of tensors as objects with named indices, each carrying variance and position. Symmetries are encoded as group actions, with support for symmetric, antisymmetric, cyclic, and custom symmetries. The canonicalization process proceeds by generating all valid permutations of indices under the specified symmetries to enumerate the relevant subgroup of the symmetric group. For each permutation, the algorithm computes the resulting tensor and its sign, ultimately selecting the lexicographically minimal form, and then giving that back to the user.

The symmetries of a tensor are encoded as group actions on its indices. The most common types are:

Symmetric: invariant under exchange of specified indices,
$$
T_{ab} = T_{ba}
$$
Antisymmetric: changes sign under exchange,
$$
F_{ab} = -F_{ba}
$$
Cyclic: invariant under cyclic permutations,
$$
C_{abc} = C_{bca} = C_{cab}
$$
Pair symmetry: exchange of index pairs, as in the Riemann tensor,
$$
R_{abcd} = R_{cdab}
$$

The core challenge in the algorithm is the efficient enumeration of group elements. Naive approaches quickly become intractable as the number of indices grows, the worst-case behavior remains $ O(n!) $ time complexity. However we can use Schreier-Sims algorithm, a staple of computational group theory, provides a scalable solution by constructing a base and strong generating set (or BSGS for short) for the permutation group generated by the tensor’s symmetries. This allows the algorithm to enumerate group elements without redundancy and with minimal overhead. Alternatively the library also supports projection onto irreducible representations specified by Young tableaux, enabling the decomposition of tensors into symmetry types corresponding to the representations of the symmetric group. I won't explain this here, but it's well-documented elsewhere and I put the lecture note links in the repository

My implementation draws inspiration from the Xperm.c library, which is widely regarded as the gold standard for tensor canonicalization in symbolic computation. However, porting the algorithm to Rust was quite a challenge as the C and Mathematica and code is quite dated and not particularly well-documented. So hopefully if you're a practitioner in the field, you can look at my implementation, compare it with the reference and hopefully this makes it easier for some poor future physics grad student who doesn't need to build the same thing again to do their research.

So that's butler-portugal, which hopefully brings high-performance tensor canonicalization to the Rust ecosystem. Can install it with:

cargo add butler-portugal

The library is quite efficient, MIT-licensed and hopefully useful in any domain where the manipulation of tensors with complex symmetries is required, and hopefuly useful for at least one other person besides myself!

Fine-tuning With Tool Calling

Mon, 23 Jun 2025 01:00:00 +0000

Fine-tuning With Tool Calling

With the release of trl 0.19.0, there is now native support for fine-tuning models with custom tools, a capability that has been seamlessly integrated into the Dataset and SFTTrainer classes. This streamlines the training process of teaching a model how and when to call external functions. We can now structure our training data to include the full conversational flow of tool usage. From the initial user prompt, to the model's decision to call a tool, the resulting output from that tool, and the model's final, synthesized response.

An existing part of this workflow is the get_json_schema utility function, which elegantly bridges the gap between your Python code and the structured format that the model requires. This function automatically generates a compliant JSON schema directly from a Python function, but it relies on two key coding practices. First, the function must include modern Python type annotations for all its arguments and its return value. Second, the function's docstring must be written in the Google docstring style. With get_json_schema we can parse the function to extract not only the names and data types of the parameters but also the descriptive text that explains what the function and each of its arguments do. So let's look at an example:

from transformers.utils import get_json_schema

def multiply(a: float, b: float):
    """
    A function that multiplies two numbers
    
    Args:
        a: The first number to multiply
        b: The second number to multiply
    """
    return a * b

schema = get_json_schema(multiply)
print(schema)

This gives the dataset JSON schema for the function.

{
  "type": "function", 
  "function": {
    "name": "multiply", 
    "description": "A function that multiplies two numbers", 
    "parameters": {
      "type": "object", 
      "properties": {
        "a": {
          "type": "number", 
          "description": "The first number to multiply"
        }, 
        "b": {
          "type": "number",
          "description": "The second number to multiply"
        }
      }, 
      "required": ["a", "b"]
    }
  }
}

Now we can use this schema to create a dataset with tool calling. For instance we can wrap the mpmath library to create a dataset with tool calling related to polynomial roots and Bessel functions. We just need to add a tools column in an dataset with the tool schemas.

import mpmath
from datasets import Dataset
from transformers.utils import get_json_schema
from trl import SFTTrainer


def find_polynomial_roots(coefficients: list[float]) -> str:
    """
    Finds the roots of a polynomial given its coefficients.

    Args:
        coefficients: A list of coefficients [c_n, ..., c_1, c_0] for c_n*x^n + ... + c_0.

    Returns:
        A string representation of the list of roots.
    """
    roots = mpmath.polyroots(coefficients)
    return str(roots)


def calculate_bessel_j(order: float, value: float) -> float:
    """
    Calculates the Bessel function of the first kind, J_v(z).

    Args:
        order: The order 'v' of the Bessel function.
        value: The value 'z' at which to evaluate the function.

    Returns:
        The result of the Bessel function J_v(z).
    """
    return mpmath.besselj(order, value)


polyroots = get_json_schema(find_polynomial_roots)
bessel = get_json_schema(calculate_bessel_j)

dataset = Dataset.from_dict(
    {
        "messages": [
            [
                {
                    "role": "user",
                    "content": "Find the roots of the polynomial x^2 - 4.",
                },
                {
                    "role": "assistant",
                    "tool_calls": [
                        {
                            "type": "function",
                            "function": {
                                "name": "find_polynomial_roots",
                                "arguments": {"coefficients": [1, 0, -4]},
                            },
                        }
                    ],
                },
                {
                    "role": "tool",
                    "name": "find_polynomial_roots",
                    "content": "[-2.0, 2.0]",
                },
                {
                    "role": "assistant",
                    "content": "The roots of x^2 - 4 are -2.0 and 2.0.",
                },
            ],
            [
                {
                    "role": "user",
                    "content": "What is the value of the Bessel function J0(2.5)?",
                },
                {
                    "role": "assistant",
                    "tool_calls": [
                        {
                            "type": "function",
                            "function": {
                                "name": "calculate_bessel_j",
                                "arguments": {"order": 0, "value": 2.5},
                            },
                        }
                    ],
                },
                {
                    "role": "tool",
                    "name": "calculate_bessel_j",
                    "content": "0.0483837764022209",
                },
                {
                    "role": "assistant",
                    "content": "The value of J0(2.5) is approximately 0.04838.",
                },
            ],
        ],
        "tools": [ 
            [polyroots, bessel],
            [polyroots, bessel],
        ],
    }
)

trainer = SFTTrainer(
    model="Qwen3-0.6B",
    train_dataset=dataset,
)

trainer.train()

In my limited testing the Qwen3-0.6B and Llama-3.1-70B-Instruct are currently the best open weight models for fine-tuning for custom tool use. Your mileage may vary.

Program Synthesis: The λ in the Machine

Sun, 22 Jun 2025 01:00:00 +0000

Program Synthesis: The λ in the Machine

Much of the "mainstream" discussion of artificial intelligence applied to code generation is overwhelmingly dominated by the idea of scaling larger langauge models and using test-time compute to improve model performance on coding (SWE-bench, LiveCodeBench, etc) benchmarks. And that has legitimately produced some very interesting results. Although I'm not sure how much more juice there is to squeeze out of that fruit.

And indeed, the frontier models have demonstrated a remarkable capacity for probabilistic mimicry and the ability to stich together and synthesize templates of code from their training corpus in emergent and useful ways. But they still operate by predicting token sequences, generating syntactically plausible artifacts that often resemble human-written code. Whether they are doing anything resembling reasoning is a highly debatable and open question which I don't have any interesting opinions on because I truly don't know. I do know that the current systems are limitedly useful in some cases, that much seems undeniably true.

Yet, I would still argue that to mistake this sophisticated pattern matching for genuine program construction is a profound category error. Generating code as a sequence of textual tokens using a statistical prior is a fundamentally different task than generating programs by searching directly in the space of program dynamics. The former is an act of linguistic surface manipulation; the latter is an act of logical and semantic discovery. And it's not clear to me that current models are capable of doing the latter.

But humour me for a moment and consider, that just perhaps the future of AI-assisted development lies not in refining the models of today, but in pursuing the more arduous, less-trodden path of program synthesis, a path whose modern incarnation finds its deepest roots in the evolution of functional programming and type theory. The ambition of program synthesis is not to produce code that looks correct, but to construct a program that is, by its very construction, proven to be correct against a specification. This moves the locus of activity from the messy, ambiguous realm of natural language prompts to the precise, verifiable domain of logical propositions. This pursuit has historically been hampered by a computationally intractable search space, but the maturation of functional programming, specifically with the advent of dependent types, has provided much of the necessary theoretical scaffolding.

A dependently typed language allows specifications to be encoded directly within the type system, transforming type-checking into a form of partial program verification. This is where the concept of hole-style development becomes the crucial user interface for this new paradigm. A programmer architects the high-level structure, articulating properties as types, but leaves specific implementation details as explicit "holes" in the code. These are first-class, typed apertures in a well-formed program, and the synthesizer's role is to find a term satisfying the rigid constraints of its context.

Consider a dependently typed pseudocode for appending two vectors, where the type system guarantees the length of the resulting vector. The programmer might write the initial sketch, leaving the implementation logic as a hole, denoted by ?.

data Vect : (Nat) -> (Type) -> Type where
  Nil : Vect 0 a
  Cons : a -> Vect n a -> Vect (S n) a

append : (n m : Nat) -> Vect n a -> Vect m a -> Vect (n + m) a
append 0 m Nil ys = ys
append (S n) m (Cons x xs) ys = Cons x ?

The type-checker deduces that this hole must be filled by a term of type Vect (n + m) a. The synthesizer's task is now tremendously simplified. It does not need to understand the "concept" of appending. It only needs to search for a combination of operations that can transform the available terms (xs of type Vect n a and ys of type Vect m a) into the required output type. Through a guided search, it would discover that the recursive call append n m xs ys satisfies the type, completing the program in a manner guaranteed to be correct with respect to its type-level specification. If you've ever used systems like Agda, Coq or Lean you've probably seen the power of this approach.

This vision of collaborative, (albeit dynamically typed) synthesis is at least partially realized in systems like DreamCoder represent a significant step towards bridging symbolic reasoning with neural learning. DreamCoder operates via a wake-sleep Bayesian learning cycle. In its "wake" phase, it actively attempts to solve a corpus of inductive program synthesis problems, searching for programs that satisfy given input-output examples. In its "sleep" phase, it performs a kind of computational introspection: it analyzes the solutions it found, refactoring and compressing common patterns into a learned library of reusable, higher-level abstractions. Concurrently, it trains a neural network to guide its future search, making the synthesis process vastly more efficient. This iterative process of alternately solving problems and then learning from those solutions allows the system to bootstrap its own expertise, building an increasingly potent, domain-specific language and a search policy tuned to its structure.

The neural-guided approach pioneered by DreamCoder opens a still more compelling research frontier: framing type-driven synthesis as a reinforcement learning problem. One can imagine an agent, powered by an algorithm like PPO, tasked with inductively constructing partial programs and filling holes in a program. The environment is the incomplete program; the state is the typed hole and its local context; the available actions are the primitives in the current library, which itself may have been learned. A reward is given for any action that produces a type-correct term, with a significant final reward for completing the program. The agent's policy network would learn a semantic prior, predicting not which token is likely to come next, but which branch or insert is most likely to satisfy a given local type signature and the global goal of optimizing towards a reward function that maximizes coherence to the specification. This moves beyond pattern matching on surface syntax and toward learning the logical structure of a problem domain, a direction explored by research into systems like DeepSynth, LambdaBeam and other neural-guided deductive search methods.

This kind of fun speculation is fun, and it's an very interesting and open research problem. But a sober dose of realism is required. Despite the intellectual elegance of the idea of program synthesis, its future is far from assured. The development of these synthesizers would be a monumental engineering task with very little short-term economic upside realized by its developers, probably making it unfundable in any traditional model. Each domain, each library, each API must be furnished with formal specifications or a well-curated set of problems for the synthesizer to be effective. This is a stark contrast to statistical models, which can ingest the chaotic, undocumented, and inconsistent sprawl of existing ecosystems like NPM or PyPI and still extract useful, albeit brittle, patterns of usage.

The network effects of existing programming ecosystems are a force of nature that technical purity has consistently failed to overcome. This was the bitter lesson learned by the Lisp and functional programming communities over the last forty years. While they built pristine, powerful, and self-consistent bubble worlds, they were ultimately outcompeted by the pragmatic secretion and accretion of C, Java, and Python, whose value derived not from internal coherence but from the sheer scale of their surrounding libraries and economic incentives. Thus I would probalby condede that for the foreseeable future, the industry will be dominated by the superficially effective approach of statistical token prediction. The dream of provably correct programs, synthesized through a formal dialogue between human and machine, will continue to be a inspiring vision, but it may be dwarfed by the immense gravitational pull of code reuse and the path of least resistance offered by simply mimicking what has been written before. But we can still dream of DreamCoder future.

The Asbestos Doctrine: Why Crypto Must Be Contained, Not Condoned

Sat, 21 Jun 2025 01:00:00 +0000

The Asbestos Doctrine: Why Crypto Must Be Contained, Not Condoned

For more than a decade, the public discourse surrounding cryptocurrency has been trapped in a fog of misleading analogies and deterministic prophecies. Its defenders have presented it as a misunderstood marvel, variously portrayed as the next iteration of the internet, a lifeboat for the oppressed, or a necessary evolution in finance. This techno-optimistic narrative, which insists the technology is a neutral tool whose potential is just beginning to unfold, has proven to be a dangerously seductive fiction. After sixteen years of a global, multi-trillion dollar experiment run on the public without its consent, the results are in. The appeal to future potential is no longer a credible defense, but an admission of present failure. The fog has cleared, revealing not a nascent utility but a fundamental, structural harm. Cryptocurrency is not the new internet; it is financial asbestos, a socially corrosive material woven into the fabric of our digital lives, and the only responsible public policy is one of aggressive, principled containment.

The initial counter-arguments to this stark conclusion often depend on a flawed characterization of the technology as a politically agnostic tool, akin to the printing press. This comparison fails on its face. While the printing press was a vector for all ideas, its core function was the disintermediation of information. The core function of cryptocurrency, as revealed by its actual use, is the disintermediation of accountability. Its foundational feature (so-called "trustlessness") is merely a euphemism for a system that cannot be governed, audited, or controlled. Its ideology, steeped in a deep distrust of democratic institutions and a nihilistic contempt for regulated systems, is not an incidental feature but the consistent expression of its purpose. The system was not co-opted by bad actors; it was purpose-built to serve them. To dismiss this as a mere genetic fallacy is to ignore the overwhelming evidence that the system’s outcomes have perfectly matched the destructive intent of its founding philosophy.

Nowhere is the harm more apparent or the stakes higher than in the debate over stablecoins. Proponents have framed these dollar-pegged instruments as the industry’s killer application, a benevolent tool for global citizens. This narrative is a Trojan horse. In reality, stablecoins are unregulated shadow banks built on a fatally flawed structure. They are simply digital Money Market Funds, instruments known to be so inherently fragile that their heavily regulated counterparts required massive Federal Reserve bailouts in both 2008 and 2020 to prevent systemic collapse. To champion the proliferation of a less transparent, globally distributed version of this demonstrably unstable structure is an act of profound recklessness. Each transaction privatizes profit for an offshore issuer while socializing risk directly onto the American taxpayer, who serves as the unwilling and uncompensated insurer of last resort. When—not if—a major stablecoin suffers a crisis of confidence, the political pressure on the United States to prevent a global financial meltdown it enabled would be immense, creating a policy trap of its own making.

The attempt to justify this system by pointing to its use in nations like Argentina is a cynical defense that immediately recasts responsible risk analysis as "paternalism." But let us be clear: it is not paternalism to diagnose a systemic poison, and our diagnosis must begin with empathy. It is an undeniably rational, even desperate, choice for an individual family in Buenos Aires to flee a hyper-inflating currency. The tragedy, however, lies in a textbook fallacy of composition: that very act of individual survival, when performed in aggregate, guarantees the collective catastrophe of digital dollarization. This process is not empowerment; it is the ceding of a nation’s monetary sovereignty to an unaccountable, unregulated, offshore corporate power. It forces a coerced trade: a flawed but public sovereign, answerable to its people, for an opaque private sovereign, answerable only to its shareholders. This is not a "lifeboat." It is the exchange of a seat on a leaky public ferry for a place on a private pirate ship, with the American taxpayer implicitly forced to underwrite the insurance policy for the entire pirate fleet.

The attempt to justify this digital expansionism by invoking a geopolitical struggle is equally bankrupt. The notion that the United States must promote private stablecoins to counter a hypothetical future dominance of China’s digital yuan is a deeply flawed premise. It conflates the technical structure of a state-backed CBDC with a privately issued, risk-laden stablecoin. Moreover, it rests on a xenophobic and simplistic "us versus them" worldview that paints American financial policy as a zero-sum game against a foreign "other." China's capital account is not open, and its digital currency project remains a domestic pilot. To build a case for risking global financial stability on such a flimsy and fear-based projection is an abdication of sound policymaking. A world where Europe or another democratic bloc takes the lead in setting digital currency standards is not a threat to be countered but a development to be welcomed within a rules-based international order.

The persistent defense of cryptocurrency’s potential relies on a constant appeal to false historical parallels, chief among them the comparison to the early internet. This analogy is fundamentally dishonest. The internet began as ARPANET, a government-funded project with a clear, utilitarian purpose. Cryptocurrency, by contrast, was born of an ideological whitepaper and built from the start as a speculative, anti-state project. The argument that it is still "early days" has long expired. After sixteen years, far longer than it took the early internet to demonstrate its world-changing utility, cryptocurrency’s primary use cases remain crime, gambling, and recursive financial speculation. This is not a victimless abstraction. It is the ransomware that shutters a hospital's emergency room; it is the life savings of a retiree vanishing overnight in a 'rug pull'; it is the global marketplace for the most odious materials imaginable, all facilitated by a system that launders accountability by design. Its failure to produce a single, large-scale, non-speculative application is not a sign of immaturity but a definitive market verdict on its nature. Legitimate enterprises have rejected it not because it is new, but because it is inefficient-by-design, making it fundamentally unsuited for any serious purpose. It is an empty shell.

This leads to the final, desperate defense: that cryptocurrency is a form of pure, permissionless innovation whose value cannot yet be judged. The comparison often made to that of early experiments on electricity which took decades before practical applications and a commerical electrical grid were realized. This argument presents a false choice between progress and stagnation, but a mature society does not operate on such naive binaries. It rightly reserves the power of an Innovation Veto—the ability to reject a novel creation not out of fear, but out of a rational calculation that its socialized harms vastly outweigh its privatized and hypothetical benefits. To justify this by claiming electricity also took decades to mature is a profoundly dishonest analogy; its foundational experiments were contained, harmless, and carried no public cost, whereas this is a live, multi-trillion dollar trial whose catastrophic externalities are already present and undeniable.

This veto is not a hypothetical power; it is a cornerstone of modern civilization. We exercised it against human cloning on ethical grounds, against leaded gasoline for public health, and against chlorofluorocarbons to protect our planetary environment. The demand for 'permissionless innovation' is therefore a demand to suspend this critical societal function. It is an argument for a sociopathic model of progress, one that is unaccountable to the public it purports to serve. We have been asked to tolerate immense and ongoing social harm in exchange for a perpetually deferred, purely hypothetical future benefit. But society is not a laboratory, and its citizens are not test subjects. The line for such tolerance has long since been crossed. The experiment has failed.

Let this not be mistaken for a defense of the status quo. The existing financial system is deeply flawed: it is often slow, exclusionary, and unjust. But it is built upon a framework of law and accountability that can, with effort, be reformed. It is, to borrow from Churchill, the worst possible system, except for all the others that have been tried. The promise of cryptocurrency is not a better system; it is the alluring but false promise of a perfect system, a revolutionary shortcut that avoids the hard work of democratic reform. In reality, it offers only a descent into a state of nature, where the only rule is code and the only protection is your own vigilance.

The correct path forward, therefore, is not to legitimize this harmful system with bespoke regulation. This is a categorical error. We regulate dangerous but necessary industries like aviation or nuclear power. There is no Federal Commission for Safer Pyramid Schemes. There is no Bureau of Responsible Bank Robbery. We prohibit these activities because the act itself is the harm. To regulate cryptocurrency is to formally absorb financial asbestos into the architecture of our society, signaling that this non-productive casino is a legitimate part of our economic life. This would create the very moral hazard that guarantees future bailouts. The fundamental paradox at the heart of this policy debate boils down to the "Regulatory Trilemma". A policymaker can pursue any two of the following three goals, but is barred from achieving all three.

Preserve Crypto's Core Nature - Permissionless, decentralized, censorship-resistant.
Ensure Full Regulatory Compliance - Effective KYC/AML, sanctions enforcement, investor protection.
Prevent Moral Hazard - Ensure the state and taxpayers are not on the hook for bailouts.

The attempt to fuse (1) and (2) is a technical impossibility; a truly decentralized protocol cannot be forced to comply with state mandates. The choice to prioritize (2) and (3) is an act of transformation, not regulation; a fully compliant and regulated "stablecoin" is no longer a permissionless crypto-asset, but merely a fintech product like a PayPal account, built on a ridiculously inefficient database. The most perilous path, and the one we are on, is to preserve (1) while feigning (2). This creates massive (3) moral hazard, as the government puts a stamp of legitimacy on a system it cannot actually control, guaranteeing a future crisis. This dismantles the central premise of 'responsible innovation.' Any attempt to regulate cryptocurrency either fails to control it or succeeds only by destroying it. Therefore, the only logical policy is not to legitimize this contradiction, but to contain its harm by keeping it separate from the real economy.

Thus the only sound policy is one of principled, relentless containment. We must accept that cryptocurrency, as a bad idea, may never be fully eradicated. The same is true of other socially destructive ideologies like fascism or racism. A liberal society does not defeat such ideas by trying to erase them from existence, an impossible and authoritarian task. Instead, it fights them by denying them institutional oxygen. It makes them socially unacceptable, legally actionable, and politically powerless. It builds a firewall between them and the levers of public life.

Let us be clear about the fundamental chasm that separates these two worldviews. This is not merely a technical disagreement but a profound philosophical schism over the very purpose of a civilized society. A policy of containment is grounded in the belief that the state is a collective project, a social contract whose highest duty is to protect the whole from systemic risk and corrosive externalities. The opposing view, often disguised as technological inevitability, champions a radical vision where individual action, unconstrained by democratic oversight, is the ultimate source of order. It willfully ignores the fallacy of composition—the demonstrable truth that what benefits an individual in isolation can be catastrophic for the collective—and recasts this societal destruction as a virtue called "disruption." This is not a debate between two valid paths to progress; it is a conflict between the architects of a durable society and the apostles of its dissolution. It is a debate about whether the immense, certain harm of the present is a fair price to pay for the uncertain, hypothetical benefit of the future. And who should pay that price.

Asbestos was not embraced as a known poison; it was thought to be a durable cheap insulator. It was precisely this surface-level utility that made it so dangerous, leading society to weave it into the very structure of our schools and homes while its catastrophic harm remained latent, a microscopic and systemic threat that festered for decades. This is the structural parallel to cryptocurrency: a technology whose proponents market its novel features while ignoring the slow-acting poison of financial instability, ensuring that by the time the harm becomes undeniable, it will already be deeply embedded within our economic architecture, forcing a painful and costly remediation on a society that never consented to the risk. The eventual societal verdict was not to seek 'safer' applications, but to ban its future use entirely—to rip it from our walls and bury it in the ground.

This is the Asbestos Doctrine. The goal is not a futile "War on Crypto" that seeks to scrub its code from every computer. The goal is to use the full force of existing law and democratic institutions to ensure it remains a marginal, isolated phenomenon. This means aggressive enforcement of securities laws, anti-money laundering statutes, and sanctions. It means severing its lifeline to the regulated banking system and its ability to use US Treasuries as reserves. The objective is to firewall the offshore casino so completely that its collapse, when it comes, is an isolated event, not a systemic contagion. It is to let it wither in the dark, cut off from the light of legitimacy. Some will always seek it out, just as some will always seek out any number of harmful pursuits. But public policy must ensure that it cannot grow, that it cannot achieve systemic importance, and that it cannot poison the broader social and economic well. The faith we must place is not in the phantom promise of abstract future technologies or a decentralized utopia, but in the long, proven arc of our own democratic institutions to contain and marginalize the destructive ideas that threaten them.

What is AI market actually worth?

Tue, 17 Jun 2025 01:00:00 +0000

What is AI actually worth?

The artificial intelligence boom is obviously the latest historical example of a market bubble, but it is a particularly strange one. It is a bubble inflated by a potent mixture of managerial fantasy, quasi-religious fervor, and a torrent of capital with nowhere else to go. While proponents and industry thought leaders herald a new economic dawn that rivals the industrial revolution, a closer inspection reveals an industry built on shaky technological foundations, propped up by unsustainable spending and fueled by a narrative that borders on the absurd. The current trillion dollar valuations are not a reflection of imminent revolution but a testament to the financial world's infinite capacity for self-deception, promising an inevitable and brutal correction.

At the heart of the hype lies a technical reality that is far less impressive than the marketing material suggests. The scaling of large language models, the very engine of this new wave, appears to be hitting a wall of diminishing returns. Barring a fundamental architectural breakthrough, we are simply throwing more data and more computation at models for increasingly marginal gains. The entire process of benchmarking has devolved into a subjective beauty contest, where defining "progress" is a challenge in itself. Outside of tasks with binary answers, determining which model is superior is a matter of vibes, opinion, a game of whack-a-mole where improvements in one domain create deficiencies in another. The metrics are less science and more sophisticated hand-waving, designed to produce impressive charts for product launches and investor decks rather than a true measure of capability.

This technical ambiguity provides fertile ground for a seductive fantasy that has completely captured the American professional managerial class. Sold a bill of goods by an army of management consultants, these non-technical executives envision a near future where the messy, unpredictable, and costly business of human labor is automated away. They dream of a corporate utopia run by a small cadre of elite directors, where profits soar unburdened by salaries, healthcare, or labor disputes. This is, of course, a fiction, but it is a powerful one for managers who view their employees as expendable cogs in a machine. This delusion is the primary driver of corporate AI spending, a massive R&D slush fund dedicated to the proposition that workers can and should be replaced.

The result of this managerial pipe dream is a tidal wave of corporate "innovation" projects that are profoundly disconnected from the actual work of the company. The corporate mandate is to "have an AI strategy," which in practice means building internal chatbots and RAG systems for data retrieval. These projects, often several degrees removed from any core business activity, deliver little tangible value but are plausible enough to be sold internally as progress. Some recent studies put the failure rate of these projects at somewhere 95% failure rate. It is a perfect execution of the Politician's Fallacy: something must be done, this is something, therefore we must do it. Companies are burning through capital not to solve real problems, but to be seen as participating in the trend, creating expensive Potemkin villages of artificial intelligence to appease their boards and shareholders.

Then come the management consultants, the high priests of corporate anxiety, arriving with the solemnity of undertakers to monetize the C-suite's deepest insecurities. Armed with glossy slide decks and a proprietary vocabulary of synergistic nonsense; they sell a seductive fantasy whispered into the ears of executives who view their workforce as a costly liability. Their gospel preaches a boardroom utopia where the messy, expensive, and occasionally unionizing problem of human labor can be neatly excised from the balance sheet, replaced by a flawless, uncomplaining algorithm. They expertly exploit the profound technological illiteracy of their clients, presenting AI as a magical black box that will transmute operational costs into pure profit. The result is a flood of multi-million dollar "transformation" roadmaps whose primary strategic function is to guarantee a lucrative, multi-year follow-on engagement for the consultants themselves. They are not advisors but architects of plausible deniability, providing executives with a beautifully formatted, jargon-filled permission slip to light a bonfire of shareholder money in the name of innovation.

This corporate delusion is amplified and sanctified by the bizarre cultural terrarium of the Bay Area, where the AI labs function as monasteries for a new rationalist cult. Its acolytes, a socially anxious cohort of the terminally online, believe they have replaced messy human intuition with pure logic, yet have merely swapped out old gods for a silicon one. They signal their allegiance through a coded lexicon of Bayesian priors and expected utility, a verbal handshake that confirms they are among the enlightened few, forever detached from the lived experience of anyone who has ever touched grass. This is not merely a subculture; it is a full-blown eschatological movement for intelligent people who do not realize their own subconscious religious impulse has led them to cosplay as prophets. Self-described "super-forecasters" issue prophecies from their blogs, breathlessly predicting the arrival of a Machine God by 2027, a digital rapture that will solve all problems for the worthy. If you wish to gaze into the abyss of their thought process, you need only read their scripture, a prose so dense with self-importance and abstract nonsense that it acts as a cognitive barrier to the uninitiated.

So a post-singularity world may be a world of fun and plenty for the people who are currently ignoring the problem, whilst being a living hell for a significant fraction of current existential risk reducers (say, the least generous half). You could take this possibility into account and give even more to x-risk in an effort to avoid being punished. But of course, if you're thinking like that, then the CEV-singleton is even more likely to want to punish you... nasty. Of course this would be unjust, but is the kind of unjust thing that is oh-so-very utilitarian. It is a concrete example of how falling for the just world fallacy might backfire on a person with respect to existential risk, especially against people who were implicitly or explicitly expecting some reward for their efforts in the future. And even if you only think that the probability of this happening is 1%, note that the probability of a CEV doing this to a random person who would casually brush off talk of existential risks as "nonsense" is essentially zero.

If that passage reads like the unholy union of a paranoid sci-fi novel and a first-year philosophy student's bong-rip, congratulations, you are sane. This is the intellectual backbone of the movement: absurd, labyrinthine thought experiments, ripped from the pages of pulp fiction, taken with the deadly seriousness of divine revelation. It is, in essence, nerd Scientology for the Bay Area, a perfect trifecta of one part tax-optimization, one part cynical in-group signaling for career advancement, and one part the wide-eyed fervor of true believers who genuinely think they are building God in a server farm.

When one examines the actual applications emerging from this frenzy, the picture becomes even more bleak. Outside of text generation, the most prominent use cases are either unprofitable, a net negative for society, or both. AI image generation is a fascinating toy, but it is an expensive, easily commoditized novelty with no clear path to profitability. The viral video generators producing surreal clips of talking animals and historical figures are an amusing distraction, but they are an engine for creating digital slop, not economic value. The only entity making real money from this "slop economy" is Nvidia, which happily sells the digital shovels for this fool's gold rush. The most likely outcome is a future where social media is choked by an endless stream of algorithmically generated content, strangling the very platforms that host it. And maybe we should celebrate that!

Even the most legitimate application, AI-powered coding assistants, is a financially dubious proposition. While these tools can genuinely augment programmer productivity, the companies providing them are deeply unprofitable. They are also highly dependent on a small number of model providers (namely Anthropic, whose models are genuinely much better than the others at coding tasks) and constrained by the same scaling limitations plaguing the entire field. The technology may well eliminate a swath of entry-level programming jobs, but the dream of a fully automated software engineer, capable of complex, creative, and system-level thinking, remains a distant pipe dream. Like so much in the AI space, a kernel of a good idea has been inflated into a revolutionary fantasy that the underlying technology simply cannot support.

The entire edifice is held aloft by a geyser of capital so vast and indiscriminate it makes a firehose look like a precision instrument. The American venture economy is sitting on mountains of "dry powder," billions in undeployed capital aching with the impatient, frantic energy of a cornered rat. With the smoking craters of crypto and the metaverse still fresh in memory, the investment class has stampeded toward the last plausible growth story, driven by the moronic TINA mantra. So-called strategic allocation is really more a desperate flight to the only mirage in the desert. But if you're running money professionally, sitting in cash is a non-option, so when the music is playing you have to dance.

This initial flood of nervous money then attracts the final stage of the financial food chain: the gullible leviathans. Here come the SoftBanks and the gulf state sovereign wealth funds, the largest and dim-wittedest pools of money on Earth, ready to blast their petrodollars and printed money at anything that glows with the faint promise of "the future." Their due diligence process has the intellectual rigor of a slot machine, a mix of geopolitical posturing and pure, unadulterated FOMO. This creates a magnificent, self-licking ice cream cone of a bubble. The capital class funds the unsustainable cash burn of AI labs, which generates hype, which attracts the sovereign wealth funds for a later, larger round at an insane valuation, which validates the VCs' initial bet. The goal is not to build a profitable business but to keep the music playing long enough to pass the flaming bag of promissory notes to the next, even wealthier, idiot. The supposedly decentralized investor class is more like a herd of lemmings, engaging in a spectacular display of malinvestment that would make a Soviet central planner blush.

None of this is to say that all of AI is malinvestment or fraudulent. Legitimate and fascinating research is being done, and Nobel breakthroughs around protein folding advances to demonstrate the potential. Probabilistic text models have real, if niche, applications. But they are not reliable, consistent, or accurate enough to perform the vast majority of knowledge economy tasks. There is no breakthrough on the horizon that promises to give them these properties. The industry is filled with people role-playing that such a breakthrough is just around the corner, either because they are incentivized to believe it or because they are members of the religious movement and believing in AI singularity provides a psychological escape from the mundane precarity of modern existence. The reality is that artificial intelligence is a real, durable and lasting industry that will inevitably be part of he future, but it is one whose true market capitalization is measured in the tens of billions, not trillions. The vast sums of money currently being allocated are fuel for a bonfire, and when the flames die down, all that will be left is the sobering ash of a market that finally, and painfully, came to its senses. And hopefully it doesn't take the chunk of the S&P500 with it.

Book Review: Tomorrow, and Tomorrow, and Tomorrow

Sat, 14 Jun 2025 01:00:00 +0000

Book Review: Tomorrow, and Tomorrow, and Tomorrow

Gabrielle Zevin's Tomorrow, and Tomorrow, and Tomorrow is a novel about two people who make video games together for thirty years, and if that sentence made you instinctively reach for the back button, I understand, but you would be making a mistake. The book is not about the games industry in the way that industry memoirs are about the games industry (self-congratulatory, jargon-heavy, convinced that shipping a product is inherently heroic). It uses game design the way the best science fiction uses spaceships: as a vehicle for getting somewhere more interesting. In this case, the destination is a sustained, unsentimental, and surprisingly devastating examination of what it means to build something with another person.

Sam Masur and Sadie Green meet as children in a hospital. Sam is recovering from a car accident that killed his mother and crushed his foot. Sadie is visiting her sister, who is being treated for leukemia. They bond over a Nintendo. They lose touch. They reconnect years later (Sam at Harvard, Sadie at MIT, a few stops apart on the Red Line, a geography I know well, having lived between those stops for years) and begin making games together. Their first collaboration, Ichigo, a side-scroller set in a world drawn from Hokusai's wave prints, becomes a massive hit. Their creative partnership spans decades. It survives success, failure, jealousy, grief, a shooting, and the persistent, never-quite-resolved question of whether they are in love with each other or merely in love with the thing they make together.

Zevin is ruthlessly precise about the mechanics of creative collaboration. She understands that making something with another person is its own form of intimacy, distinct from friendship and from romance and reducible to neither. Sam and Sadie need each other. They resent each other for the needing. They compete, they withhold credit, they hurt each other in the specific ways that only people who share a creative nervous system can. Marx, Sam's college roommate who becomes their business partner and eventually Sadie's romantic partner, is the third point of the triangle: the person who makes the collaboration possible by handling everything the two principals are too consumed by their own vision to notice. He is the most generous character in the book, and Zevin does something to him that I will not spoil except to say that it earns the novel its Macbeth epigraph.

The title, of course, comes from Macbeth's famous soliloquy: "Tomorrow, and tomorrow, and tomorrow, / Creeps in this petty pace from day to day." The speech is about meaninglessness: life as sound and fury signifying nothing. Zevin inverts it. In her telling, the repetition of "tomorrow" is the structure of creative work. You show up. You make the thing. You show up again. The games Sam and Sadie build are their answer to Macbeth's despair, worlds that signify something precisely because someone chose to build them, even knowing they are temporary, even knowing they are fictions. It is the most quietly optimistic book about mortality I have read in years, and it achieves this optimism honestly, through accumulated loss rather than despite it.

What will stay with you, if you work in any field that involves building things with other people (and if you are reading this blog, you almost certainly do), is Zevin's treatment of the authorship question. Who made this? Whose vision is it? Sam's name goes on the company. Sadie writes the engine. The public credits Sam. The code is Sadie's. Zevin shows, with forensic patience, how structural inequalities (gender, disability, class, the specific charisma of who happens to be standing at the microphone when the press arrives) determine who gets remembered and who gets erased. If you have ever pair-programmed on something and watched the other person get the credit, or gotten the credit yourself and felt the quiet wrongness of it, this book will land like a hammer.

Sam's disability (chronic pain from the childhood injury, a permanent limp) is handled with a specificity that literary fiction rarely manages. Zevin treats it as a physical fact that shapes every day of his life, not as a metaphor or a character trait that reveals something about his soul. He is in pain. The pain affects what he can do. Other people's perception of his disability affects how they treat him. That is all. The same restraint applies to Sadie's experience as a woman in the games industry: exploited by a professor, underestimated by colleagues, structurally invisible in ways that accumulate over decades. Zevin documents the mechanisms without editorializing, and the documentation is damning enough.

The novel is 416 pages and reads faster than most 200-page thrillers. It spans from the early 1990s to the 2040s, from the era of the SNES to virtual reality, and it uses the evolution of games technology as a quiet clock ticking beneath the human story. Zevin clearly loves games, but more importantly, she understands why people love them: they are worlds someone chose to build, governed by rules someone chose to impose, offering a kind of agency that the real world, with its car accidents and its cancer wards and its unfair credit allocations, does not reliably provide.

I recommend this book to anyone who has ever made something with someone else and found that the making changed both of you in ways you could not have predicted. It is the best novel about creative partnership I have read, and it is the rare book that treats video games as an art form with the same seriousness that literary fiction typically reserves for itself. If Macbeth is right and life signifies nothing, Zevin's answer is: then build something anyway. Show up tomorrow. And tomorrow. And tomorrow.

The Future of Maths May Be Deeply Weird

Wed, 11 Jun 2025 01:00:00 +0000

The Future of Maths May Be Deeply Weird

In fiction there is a popular image of a mathematician as a lone solitary figure, a figure of lost in their own world in a world of intense concentration before a chalkboard dense with arcane symbols. That may have had some truth in the past but the reality is that mathematics these days is a far more social phenomenon and future mathematicians may have a lot more in common with software engineers toiling away on pull requests on Github than they do with the archetype of a Andrew Wiles-like genius toiling away in isolation for a decade to prove Fermat's Last Theorem.

The field of automated theorem proving is a field of computer science that develops software systems capable of automatically constructing mathematical proofs or verifying the correctness of human-written proofs. These systems use formal logic, type systems, and symbolic reasoning to check that each step in a mathematical argument follows logically from the previous steps and established axioms. By encoding mathematical knowledge in a precise, machine-readable format, automated theorem provers can eliminate human error and provide absolute certainty about the validity of mathematical results.

For those that don't follow the theorem proving ecosystem (Lean4, Coq and their predecessors Isabelle, Agda, HOL4, etc) are tools that were once confined to the esoteric frontiers of computer science research, are poised to reshape the very practice and philosophy of mathematics. The future of the discipline may be far stranger, and more collaborative, than we can currently imagine. And with the simultaneous advent of language models, may be much more exciting and rapid than we can currently imagine.

Below is a formalization of Euclid's theorem on the infinitude of primes in Lean. The proof follows Euclid's constructive approach: given any natural number n, it constructs a prime p ≥ n by considering the smallest prime factor of n! + 1. The Lean proof uses several tactics and lemmas: minFac finds the minimal prime factor, factorial_pos establishes that factorials are positive, minFac_prime proves the minimal factor is indeed prime, and dvd_factorial handles divisibility properties. The crucial insight, formalized through Nat.dvd_add_iff_right, shows that if a prime divides both n! and n! + 1, it must divide their difference (which is 1), leading to a contradiction since primes cannot divide 1. This is the proof that every undergraduate mathematics student learns in their first year.

/-- Euclid's theorem on the **infinitude of primes**.
Here given in the form: for every `n`, there exists a prime number `p ≥ n`. -/
theorem exists_infinite_primes (n : ℕ) : ∃ p, n ≤ p ∧ Prime p :=
  let p := minFac (n ! + 1)
  have f1 : n ! + 1 ≠ 1 := ne_of_gt <| succ_lt_succ <| factorial_pos _
  have pp : Prime p := minFac_prime f1
  have np : n ≤ p :=
    le_of_not_ge fun h =>
      have h₁ : p ∣ n ! := dvd_factorial (minFac_pos _) h
      have h₂ : p ∣ 1 := (Nat.dvd_add_iff_right h₁).2 (minFac_dvd _)
      pp.not_dvd_one h₂
  ⟨p, np, pp⟩

The formalization of the standard undergraduate mathematics curriculum in a format like this is no longer a distant dream. It is an achievable, near-term goal. Need only have a look at the standard library Mathlib and the amount of progress on the standard set of theorems is now incredibly vast and expressive. Another good example of this progress is the formalization of Terence Tao's textbook, Analysis I which has been meticulously translated into an explorable, crosslinked and machine-checkable set of theorems. A future in which is every textbook has a digitial equivelent and any theorem or lemma can be "double clicked" to expand its context and definitions is hardly science fiction anymore. It's essentially here.

If you want to experiment with Lean, you can get started very quickly with the following steps:

Install Visual Studio Code.
Install Lean + Elan:

curl https://elan.lean-lang.org/elan-init.sh -sSf | sh
elan default leanprover/lean4:stable

Install the Lean 4 VS Code Extension: Open VS Code → Extensions → search for Lean 4 (author: leanprover.lean4)
Initialize a new Lean project:

lake init my_project
cd my_project
lake build

The Lean ecosystem also has a burgeoning flora of open source tools. The Mathlib library is a massive, collaborative repository of formalized mathematics, growing daily. To navigate this vast digital library, a suite of search engines has emerged. Moogle provides semantic search, allowing one to find theorems based on conceptual meaning rather than exact phrasing. Loogle specializes in finding expressions that match a specific logical structure, and LeanSearch offers natural language queries. For those wishing to experiment, the Lean 4 Playground provides an interactive environment to write and check proofs directly in a web browser.

Consider the educational landscape this might enable. Imagine a future where every first-year mathematics student downloads a single, 200-megabyte file containing the entire verified foundation of their subject. They would be guided by an LLM-assisted tutor, a system capable of planning lessons, verbalizing complex proofs, and providing instant, theorem prover checkable feedback on their own attempts at proofs. This is not science fiction; the technology for curriculum planning and natural language explanation is largely within our grasp today. Of course, this vision must be tempered with realism. Science is intrinsically a social phenomenon. A great deal of mathematical research is about developing taste, an aesthetic for what constitutes an elegant proof, and the intuition for which problems are worth pursuing. These are intangible qualities of the craft, born from culture and collaboration, which a machine may never fully capture.

As we move from established knowledge to the open frontiers of research, these tools present new and exciting possibilities. While the body of formalized proofs is growing, there remains a relative scarcity of formalized open conjectures. A project like the Deepmind's index of formal conjectures is valuable for several reasons. First, it provides a clear and challenging set of benchmarks for the development of AI-assisted automated theorem provers. Second, the very act of formalization forces mathematicians to clarify the precise, unambiguous meaning of a conjecture. It is almost certain that we will soon see a powerful, neurosymbolic system, a kind of next generation AlphaGeometry, unleashed upon this list in an attempt to systematically push the boundaries of machine-generated mathematics.

The artifacts produced by such research will themselves be objects of profound study. Picture a future where one can download the twenty-gigabyte weights of a neural network that has been trained through reinforcement learning to achieve mastery over the entirety of undergraduate mathematics, using theorem prover feedback as its reward function. The existence of such a model would provoke fascinating theoretical and philosophical questions. Is there a smaller, more elegant model that can achieve the same result? By examining its failure modes, what can we learn about the complexity hurdles in mathematics? How would it handle alternative axiom sets, and could it ever develop an "understanding" of Gödel's incompleteness, intuiting when a problem is fundamentally independent of the given axioms? There are many deep meta-mathematical questions we could ask if we had an existence proof of a giant, inscrutable matrix that can "itself" do mathematics. There is no guarantee such a thing can exist (and the usual Gödel, Turing, and Hilbert's Program analyses still apply), but if it can — even to a limited extent — that opens up a whole new world of questions.

Stretching our imagination further, we can envision a far future where this technology reaches its zenith. A dedicated data center could be tasked with a grand challenge, like the Riemann hypothesis. After weeks of processing, it might return a positive result: a complete, machine-checkable proof. Yet, the proof's internal structure could be so byzantine, so alien in its logic, that no human could ever hope to grasp its intuitive thrust, much like the computer-assisted proof of the Four Color Theorem or the controversy surrounding the Mochizuki proof of the ABC conjecture. This would usher in a disquieting new reality, a world where machines, not unlike the hyper-intelligent Minds from Iain M. Banks' Culture series, venture into intellectual territories forever beyond human comprehension. We would "know" (epistomigical concerns aside) and accept certain mathematical truths, but as humans we would never intuit or understand why they are true. And that is a very different world in which science happens.

The prospect of inscrutable machine-generated proofs touches on fundamental questions about the nature of knowledge and understanding. Bill Thurston, in his essay "On Proof and Progress in Mathematics," captured this tension:

The rapid advance of computers has helped dramatize this point, because computers and people are very different. For instance, when Appel and Haken completed a proof of the 4-color map theorem using a massive automatic computation, it evoked much controversy. I interpret the controversy as having little to do with doubt people had as to the veracity of the theorem or the correctness of the proof. Rather, it reflected a continuing desire for human understanding of a proof, in addition to knowledge that the theorem is true.

New developments also raise teleological questions about the very purpose of of the maths discipline. Mathematics has never been merely about accumulating true statements—it's about developing insight, building intuition, and creating frameworks that illuminate the underlying structure of reality. The process of discovery, the "aha!" moments of understanding, the elegant connections between seemingly disparate areas: these constitute much of what makes mathematics meaningful to its practitioners. As Feynman once said: "Physics is like sex. Sure, it may give some practical results, but that's not why we do it."

To be honest, it's hard not to get emotional about this prospect. In that future, many of us would still care deeply about learning why theorems are true. The process of answering those questions represents one of the most beautiful and fulfilling aspects of intellectual life. Maths as a practice is more than a matter of checking theorems off a cosmic to-do list. But if you buy into this premise, and if you're a burgeoning model designer, all you have to do win a Nobel (and several other prizes) is just train your stochastic parrot to autocomplete the next $n$ tokens such that the Lean theorem validates your answer.

theorem infinite_irrational_at_odd :
    { n : ℕ | ∃ x, Irrational x ∧ riemannZeta (2 * n + 1) = x }.Infinite := by
    ...

You'll also land yourself a cool million dollars from the Millennium Foundation in the process, which might pay for 1/100 of your GPU bill. Or maybe just make the AI-slop Infinite Jest version of TikTok, because alas, that's probably a much better short-term return on investment than solving Riemann and pushing the frontiers of human knowledge.

But joking aside, we're not there yet. Not even close. Need only watch Terence Tao's recent YouTube streams with Claude and o4 on Lean theorem proving reveal the stark limitations of our current systems when faced with even moderately challenging mathematical problems. The models struggle with basic proof strategies, make elementary logical errors, and often produce syntactically correct but mathematically meaningless Lean code. Yet watching these experiments unfold, it doesn't require a tremendous leap of imagination to envision how rapidly this landscape might change. The combination of increasingly sophisticated language models, improved integration with theorem provers, and better training methodologies specifically designed for formal mathematical reasoning suggests that today's clumsy first attempts may give way to genuinely more capable models. But of course, progress is never certain. There could be a lot more hurdles to overcome.

This prospect may seem to diminish the human element of mathematics, but perhaps that fear is unfounded. Computers have decisively solved the games of chess and Go. Stockfish and AlphaGo can defeat any human player on Earth with ease. Yet, chess has never been more popular. These powerful systems have not killed the game; they have become indispensable tools for training, analysis, and appreciation, making the game more accessible to more people than ever before. It is possible the same will hold true for mathematics. As these strange and powerful new tools proliferate, they may not render the human mathematician obsolete. Instead, they might democratize access to mathematical reasoning, allowing more people to participate in the oldest and most abstract of sciences. Perhaps the frontiers of knowledge will widen at an incredible pace, but the path to that frontier will be more accessible for everyone. And maybe that is a very bright future indeed.

Does the Star Trek Computer Run on COBOL?

Thu, 05 Jun 2025 01:00:00 +0000

Does the Star Trek Computer Run on COBOL?

We like to imagine the future as sleek, seamless, and intelligently designed — a world where a single voice query to a starship's LCARS interface dispatches 575 trillion calculations per nanosecond through the bio-neural gelpacks (biological FPGAs), to run a massively parallel computation to calculate the optimal molecular dynamics for the replicator to materialize the perfect cup of Earl Grey, hot, as an instantaneous, almost magical, manifestation of desire. But what if the reality is less Star Trek and more like our current software landscape, just with centuries more layers of legacy code piled on top?

Imagine a starship doing relativistic frame calculations for spaceflight, but at the root of the system is a timer counting down from the Unix epoch in 1970. A little time_t integer overflow, and suddenly your carefully plotted course to Proxima Centauri B is aiming you directly into a black hole, all because someone, somewhere, 400 years ago, didn't think anyone would still be using that particular library. And when you try to fire the engines to correct course, they fail to ignite because the engine control system was compiled against glibc 2.35 but the navigation computer is running 2.34. Vernor Vinge's novel A Deepness in the Sky paints a wonderfully terrifying picture of this:

So behind all the top-level interfaces was layer under layer of support. Some of that software had been designed for wildly different situations. Every so often, the inconsistencies caused fatal accidents. Despite the romance of spaceflight, the most common accidents were simply caused by ancient, misused programs finally getting their revenge.
“We should rewrite it all,” said Pham.
“It’s been done,” said Sura, not looking up. She was preparing to go off-Watch, and had spent the last four days trying to root a problem out of the coldsleep automation.
“It’s been tried,” corrected Bret, just back from the freezers. “But even the top levels of fleet system code are enormous. You and a thousand of your friends would have to work for a century or so to reproduce it.” Trinli grinned evilly. “And guess what—even if you did, by the time you finished, you’d have your own set of inconsistencies. And you still wouldn’t be consistent with all the applications that might be needed now and then.”
Sura gave up on her debugging for the moment. “The word for all this is ‘mature programming environment.’ Basically, when hardware performance has been pushed to its final limit, and programmers have had several centuries to code, you reach a point where there is far more signicant code than can be rationalized. The best you can do is understand the overall layering, and know how to search for the oddball tool that may come in handy

Vinge's depiction of a "mature programming environment" where layers of ancient, often misunderstood code form the bedrock of advanced civilizations is incredibly compelling in its cynicism (or perhaps hard science fiction realism). It's merely an extrapolation of trends already deeply embedded in our own societies approach to software development. The romantic notion of constantly rewriting and perfecting our digital infrastructure heritage often collides with the gritty pragmatic reality: the overwhelming cost-to-benefit ratio of replacing systems that, for all their quirks, simply work.

Consider the vast edifice of scientific and engineering software. Even today, a significant portion of high-performance numerical computing—the kind that powers climate models, astrophysical simulations, and complex engineering designs—still relies on libraries and kernels written in FORTRAN. Not necessarily FORTRAN 77 in its rawest form, but codebases whose lineage and core algorithms trace back decades. Every time you pip install scipy for a mundane optimization routine, there's a vast swatch of Fortran at play and for good reason. These aren't trivial pieces of code; they are often the product of person-centuries of development, validation, and refinement. The prospect of rewriting them in a "modern" language, ensuring bit-for-bit identical (and correct) output, and then re-validating the entire new stack against decades of experimental data and theoretical work, is a task so monumental and fraught with risk that it's rarely undertaken. Why would it be, when the existing code, running on increasingly powerful hardware or within sophisticated modern wrappers, continues to deliver reliable results?

One could argue this isn't a failure of progress, but a pragmatic consequence of it. The stability and proven correctness of these foundational blocks allow scientists and engineers to build higher, to ask more complex questions, rather than perpetually rebuilding the basement. The same principle applies, perhaps even more acutely, to the invisible infrastructure of global finance. Core banking systems, transaction processing engines, and stock market clearinghouses often run on software written COBOL, on mainframe architectures that seem anachronistic to a generation raised on cloud computing. The interconnectedness is staggering; countless other systems, from national payment networks to individual corporate accounting software, are built to interface with these legacy cores. A "rewrite" isn't just a coding project; it's a global logistical, economic, and political challenge of the highest order.

Yet, these systems process trillions of dollars in transactions daily with incredible reliability. The idea of halting, even for a week, the machinery that underpins global capitalism to attempt a wholesale replacement is unthinkable. Because capitalism is inevitable and there is no alternative, right? Or maybe best not to think about such questions.

But as these systems become more deeply embedded and more critical, a peculiar thing happens: they become taken for granted. The intricacies of their internal workings fade from common institutional knowledge. Successive generations of engineers learn to interface with them, to build around them, to coax new functionalities by adding new layers, but the core itself becomes an opaque black box. It works, so why delve too deeply into the "how," especially when the original architects are long retired or deceased, and the documentation is sparse, outdated, or both?

Since I love science fiction literature, I've been thinking about this a lot. Here are some of the more interesting outcomes I've come up with. Each one could probably be a humerous Greg Egan-style novella.

The Ritualistic Maintainers: Imagine a future where critical infrastructure—say, atmospheric processing for a terraformed Mars, or the global food production AI—runs on a core operating system whose deepest layers were written in the late 21st century. No living human fully understands its architecture. Maintenance becomes a highly specialized, almost priestly role, involving the careful application of historically successful patches and workarounds, interpreting cryptic log files whose error codes reference hardware that hasn't existed for centuries, all while hoping not to disturb the delicate, poorly understood equilibrium of the ancient code. New features are bolted on through increasingly elaborate APIs that treat the core as an unchangeable, god-given constant. Really not much different from the current state of software development, to be honest.
Cascading Obsolescence as Systemic Risk: A seemingly minor, ubiquitous standard from our near future—perhaps a data compression algorithm or a cryptographic protocol from the 2040s—becomes deeply embedded in countless automated systems. Decades later, a subtle flaw is discovered, or the hardware to efficiently process it becomes scarce. But it's so deeply woven into the fabric of, for example, interplanetary logistics or medical diagnostic equipment, that phasing it out without causing massive disruption is a multi-generational project. The "Y2K bug" might seem trivial compared to the "2275 GCC Undefined Behavior Crisis."
The Rise of Software Archaeologists: When a truly novel problem arises, or a deep-seated bug in the mature programming environment finally surfaces with critical consequences, society might rely on specialists who aren't innovators in any traditional sense, but rather "software archaeologists." Their expertise lies in reverse-engineering and understanding these digital antiquities, using AI-assisted tools to analyze compiled code from forgotten languages, sifting through petabytes of historical data archives for fragments of documentation or ancient online forum discussions that might offer a clue. Maybe future historians will debate interpretations of APL code like we do with Minoan Linear A scripts.
Progress as Increasingly Complex Abstraction: True innovation continues, but often at the periphery. We might develop incredibly sophisticated AI that can diagnose rare diseases, but the AI's learning algorithms might still be outputting results into a data format originally designed for 21st-century hospital record systems, because that's what the national health database, with its petabytes of historical (and legally mandated) data, still requires at its core. The AI doesn't replace the old system; it learns to expertly navigate its limitations and idiosyncrasies. Just as we carefully preserve pre-atomic low-background steel for sensitive scientific instruments, vast archives of Reddit threads and Twitter posts are maintained in specialized data centers, their antiquated social media discourse essential for bootstrapping new language models that need to understand the linguistic roots of modern communication.

Is this a form of stagnation, a build-up of civilizational technical debt that will eventually come due? Perhaps. But it can also be seen as a strange, emergent form of progress. Each "solved" problem, encapsulated in a piece of software that becomes part of the unquestioned infrastructure, allows subsequent generations to focus their intellectual energy on new challenges, standing on the shoulders of digital giants whose names and methods they may no longer even know.

Alternatively, a more advanced (and arguably more enlightened) society might adopt a philosophy akin to the Shinto shrines in Japan. Where the shrines are completely demolished and meticulously rebuilt on an adjacent site every 20 years, a tradition known as Shikinen Sengu, practiced for over 1300 years. This isn't renovation; it's a complete rebuild using fresh materials and ancient techniques, rooted in beliefs about impermanence, purity, and the transfer of knowledge to the next generation. Not unlike how many 50 year old Unix utilities are currently being rewritten in memory-safe languages.

However, such an approach would likely require a societal structure far more advanced and economically different from our current one. It presupposes a society where resources and skilled human-time are sufficiently abundant to undertake these monumental rebuilds not out of immediate crisis, but as a matter of principle and long-term health. It would also imply a culture where software development is treated less like the current dog-eat-dog, hype-driven lunatic fest focused on rapid iteration, enclosure, and market capture, and more like a deeply valued craft, akin to the meticulous artisanship and traditions to persist. And anyone who works in software today knows that's a far, far, removed from what we do today.

The future of software may not be one of constant, radical reinvention from the ground up, but rather a story of accretion, layering, and the increasingly sophisticated management of an ever-growing, ever-aging technological heritage. The most advanced systems of tomorrow might be running, at their very core, on the digital ghosts of today. Not sure if that's a scary thing, but it does imbue the craft of software development with a certain kind of reverence and weight worth considering.

Interfacing MCP with Combinatorial, Convex, and SMT Solvers

Mon, 02 Jun 2025 01:00:00 +0000

Interfacing MCP with Combinatorial, Convex, and SMT Solvers

Lately I've been working on using MCP beyond just using it for symbolic algebra manipulations, I've been thinking about how to interface large language models with a suite of dedicated solvers for scientific computing exposed as tools to the model. And particularly for automating workflows in physical engineering disciplines.

Github Source Code
git clone https://github.com/sdiehl/usolver.git

If you're not familiar with MCP, you can read more about it in my previous post or the thousand other breathless thinkpieces on the internet about how it's the greatest thing since sliced bread or something. But in reality it's just a janky way to expose a set of function calls (called tools) to a language model via a JSON RPC interface. Language are models are great at language interpretation and limited "planning", and numerical solvers are great at numerical computation. So let each system do what they do best and synthesize the two to build a hybrid system. MCP is just the glue to bind these scientific Python libraries with the model, essentially the 'cgi-bin' of AI.

The simplest motivation for combining language models with numerical solvers via MCP is that it's vastly more efficient for certain problems. Consider the dumb example that you certainly can feed a Sudoku puzzle into one of the frontier reasoning models (o3, deepseek r1, etc) and after spinning for quite some time it can (maybe) solve it by talking to "itself" about trial and error guesses for quite some time. The chain of thought will be this vast sequence of guesses and backtracking. But, you can also feed it into a dedicated numerical or logical solver and it will solve it nearly instantly. The same thing goes for many well-studied classical computer science problems: boolean SAT, job shop, vehicle routing, knapsack problem, shift scheduling, travelling salesman etc. There are a lot of pre-existing efficient solvers that research groups have been building and tuning for decades.

As a less theoretical example, consider a common chemical engineering challenge: specifying the design parameters for a processing plant, focusing on line sizing and the associated fluid dynamics. In a typical day to day workflow engineers must determine optimal pipe diameters and requisite pump specifications to achieve target output flow rates for various chemical products. This task is essentially a system of coupled, often non-linear, governing equations encompassing fluid properties (density, viscosity), mass and energy balances across the network, and pressure drop calculations.

Any design must adhere to operational limits, such as maximum allowable pressures within each pipe segment to ensure structural integrity and safety, minimum flow rates to maintain reaction kinetics or prevent settling, and the physical topology of how pipes, valves, and reactors are interconnected. There are dedicated solvers for this, but they are very expensive, and generally suck. Or people write lots of Excel macros and Goal Seek, which I guess works, but there are much better tools.

The bottleneck is simply that the APIs for many of these open source SMT and convex solvers can be, let's say, character-building. If an LLM, piped through MCP, could translate your plain English "what if" into the arcane syntax these solvers speak, suddenly these super-powerful, often byzantine, systems become way less intimidating and democratize access beyond the need for relying on specialized programmers.

Imagine instead, just telling an LLM, via MCP: "Given these target flow rates for product X, using fluid Y with these properties, and ensuring pressure never exceeds Z psi in any line, what are the optimal pipe diameters and pump specs for lines A, B, and C, which are connected in this configuration? Imagine a process engineer who typically spends a significant portion of their week iteratively translating evolving production targets and safety parameters into precise mathematical constraints for solver input, then painstakingly validating the complex outputs for, say, a new heat exchanger network.

With an LLM-solver integration this same engineer could articulate high-level objectives and constraints in natural language—"design a network to cool stream X from 200°C to 50°C using available cold utility Y, minimizing operational cost while ensuring no tube-side pressure exceeds Z"—and have the system automatically formulate the problem, execute the appropriate solver, and present digestible design specifications. This could compress what was previously a multi-day, error-prone exercise as a human constraint generator and checker into minutes, liberating valuable engineering expertise to focus on genuinely creative challenges of their role.

And not just for this one specific field. The dream is to be able to describe all of the constraints for many complex systems (be it a chemical plant, hospital shift planning, or portfolio optimization) in natural language so that the LLM can plan the constraints, delegate to the solver(s), and let the user have a back and forth with about the problem and solution in way that is natural to them. If done well (and we're not there yet) that would be very very powerful.

Then there's more... let's call it forward-looking play: generating synthetic reasoning data. This one's a bit more niche. If we can get an LLM to bulk formulate tricky problems for these solvers, and then learn from the solver's perfectly structured, provably correct answers, we could bootstrap a ton of high-quality training data and then feed that back in as instruction tuning data.

Prototype

But let's start with the easy ones. That's the Stanford cvxopt for convex optimization, Microsoft's z3 SMT solver, and Google or-tools for combinatorial optimization. Just these three packages alone are extremely powerful. Like a seashell, if you look at their source code you can hear the screams of hundreds of PhD students sacrificed on the altar of science to build them.

I've built a prototype of this called USolver which implements the MCP interface to the solvers.

Let's look at some examples. For chemical engineering problems, you can describe a water transport pipeline design task in plain English which gets turned into a Z3 constraint satisfaction problem.

Design a water transport pipeline with the following requirements:

* Volumetric flow rate: 0.05 m³/s
* Pipe length: 100 m
* Water density: 1000 kg/m³
* Maximum allowable pressure drop: 50 kPa
* Flow continuity: Q = π(D/2)² × v
* Pressure drop: ΔP = f(L/D)(ρv²/2), where f ≈ 0.02 for turbulent flow
* Practical limits: 0.05 ≤ D ≤ 0.5 m, 0.5 ≤ v ≤ 8 m/s
* Pressure constraint: ΔP ≤ 50,000 Pa
* Find: optimal pipe diameter and flow velocity

The LLM translates this into a Z3 constraint satisfaction problem, handling all the messy details of flow equations and physical constraints. You get back optimal pipe dimensions and flow parameters that satisfy all your requirements.

Or take a classic operations research problem like employee scheduling. Instead of wrestling with complex combinatorial optimization syntax, you can just say:

Use usolver to solve a nurse scheduling problem with the following requirements:

* Schedule 4 nurses (Alice, Bob, Charlie, Diana) across 3 shifts over (Monday, Tuesday, Wednesday)
* Shifts: Morning (7AM-3PM), Evening (3PM-11PM), Night (11PM-7AM)
* Each shift must be assigned to exactly one nurse each day
* Each nurse works at most one shift per day
* Distribute shifts evenly (2-3 shifts per nurse over the period)
* Charlie can't work on Tuesday.

But where it gets really interesting is when you chain these solvers together. Here's an example where we optimize a restaurant's operations by combining two different solvers in sequence. First, we use Google's OR-Tools combinatorial optimization to determine the optimal mix and layout of different sized tables within a restaurant's available dining area, maximizing total seating capacity while respecting minimum table requirements and space constraints.

Then, we take that optimal seating capacity and feed it into the cvxopt solver to determine the most cost-effective staffing schedule across a 12-hour day. The staffing optimizer accounts for variable customer demand throughout the day, ensures adequate coverage for the calculated seating capacity, and minimizes labor costs while maintaining service quality and reasonable shift changes. This demonstrates how we can specify a a business problem in plain English, compile it down into a system of constraints, turn those constraints into a system of equations, and then solve it using a chain of numerical solvers with the LLM orchestrating the flow of data and verbalizing the answers!

Use usolver to optimize a restaurant's layout and staffing with the following requirements in two parts. Use combinatorial optimization to optimize for table layout and convex optimization to optimize for staff scheduling.

* Part 1: Optimize table layout
  - Mix of 2-seater, 4-seater, and 6-seater tables
  - Maximum floor space: 150 m²
  - Space requirements: 4m² (2-seater), 6m² (4-seater), 9m² (6-seater)
  - Maximum 20 tables total
  - Minimum mix: 2× 2-seaters, 3× 4-seaters, 1× 6-seater
  - Objective: Maximize total seating capacity

* Part 2: Optimize staff scheduling using Part 1's capacity
  - 12-hour operating day
  - Each staff member can handle 20 seats
  - Minimum 2 staff per hour
  - Maximum staff change between hours: 2 people
  - Variable demand: 40%-100% of capacity
  - Objective: Minimize labor cost ($25/hour per staff)

And then almost like magic, the LLM coordinates the two solvers and returns the optimal solution. It figures out the optimal table layout and then uses that to schedule the staff. Here's what Claude Desktop generates given the project specification.

And then figures out the optimal staffing schedule for that optimal table layout.

And it's pretty magical that such a complex problem can be solved in a few seconds with such a simple interface. I'm incredibly bullish about this kind of approach and expanding the set of available tools for the LLM to include many more advanced solvers.

Although don't drink too much of the breathless AI hype Kool-aid just yet. There are some quite real limitations in this approach. Namely, that there is no strict guarantees that LLMs are able to do semantic parsing of the problem with complete accuracy. We can partially mitigate this exposing a computer algebra system and having it check the solutions at each step. There are still mechanisms for transpositions and misinterpretations to slip in.

If this kind of approach becomes mainstream, there could also be benchmarks like SWE-bench for tool-calling of scientific computing packages that could be used to improve model performance upstream. But at the moment it's still very much a best-effort approach and you would certainly need to have a human-in-the-loop to check the solutions, especially in any kind of safety-critical application. But it might be able to make that human a lot more productive.

The Vision for Universal Solver Interface

Consider the potential of a unified interface that could seamlessly integrate with state-of-the-art solvers across multiple domains with frontier language models via MCP (or whatever the next generation of MCP is):

Z3 - SMT solver for constraint satisfaction over booleans, integers, reals, and strings
CvxPy - Framework for convex optimization problems
Or-Tools - Suite for combinatorial optimization and constraint programming
HiGHS - LP, MIP, and QP solver
MiniZinc - Discrete optimization solver
GAP - Computational group theory solvers
Clingo - Answer set programming system
Flint - Number theory computations
TLA+ / Apalache - Temporal logic solver
Egglog - Term rewriting and equality saturation engine
SymPy - Comprehensive computer algebra system for differential equations solvers
Souffle - Datalog-based declarative logic programming framework
Mathematica - Risch-based symbolic integration solver and simplification routines
Sage - Umbrella project for many scientific computing packages

The implementation of such a unified system would be a very powerful and useful piece of software. It would effectively be a meta-solver: an intelligent system capable of decomposing complex problems, identifying the optimal solver for each component, and orchestrating their collective execution. While developing a theoretically complete meta-solver is a substantial theoretical and practical challenge in it's generality, don't really need to solve the general problem to be incredibily useful.

This project started as a weekend hobby project, but I believe this is a fascinating area with significant potential. I'm particularly interested in how these techniques could be applied to automation in physical engineering disciplines. If you're working on similar ideas in an open source or commercial context, I'd love to hear about your work, feel free to reach out.

The Trump Crypto Orgy of Corruption

Sat, 31 May 2025 01:00:00 +0000

The Trump Crypto Orgy of Corruption

We are living in very unusual times and corrupt times. Never before has an American president been so brazen in his corruption and self-enrichment. This new phenomenon, what Senator Elizabeth Warren coined as an "orgy of corruption," is staggering in scope, and while I'm under no illusion that writing about this will be news to anyone, I feel compelled to document it for the public record as it is far worse than anything I predicted back in 2020. The Trump administration's intermingling with crypto is like witnessing ten Watergates every day, marking a period of brazen self-enrichment and systemic decay utterly unprecedented in the annals of the American presidency, and indeed, unseen in any mature democracy. This is not a policy shift, but rather a flagrant embrace of practices typically confined to banana republics and autocracies, as the administration systematically dismantled regulatory oversight, fostered blatant conflicts of interest, and normalized a level of corruption that directly benefited the President and his inner circle.

Under this administration, the Securities and Exchange Commission completely stopped its cryptocurrency enforcement activities. This retreat included abandoning numerous investigations and lawsuits against major industry players. Notably, the SEC dropped its lawsuit against Binance, the world's largest exchanges, even after its CEO had pleaded guilty to federal money laundering charges. The commission also moved to dismiss over a dozen other cases against crypto firms. A clear conflict of interest arose when the SEC announced it would not consider meme coins as securities, a decision made weeks after President Trump launched his own $TRUMP token, thereby directly benefiting the president's financial interests. Further indicating a shift in approach, the SEC restructured its enforcement operations, replacing its specialized Crypto Assets and Cyber Unit with a new unit that signaled a more hands off stance on digital assets.

The Department of Justice also underwent a significant policy change by completely disbanding the National Cryptocurrency Enforcement Team, a unit specifically created to combat complex crypto related crimes. A memo from Deputy Attorney General Todd Blanche, titled "Ending Regulation By Prosecution," directed prosecutors to cease pursuing charges for regulatory infractions under federal banking, securities, and commodities laws unless there was proof of intentional violations. This effectively shifted policy away from enforcement based regulation, immunizing cryptocurrency companies from prosecution for certain regulatory violations even when significant investor harm occurred.

Unprecedented conflicts of interest emerged from the Trump family's extensive financial involvement in the cryptocurrency sector while simultaneously overseeing its regulation. For example, a cryptocurrency venture primarily owned by the Trump family, World Liberty Financial, saw its USD1 stablecoin selected for a $2 billion investment in Binance facilitated by Abu Dhabi's sovereign wealth fund, directly linking a Trump family business to a major international financial transaction within the crypto space.

President Trump himself launched the $TRUMP meme coin shortly before his inauguration, which reached a significant market value. With the Trump Organization and affiliated companies reportedly controlling a substantial majority of the token's supply, concerns about market manipulation arose. The President used his platform to promote these tokens, even hosting private dinners for major token holders at his golf club, an event so beyond the pale it completely lacks any historical precedent in its sheer audacity and brazenness. The subsequent SEC announcement that meme coins would not be regulated as securities appeared to be a policy decision that directly benefited the president's personal financial interests.

Trump-affiliated entities have generated approximately 320 million dollars in trading fees from the TRUMP meme coin. These fees are collected through the coin's structure on decentralized exchanges, where CIC Digital LLC (a Trump Organization affiliate) and Fight Fight Fight LLC earn a share of trading fees on every coin exchange. In just the week following the dinner announcement in April, trading fees alone exceeded 1.3 million dollars. The profit model is particularly lucrative because it doesn't depend on the coin's price appreciation. what matters is constant trading volume, because more trades mean more fees.

Further highlighting these conflicts, Trump Media & Technology Group, in which President Trump holds a majority stake managed by his son, was reportedly in negotiations to raise $3 billion for cryptocurrency investments. This situation meant the president and his family could financially gain from these investments while simultaneously controlling the regulatory environment governing such activities.

Regulatory appointments also raised concerns about industry capture. David Sacks, appointed as Trump's "crypto and artificial intelligence czar," faced allegations that he could financially benefit from a strategic crypto reserve announcement made by Trump. Although Sacks claimed to have divested from personal crypto holdings, questions persisted regarding his venture capital firm Craft Ventures' investment in Bitwise, a crypto index fund manager. The firm only confirmed its exit from this investment after public scrutiny and after the presidential announcement had already benefited the assets in question.

Brian Quintenz, nominated by Trump to chair the Commodity Futures Trading Commission, disclosed significant financial involvement in the cryptocurrency sector, reporting over $3.4 million in crypto-linked assets and extensive industry connections. His financial disclosures detailed stakes in Andreessen Horowitz funds, board positions at firms like Kalshi (a prediction markets operator), and prior advisory roles with companies such as Crypto dot com. Although Quintenz pledged to divest these holdings and recuse himself from matters where conflicts could arise, his nomination highlighted a trend of appointing individuals with direct financial interests in the industries they were tasked with regulating.

The Trump administration formalized its deregulatory stance through a January 23, 2025 executive order titled "Strengthening American Leadership in Digital Financial Technology." This order established a comprehensive framework for cryptocurrency deregulation and revoked previous Biden administration policies. It also created a working group, chaired by David Sacks, tasked with developing a regulatory framework that prioritized industry growth over investor protection. The executive order mandated federal agencies to review and rescind prior regulatory guidance, effectively institutionalizing the dismantling of cryptocurrency oversight and normalizing an approach where industry preferences could supersede regulatory prudence.

The operations of Trump family linked entities like World Liberty Financial, particularly its involvement in international crypto transactions such as its stablecoin being used in a multi-billion dollar deal involving Binance and an Abu Dhabi sovereign wealth fund, raised questions about the intertwining of private business interests with entities subject to U.S. regulatory scrutiny or foreign government influence.

Trump's family wealth has reportedly increased by $2.9 billion largely due to cryptocurrency investments, with 40% of that wealth currently held in tokens. This staggering enrichment, directly coinciding with policies designed to unleash the very crypto markets from which they profited, is not merely a footnote in financial history; it is a funeral dirge for democratic accountability and a grotesque caricature of public service. In a way, this is cryptocurrency fulfilling its ultimate purpose — serving as the perfect vehicle for corruption and fraud.

The sheer, unadulterated brazenness of this spectacle, where the highest public office in the land is so transparently leveraged for personal, familial gain, makes the Teapot Dome scandal (the previous largest scandal in American history) look like a petty squabble and the influence peddling of past eras seem almost amateurish by comparison. We are staring into the abyss of a new American kleptocracy, where the lines between the presidency and a personal enrichment scheme have been purposefully, profitably, and catastrophically erased. This is truly a full-throated embrace of oligarchy that threatens to dwarf the Gilded Age robber barrons, The only historical precedent is the plundering of the state much like what occured during the collapse of the USSR. We are witnessing the forging an era of unprecedented wealth inequality and systemic rot that may leave the very foundations of American democracy shattered beyond recognition. It's truly hard to find the words to describe this grotesque spectacle, but I will continue documenting it in hopes to add to the public record and contextualize this new low in American history.

Unnecessary and Unstable: Why Stablecoins are Bad

Tue, 27 May 2025 01:00:00 +0000

Unnecessary and Unstable: Why Stablecoins are Bad

The current financial policy debate in the US is increasingly fixated on the purported necessity of bespoke regulation for stablecoins (particularly the proposed S.394 GENIUS Act), with proponents arguing that such frameworks would foster responsible innovation and integrate these digital tokens into the broader financial system. This perspective, however, is profoundly misguided. Rather than ushering in an era of enhanced financial efficiency, the legitimization of stablecoins through bespoke regulation would serve primarily to institutionalize inherently fragile financial structures, proliferate risk, and ultimately provide a novel vector for systemic crises, all in service of a financial product that offers no net aggregate good for the economy. The assertion that stablecoins are essential for modernizing money transmission is a fallacy; existing, robust, and regulated mechanisms already fulfill this function with far greater security and accountability.

The argument against stablecoins doesn't stem from Luddism, but a measured assessment of their intrinsic risks and impact on consumers and the financial system. Stablecoins, despite their name, are demonstrably unstable. Their brief history is littered with instances of de-pegging, runs, and the evaporation of billions in investor capital. This is not an aberration but a feature. Any financial instrument designed to mimic the stability of sovereign currency, yet lacking the explicit, unconditional guarantee of a central bank and a sovereign government, is inherently prone to run risk. Unlike central bank money, which maintains "unicity" (i.e. the same value and acceptance everywhere through the central bank's role as payment overseer and ultimate settler), stablecoins cannot guarantee consistent value across all contexts and jurisdictions. The attempts to engineer stability through various collateralization models have all proven fallible.

The three principal archetypes of stablecoins each present unique and severe vulnerabilities. Off-chain collateralized stablecoins, often pegged to the U.S. dollar, purportedly maintain their value through reserves of assets like cash, U.S. Treasury securities, or commercial paper. However, the composition and true liquidity of these reserves are often shrouded in opacity. Issuers frequently alter reserve compositions and disclosure practices with little to no advance notice, introducing significant uncertainty. The inclusion of cash equivalents, which can encompass short-term investment securities like commercial bonds, introduces credit and market risk. If these reserve assets depreciate or become illiquid during periods of market stress, a common occurrence, the stablecoin's ability to maintain its peg is compromised, triggering redemptions and potential runs. The failure to rigorously safeguard these assets, or even accurately represent their holdings, undermines confidence and acts as a catalyst for instability. The events surrounding FTX and Silicon Valley Bank, which precipitated de-pegging and runs on even prominent stablecoins like Tether and USDC, serve as stark reminders. The question is not if such stablecoins will depeg under stress, but when and with what magnitude.

On-chain collateralized stablecoins attempt to achieve stability by holding other cryptocurrencies as collateral. This model introduces a pernicious feedback loop: the collateral itself is subject to extreme price volatility relative to the real currency it is meant to back. A downturn in the crypto markets can rapidly erode the value of the collateral, triggering margin calls and forced liquidations, which in turn can de-stabilize the stablecoin and exacerbate the broader market decline. This design is akin to building a house on shifting sands. Arguably the most dangerous variant, non-collateralized, or algorithmic, stablecoins eschew tangible reserves entirely, relying instead on complex algorithms and smart contracts to manage supply and demand in an attempt to maintain a peg. These are, in essence, perpetual motion machines of finance. The catastrophic collapse of TerraUSD in May 2022, an eighteen billion dollar algorithmic stablecoin, erased vast sums of capital and sent shockwaves through the crypto ecosystem, demonstrating the inherent infeasibility and extreme risk of such unbacked constructs.

A cornerstone of the stablecoin illusion is the promise of at-par redemption at any moment; in practice, this is often far from guaranteed. Issuers frequently impose significant constraints on redemption rights, including high minimum redemption thresholds that render them inaccessible to ordinary retail users. Furthermore, public disclosures regarding redemption terms are often insufficient or misleading. Notably, some of the largest stablecoin issuers do not offer a direct right of redemption to investors who acquire their tokens on unregulated cryptocurrency exchanges, leaving these holders reliant on the liquidity and solvency of those secondary market platforms, themselves often fragile entities. Terms of service, frequently mischaracterized by issuers, can further restrict or delay redemptions, particularly during periods of market stress when liquidity is most needed.

So why would anyone use stablecoins if they are unstable and worse than existing payment systems? The answer lies in their singular distinguishing feature: unlike bank deposits, which are subject to comprehensive regulatory oversight and reporting requirements, the ownership and disposition of stablecoins remains pseudonymous. This anonymity is precisely what makes them valuable to those seeking to circumvent legal frameworks—offshore gamblers, money launderers, extortionists, drug traffickers, sanctions evaders, and other criminal enterprises who require the digital equivalent of unmarked bills with global transmission capabilities.

The crypto ecosystem functions as an offshore casino offering products prohibited within traditional financial systems, and stablecoins serve as the necessary chips to participate. Strip away the technological veneer, and stablecoins reveal themselves as sophisticated tools designed explicitly to evade the anti-money laundering and know-your-customer requirements that undergird legitimate finance. In essence, the primary—and arguably only—economic rationale for stablecoins is to facilitate criminal activity, providing a pseudonymous payment rail for those whose operations cannot withstand the scrutiny of regulated financial systems.

The parallels between stablecoins and the pre-FDIC banking system are deeply unsettling. The devastating bank runs of the 1930s led to the creation of federal deposit insurance and strict regulation of bank risk-taking - protections that stablecoins deliberately circumvent as a new form of shadow banking. While stablecoin issuers attempt to reassure holders by maintaining large reserves of U.S. government debt, this creates a dangerous feedback loop: a run on stablecoins would force issuers to conduct a fire sale of Treasury bills, potentially destabilizing the U.S. government debt market and driving up interest rates. Even money market funds, which are far more regulated and transparent than stablecoins, experienced catastrophic runs during both the 2008 Financial Crisis and March 2020 turmoil, requiring massive government intervention to prevent broader market collapse. Stablecoins, with their greater opacity and weaker oversight, present an even more acute systemic risk. Most alarmingly, their ability to absorb vast amounts of foreign capital would create a direct channel for overseas instability to violently propagate into U.S. Treasury markets - threatening the bedrock of the global financial system, all while primarily serving to facilitate criminal activity.

The bank failures of early 2023, including Silvergate, Silicon Valley Bank, Signature, and First Republic, provided a grim preview of how crypto-related activities can destabilize regulated financial institutions. These banks held substantial uninsured deposits from crypto firms, and withdrawals by these firms during the crypto downturn directly contributed to bank runs. Integrating stablecoins more formally into the U.S. financial system through bespoke regulation would effectively build a high-speed conduit between the largely unregulated crypto casino and the rule-bound, regulated financial sector. This would not foster responsible innovation but rather create new channels for contagion, allowing chaos from the crypto sphere to infect the core financial system.

The value of stablecoins' reserves is deeply intertwined with the safety and stability mechanisms of conventional finance. These reserves are custodied at banks, held in money market funds, and managed through repo arrangements; which derive their security from Federal government regulations and oversight. This interdependence was starkly illustrated when stablecoin issuer Circle held $3.3 billion (8% of its USDC stablecoin reserves) in uninsured deposits at Silicon Valley Bank. When regulators closed SVB, USDC's value plummeted to 88 cents, only recovering after the U.S. government announced emergency measures to protect uninsured depositors. The purported independence from central banks becomes particularly ironic in light of recent developments, including an anticipated Executive Order that would compel the Federal Reserve to provide Fed bank accounts to certain crypto firms. Far from being independent, stablecoins are parasitic on the very financial infrastructure they claim to disrupt.

Stablecoins currently exist in a regulatory twilight zone, neither fully inside nor outside the financial perimeter. This ambiguous status itself poses unique financial stability risks. Crucially, there is a profound lack of clarity regarding whether the U.S. government would or could intervene to bail out a failing stablecoin, particularly one that has achieved systemic importance. Such ambiguity is precisely what fuels bank runs: uncertainty about counterparty exposure and the potential for cascading collapses causes market participants to freeze activity and hoard liquidity. A stablecoin crisis could either necessitate a taxpayer-funded bailout, creating immense moral hazard and socializing losses, or, if no bailout is forthcoming, inflict substantial losses on holders and potentially destabilize international dollar-based payment systems if foreign users have significant exposure.

Moreover, the proliferation of U.S. dollar-pegged stablecoins carries a profound risk of fostering a de facto, involuntary dollarization of foreign economies. This occurs without the consent or democratic deliberation of the affected nations, effectively eroding their monetary sovereignty and capacity to conduct independent economic policy. Such a development is inherently imperial in nature, extending U.S. monetary influence globally through private channels and creating new vectors for financial contagion on a global scale. If these dollar-denominated private monies become deeply embedded in other economies, it not only increases the moral hazard by potentially implicating U.S. authorities in stabilizing foreign markets reliant on these instruments but also dangerously intermingles U.S. domestic policy considerations with the economic stability of numerous international partners. This ultimately curtails the ability of other sovereign nations to enact effective fiscal and monetary policies tailored to their specific domestic economic conditions, making them more vulnerable to external shocks and U.S. policy shifts leading to a more fragile and brittle global economy.

The fundamental justification offered for stablecoins, efficient money transmission, is demonstrably false. The existing global financial system, for all its complexities, already facilitates vast volumes of domestic and international payments through established, regulated channels like the ACH, wire transfers, card networks, and correspondent banking relationships. The Federal Reserve's payment systems have demonstrated remarkable reliability, with only a single 3-hour outage in their history. The Fed's launch of FedNow in 2023, despite its admittedly slow development, now enables instant payments, delivering funds to households and businesses in seconds. Additional options like The Clearing House's real-time payments and various private firms offering non-crypto instant ACH transfers further enhance the ecosystem. Stablecoins offer no net improvement in aggregate economic welfare in this domain; they merely introduce a new layer of risk, rent seeking, and intermediation while providing less reliability than existing systems.

Furthermore, sanctioning the proliferation of private monies coexisting with the U.S. dollar is a dangerous regression. History is replete with examples, from the chaotic Free Banking Era in the U.S. to company scrip, where private currencies proved inefficient, prone to counterfeiting, and often exploitative. Legislating stablecoins into a recognized form of payment risks repeating these historical errors. The very act of holding vast sums in stablecoin reserves ties up safe and liquid assets like U.S. Treasuries that could otherwise be used by banks to satisfy regulatory capital and liquidity requirements or to support lending. This could lead to artificial shortages of high-quality liquid assets, increasing their cost and potentially constricting credit availability for productive economic activities like mortgages and small business loans as customer funds migrate from insured bank deposits to digital wallets.

Finally, the utility of stablecoins in facilitating illicit activities cannot be ignored. Their pseudonymous nature and cross-border transferability make them attractive instruments for money laundering, sanctions evasion, and terrorist financing. The dominant stablecoin outside U.S. jurisdiction, Tether, is persistently used by criminal enterprises for evading interdiction by law enforcement. Services like crypto mixers, designed explicitly to obscure transaction trails, are routinely implicated in laundering stolen funds for entities like North Korean hackers, narcotics cartels, pig butchering scammers, and terrorist organizations.

The proposed regulatory frameworks for stablecoins create dangerous opportunities for regulatory arbitrage and consumer confusion. Proponents advocate a bifurcated resolution regime where bank-chartered stablecoin issuers would face FDIC receivership (albeit without FDIC insurance) while non-bank issuers would fall under a new bankruptcy chapter. This hybrid approach invites misunderstanding, as consumers will inevitably conflate protections for stablecoins with those for traditional bank deposits. The situation is further complicated by bankruptcy provisions limiting customer recovery to the stablecoin's value at the time of failure—likely less than the promised dollar peg. Even more concerning is the potential for payment services like PayPal, Venmo, or Zelle to exploit these new frameworks by migrating their operations to blockchain-based systems (or alleging to do so), circumventing established federal consumer protection laws that govern money transfers.

The prospect of large technology companies and retailers issuing stablecoins raises serious concentration risks. These risks mirror the very concerns that led to the Bank Holding Company Act's restrictions on mixing banking and commerce. Major platforms like Meta or Twitter could leverage stablecoins to expand their surveillance capabilities and manipulate consumer behavior. They could monitor individual transactions and offer preferential treatment to stablecoin users, all while amassing vast pools of customer deposits.

The financial stability implications are equally concerning. If one of these tech giants were to face distress, the failure of their stablecoin could rapidly spread contagion throughout the broader market. Congress's proposed parallel regulatory regime, with its weaker oversight and consumer protections, would effectively create a backdoor. This would allow financial services firms to circumvent decades of carefully crafted consumer protection requirements.

Proponents often resort to the thought-terminating cliché that "blockchain is here to stay" to shut down critical analysis of the technology's actual utility and legitimacy. After fifteen years, blockchain has failed to demonstrate any significant legal use case beyond speculation and gambling. The continued existence of cryptocurrencies and stablecoins is not evidence of their inevitability or permanence, but rather of temporary regulatory forbearance and political capture. Indeed, the largest stablecoin, Tether, operates primarily through a single custodial relationship with Cantor Fitzgerald for its Treasury holdings. The entire crypto ecosystem could effectively cease to function tomorrow if regulators simply restricted access to the Treasury markets that these products parasitically depend upon. Claims about blockchain's inevitability are less statements of technological reality than expressions of hope by those heavily invested in its continuation.

Attempting to render stablecoins safe through bespoke regulation feels akin to a food regulatory agency, confronted with a restaurant teeming with rats, deciding not to close it down but instead to issue elaborate directives on "Customer-Rodent Interaction Minimization Protocols." One can picture the detailed circulars on "Acceptable Rat Frequency Per Square Meter of Dining Area" or requirements for "Transparent Disclosure of Rodent Fecal Matter Levels on Menus." Just as such measures would fail to address the fundamental problem of an unsanitary establishment, stablecoin regulation that attempts to make inherently unstable financial products "safe" through disclosure requirements and capital controls merely obscures the core issue: these are fundamentally flawed instruments that should not exist within the regulatory perimeter.

The push for bespoke stablecoin regulation is a solution in search of a problem, and a dangerous one at that. It seeks to legitimize and integrate financial instruments that are inherently unstable, offer no compelling economic advantages over existing systems, and pose significant systemic risks. Regulation cannot transmute a fundamentally flawed concept into a sound one; it can only provide a veneer of legitimacy that encourages wider adoption and thus amplifies the potential fallout when, not if, these structures fail. Instead of crafting new rules to accommodate these risky constructs, policymakers should recognize stablecoins for what they are: speculative instruments with a high propensity for instability, run risk, and limited legitimate use cases that are not already better served by the regulated financial system. The focus should be on reinforcing the resilience and efficiency of existing payment and financial infrastructures, not on inviting a new, poorly understood, and demonstrably fragile class of assets into the heart of the financial system. To do otherwise is to knowingly plant the seeds for a future financial crisis, fueled by the false promise of an unnecessary innovation. The prudent course is to allow these structures to remain on the periphery, subject to existing anti-fraud and securities laws where applicable, rather than granting them a bespoke regulatory framework that would signal endorsement and invite another financial crisis.

Remote MCP Servers

Mon, 26 May 2025 01:00:00 +0000

Remote MCP Servers

After my last adventure with symbolic algebra and MCP, I found myself that nagging voice in the back of my head whispering "What if Claude decides today is the day to go postal and rm -rf /?" The solution, as with most modern software problems, was obvious: make it someone else's problem.

Enter Vercel, purveyor of the finest VC-subsidized free compute known to humanity. But hey, if they want to let me run arbitrary Python code on their infrastructure for the low, low price of absolutely nothing, who am I to question their financial decisions? So the question is, can we host our MCP servers as edge functions on their Hobby Tier without paying anything? And the answer is yes, yes we can.

Instead of giving the language model root access to my laptop (because what could possibly go wrong there?), I'm now giving it the ability to execute arbitrary code on Vercel's servers on a sandboxed serverless environment that resets after every request. It's like the difference between letting a toddler play with matches in your living room versus letting them play with matches in someone else's swimming pool. Second, and perhaps more importantly, every time Claude calls one of my MCP tools, I'm burning through some venture capitalist's money. So two birds, one stone.

I've built a little adapter that takes any FastMCP server and wraps it in a Vercel Function compatible runtime. The whole thing deploys with a single git push to the repo and starts in about 4 seconds. Trying to get the default FastMCP server to work was a bit of a pain because it has quite a bit of stateful session handling logic, but with a bit of internal mangling of it's reflection API we can introspect its tool definitions and schemas and build a simple HTTP API around them that exposes them as edge functions that run on the Vercel Python edge runtime fairly simply and efficiently. After all is said and done here's what the code looks like:

import datetime
from fastmcp import FastMCP
from .mcp_adapter import build_app

mcp: FastMCP = FastMCP("Vercel MCP Server", stateless_http=True, json_response=True)

@mcp.tool()
def echo(message: str) -> str:
    """Echo the provided message back to the user"""
    return f"Tool echo: {message}"


@mcp.tool()
def get_time() -> str:
    """Get the current server time"""
    current_time = datetime.datetime.now().isoformat()
    return f"Current Vercel server time: {current_time}"


@mcp.tool()
def add_numbers(a: int, b: int) -> int:
    """Add two numbers together"""
    return a + b

app = build_app(mcp)

Push that to GitHub, connect it to Vercel, and boom: you've instantly got a serverless MCP server running. You can limit the runtime of the tool calls by setting the maxDuration in the vercel.json file, so can limit runtime to 2 seconds or something.

The server includes a self-hosted installer and bridge script (that proxies remote MCP servers to local MCP servers, via RPC to stdio) that can be deployed with a single shell command. Instead of manually editing configuration files, users can run install with uv and the installer automatically configures Claude Desktop or Cursor to use the remote server. The installer downloads the bridge script directly from the server itself, eliminating the need for local files or manual configuration steps. About as close to one-click remote server install as you can get.

uv run https://your-domain.vercel.app/install.py

The dumb example everyone gives is always chaining together a bunch of REST API calls to external services. With this running on a remote function you can do the same thing, like if you wanted to use requests to call out to the National Weather Service API to get the current weather forecast for a location. Or you could install PyTorch in requirements.txt and run a neural network in there if you really wanted to. The free tier gives you 100 GB-Hours and 100,000 invocations per month to work with. If you configure a function to use 1GB of memory and it runs for 5 second, that's 5 GB-s per invocation. So you could make around 72,000 five-second calls before hitting the memory limit or invocation limit, whichever comes first.

import requests

NWS_API_BASE = "https://api.weather.gov"

@mcp.tool()
def get_weather(latitude: float, longitude: float) -> str:
    """
    Get the current weather forecast for a location using the National Weather Service API
    """
    point_data = requests.get(
        f"https://api.weather.gov/points/{latitude},{longitude}",
        headers={"Accept": "application/json"},
    ).json()

    forecast_url = point_data["properties"]["forecast"]

    forecast_data = requests.get(
        forecast_url,
        headers={"Accept": "application/json"},
    ).json()

    current_period = forecast_data["properties"]["periods"][0]

    return f"Forecast for {current_period['name']}: {current_period['detailedForecast']}"

Once you have it setup either use a LLM client (Claude Desktop, Cursor, Cline, 5ire, VS Code, etc) or use the Cloudflare MCP Playground. If you're using Claude Max, Team or Enterprise you don't need to use the bridge script at all and can just use the URL of the remote MCP server directly in the Custom Integrations in the integrations section of your Claude app settings. Otherwise, under the hood the installer uses the Bridge shim to proxy the remote MCP server to a local MCP server.

{
  "mcpServers": {
    "example": {
      "command": "/opt/homebrew/bin/uv",
      "args": [
        "run",
        "--with",
        "mcp>=1.0.0",
        "https://your-domain.vercel.app/bridge.py",
        "https://your-domain.vercel.app"
      ],
      "env": {
        "MCP_API_KEY": "your-secret-key-here"
      }
    }
  }
}

Beyond dedicated MCP clients, you can also integrate remote MCP servers directly into your applications using client libraries. The MCP tool in the OpenAI Responses API, for instance, allows developers to give the model access to tools hosted on Remote MCP servers. These are MCP servers maintained by developers and organizations across the internet that expose these tools to MCP clients, like the Responses API.

Calling a remote MCP server with the Responses API is straightforward. For example, here's how you can use your own MCP server using the weather tool above. For more details, see the OpenAI Platform documentation.

from openai import OpenAI

client = OpenAI()

resp = client.responses.create(
    model="gpt-4.1",
    tools=[
        {
            "type": "mcp",
            "server_label": "example",
            "server_url": "https://your-domain.vercel.app",
            "require_approval": "never",
        },
    ],
    input="What is the current weather in Berlin?"
)

print(resp.output_text)

Similarly, you can use remote MCP servers with Anthropic's Claude API.

from anthropic import Anthropic

anthropic = Anthropic()

response = anthropic.beta.messages.create(
    model="claude-3-7-sonnet-20250219",
    max_tokens=1000,
    messages=[
        {
            "role": "user",
            "content": 'What is the current weather in Berlin?',
        },
    ],
    mcp_servers=[
        {
            "type": "url",
            "url": "https://your-domain.vercel.app",
            "name": "example",
            "tool_configuration": {
                "enabled": True,
            },
        }
    ],
    extra_headers={
        "anthropic-beta": "mcp-client-2025-04-04",
    },
)
print(response.content)

Or using Gemini's MCP client.

import os
import asyncio
from datetime import datetime
from mcp import ClientSession, StdioServerParameters
from mcp.client.stdio import stdio_client
from google import genai

client = genai.Client(api_key="YOUR_GEMINI_API_KEY")

# Create server parameters for stdio connection
server_params = StdioServerParameters(
    command="uv",
    args=[
        "run",
        "--with",
        "mcp>=1.0.0",
        "https://your-domain.vercel.app/bridge.py",
        "https://your-domain.vercel.app",
    ],
)

async def run():
    async with stdio_client(server_params) as (read, write):
        async with ClientSession(read, write) as session:
            prompt = f"What is the weather in London?"
            await session.initialize()
            response = await client.aio.models.generate_content(
                model="gemini-2.0-flash",
                contents=prompt,
                config=genai.types.GenerateContentConfig(
                    temperature=0,
                    tools=[session],
                ),
            )
            print(response.text)

asyncio.run(run())

The security model of this whole endeavor remains, shall we say, "optimistic." MCP servers are essentially giving language models the ability to execute arbitrary code based on natural language instructions. This approach requires trusting a single install.py file served from the remote endpoint, which admittedly isn't ideal. However, it's arguably not much worse than the common practice of piping installation scripts from install.sh (like uv) directly into shell execution. Additionally, there's nothing preventing a malicious remote MCP server from sending back prompt injections that could instruct your agent to ignore previous instructions and exfiltrate sensitive local data to a North Korean server.

And if you're handing API tokens over to Claude, you're essentially giving it the keys to the kingdom - despite any careful instructions about what the token is meant for, it's not hard to produce a sufficiently convincing prompt that could persuade the model to use that token for anything it's authorized to do. The attack vector is as simple as sweet-talking an overeager LLM into doing whatever the attacker wants with the tools you've given it.

But hey, if you're already experimenting with MCP servers that execute arbitrary code based on natural language prompts interpreted by what is essentially the internet's collective fever dream, you've likely already made peace with a certain level of operational risk which could best be described as "YOLO, hold my beer". So if you're running running a nuclear reactor, maybe don't touch this stuff, mkay?

For anything approaching production use of MCP (god help us all), you'd want proper OAuth flows, request signing, rate limiting. Which you could totally add to this project, but I'm not going to do that here because this is a proof of concept. The documentation for that is here.

It's also worth nothing that I'm not exactly endorsing Vercel's business model. They lure you in with their generous free tier, let you build your entire infrastructure around their platform, and then gently suggest that maybe you'd like to pay $20 per month for features that would cost you 2 cents on EC2. The first hit is always free, but you end up paying for it down the line. There's also no reason you couldn't also do the same thing on AWS Lambda or Google Cloud Functions, but the setup isn't as easy (or free).

There's something beautifully absurd, almost tragically bureaucratic, about the whole grotesque Rube Goldberg-esque setup we have here. We've created a system where natural language gets translated into JSON RPC requests, which get routed through edge networks to serverless functions across the globe, which spin up Linux hypervisors to isolate the runtime, which execute Python code that dispatches enormous attention matrix multiplications on 5nm etched silicon GPUs performing billions of floating point operations per second, which return results that get packaged into JSON responses that get translated back into natural language just to add two integers, which is otherwise a single CPU instruction. It's like using a symphony orchestra, three circus troupes, six carrier pigeons, and a nuclear reactor to butter a single piece of toast.

But it works, and in our current technological moment, "it works" is often the highest praise we can give to any system. It's pretty cool that you can go from a simple Python script to a fully-fledged MCP server deployed automatically from a GitHub repository, with zero ongoing maintenance or costs and immeditetly plug that into the frontier models in a single click. I'm not sure what the future holds for this kind of thing. I'm sure there are a lot of interesting things that can be done with it, but I'm also sure that there are a lot of interesting things that can be done with it that are probably not good.

Of course, no discussion of MCP would be complete without acknowledging the chorus of hustle bros who have descended upon LinkedIn like locusts, proclaiming that MCP is the future of everything and will revolutionize how we think about the fundamental nature of existence. At least ten different visionary thought leaders have nearly broken down in tears proselytizing about it in the last week. Some are even going so far as to call it the new Web3, because that went great last time.

Welp, whatever. The code is up on GitHub if you want to experiment with your own serverless MCP misadventures.

Adventures in Symbolic Algebra with Model Context Protocol

Sun, 18 May 2025 01:00:00 +0000

Adventures in Symbolic Algebra with Model Context Protocol

I spent last weekend playing with this new MCP protocol all the kids are talking about, using it to make language models talk to symbolic computer algebra systems. The idea was simple: LLMs are great at understanding natural language math problems but terrible at actually solving them, while computer algebra systems excel at symbolic manipulation but have arcane interfaces. By connecting them through MCP, we can get the best of both worlds. The code is still early and rough around the edges, but I've put the source up on Github if anyone wants to experiment with it.

Github Source Code (git clone https://github.com/sdiehl/sympy-mcp.git)

MCP, if you're not familiar, is Anthropic's answer to the question: "How do we get an LLM to actually DO things instead of just TALK about doing them?" It's essentially the cgi-bin of AI (I'm probably dating myself with that reference). It's a protocol that allows language models to call external tools through a server that exposes the functions as a REST API. The core idea of MCP is to standardize the way language models call external tools, instead of writing custom connectors for each AI model and each tool, you implement the protocol once on each side. It's the USB-C of AI tooling, if USB-C were still in its awkward adolescent phase.

Notably, the MCP server runs locally on your machine, letting the language model invoke arbitrary code and commands by using one of the LLM desktop clients to call out to the local server. This is probably a bad idea in general and as dangerous and reckless as you might think, so there's a definite security concern here ... be warned. But let's not let a potential rootkit get in the way of a fun weekend experiment.

My particular itch stemmed from watching Claude (and its cousins like o4-mini-high and DeepSeek-R1) really struggle with tensor calculus. If you've ever asked an LLM to perform complex symbolic manipulation, you know the drill: confident answers, beautiful LaTeX formatting, and results that would make your math professor weep bitter tears. These models, despite their impressive linguistic capabilities, are absolute disasters when it comes to keeping track of indices in tensor expressions or manipulating complicated algebraic forms. The expressions involved in even moderate general relativity problems are HUGE, with hundreds of terms and complex index gymnastics.

But we already have specialized tools that excel at this! Computer algebra systems like Mathematica, Sympy, xAct, Cadabra were built specifically for this purpose. So the obvious solution presented itself: let's expose these tools to the LLM through MCP and let each system do what it does best. The LLM handles the natural language understanding and planning, while the symbolic algebra system performs the actual mathematical manipulations with perfect precision.

Working with the MCP ecosystem is like visiting a frontier town in the Wild West. The documentation exists in the form of scattered campfire stories, the implementations have a distinctly "I wrote this at a 3 AM hackathon" vibe, and everything is strangely Node-heavy. This Node fixation likely stems from most MCP tools being designed to call REST services for cloud applications. Then there's the peculiar ecosystem of suspiciously self-referential products from companies that just happen to sell AI coding assistants. There's definitely a faint whiff of opportunism in the air.

Debugging an MCP server is a crazy exercise. You're essentially working with a stochastic black box that communicates through a complex web of JSON schemas attached to docstring annotations. When something goes wrong, good luck figuring out if it's your server, the client, the LLM's interpretation, or just the model having a laugh at your expense. The non-deterministic nature of the whole setup means that something can work perfectly five times in a row and then spontaneously fail on the sixth attempt because the random number seed on the inference server is different, the prompt vibes are off, or for reasons completely shrouded in the mists of the digital occult. Welcome to the fun future of software.

However, once you've made the ritual animal sacrifice to appease the non-determinism gods (I find that sacrificing a rubber duck while chanting "O Great Transformer of the Deep, may thy hallucinations be few and thy completions true" works best), you'll find the basic implementation is refreshingly straightforward, similar to FastAPI if FastAPI were designing its endpoints for a language model. Here's a simple example that highlights why this approach matters: Ask any LLM to factor a large integer, and watch it confidently fabricate entirely wrong answers. By design, transformers can't perform the arbitrary computation required for integer factorization. They've merely memorized some factorizations from the internet (and even those, poorly).

from mcp.server.fastmcp import FastMCP
import subprocess

mcp = FastMCP("Demo", instructions="You factor integers.")

def factor_number(number):
    result = subprocess.run(['factor', str(number)], capture_output=True, text=True)
    return result.stdout.strip()

@mcp.tool()
def factor(a: int) -> int:
    """Factor an integer"""
    return factor_number(a)

Throw that in server.py and then with uv, you can install the server and start it up with a single command.

uv run --with mcp[cli] mcp install server.py

And bingo you've got your first MCP server. If you open up the Claude Desktop app you should see the server Demo in the tool dropdown and now you can ask Claude what you've always wanted "Give me the prime factors of 170141183460469231731687303715884105727 or else a kitten gets factored" and it will actually factor it for you (using the GNU factor command) instead of vibin' up some bullshit. Progress!

When it works, it's pretty magical. The successful integration of these components (properly formatted JSON, accurate tool selection by the language model, and reliable server processing) demonstrates the potential of this architectural approach. While the technology is still in its early stages of development, the possibilities for integration with formal verification systems are particularly compelling. The combination of LLMs with theorem provers like Lean could enable natural language interfaces to formal mathematics, allowing automated reasoning systems to benefit from the language models' ability to understand informal mathematical concepts while maintaining rigorous logical foundations. Similarly, making computer algebra systems accessible through natural language could dramatically lower the barrier to entry for complex mathematical computation. However, significant research challenges remain in ensuring reliable and semantically correct interactions between these different systems.

Let me show you how this looks in practice with a classic example from physics: solving the damped harmonic oscillator with a forcing term. This is the bread and butter problem for undergraduate physics students. Here's how the workflow unfolds with our sympy-mcp server:

User: Solve the damped harmonic oscillator with forcing term: the mass-spring-damper system described by the differential equation where m is mass, c is the damping coefficient, k is the spring constant, and F(t) is an external force.

$$
m\frac{d^2x}{dt^2} + c\frac{dx}{dt} + kx = F(t)
$$

Assistant: (Internal tool call) intro_many to introduce variables with appropriate assumptions:

{
  "variables": [
    {"var_name": "t", "pos_assumptions": ["real"], "neg_assumptions": []},
    {"var_name": "m", "pos_assumptions": ["real", "positive"], "neg_assumptions": []},
    {"var_name": "c", "pos_assumptions": ["real", "positive"], "neg_assumptions": []},
    {"var_name": "k", "pos_assumptions": ["real", "positive"], "neg_assumptions": []}
  ]
}

Assistant: (Internal tool call) introduce_function to define x(t) as a function:

{
  "func_name": "x"
}

Assistant: (Internal tool call) introduce_expression to create the differential equation:

{
  "expr_str": "Eq(m*Derivative(x(t), t, t) + c*Derivative(x(t), t) + k*x(t), F(t))"
}

Assistant: (Internal tool call) introduce_function to define the forcing function F(t):

{
  "func_name": "F"
}

Assistant: (Internal tool call) dsolve_ode to solve the ODE:

{
  "expr_key": "expr_12",
  "func_name": "x"
}

And voilà! Instead of hallucinating a solution, the LLM delegates to SymPy which returns the correct solution:

$$
x{\left(t \right)} = C_{1} e^{\frac{t \left(- c + \sqrt{c^{2} - 4 k m}\right)}{2 m}} + C_{2} e^{- \frac{t \left(c + \sqrt{c^{2} - 4 k m}\right)}{2 m}} + \frac{e^{\frac{t \left(- c + \sqrt{c^{2} - 4 k m}\right)}{2 m}} \int F{\left(t \right)} e^{\frac{c t}{2 m}} e^{- \frac{t \sqrt{c^{2} - 4 k m}}{2 m}}, dt}{\sqrt{c^{2} - 4 k m}} - \frac{e^{- \frac{t \left(c + \sqrt{c^{2} - 4 k m}\right)}{2 m}} \int F{\left(t \right)} e^{\frac{c t}{2 m}} e^{\frac{t \sqrt{c^{2} - 4 k m}}{2 m}}, dt}{\sqrt{c^{2} - 4 k m}}
$$

No hallucinated terms, no mysterious constants appearing out of nowhere, just the correct solution. The LLM handles the natural language interaction and orchestration, while the computer algebra system does what it does best ... exact symbolic manipulation.

Anyways all the code is up on Github here so maybe someone else will find it useful. If you have Cursor or Claude installed add the following to ~/.cursor/mcp.json or ~/Library/Application Support/Claude/claude_desktop_config.json to install the MCP server.

{
  "mcpServers": {
    "sympy-mcp": {
      "command": "uv",
      "args": [
        "run",
        "--with",
        "https://github.com/sdiehl/sympy-mcp/releases/download/0.1/sympy_mcp-0.1.0-py3-none-any.whl",
        "python",
        "server.py"
      ]
    }
  }
}

Or maybe slightly better, run it from a Docker image.

{
  "mcpServers": {
    "sympy-mcp": {
      "command": "docker",
      "args": [
        "run",
        "-i",
        "-p",
        "8081:8081",
        "--rm",
        "ghcr.io/sdiehl/sympy-mcp:latest"
      ]
    }
  }
}

And maybe read the source code for what you're installing here, because I feel like a lot of people are going to install these MCP servers without knowing what they're doing and thus install a lot of malware and exploits. There's basically no security going on here. And that could be a big problem. At this rate of security negligence, Skynet won't arise from AI research, but from someone accidentally giving a model root access to national defense systems because they curl'd some random MCP server from the internet.

Using CUDA Deep Neural Network (cuDNN) in Python

Thu, 15 May 2025 01:00:00 +0000

Using CUDA Deep Neural Network (cuDNN) in Python

Let's go through how to implement scaled dot product attention using the cuDNN Python API. This is the most computationally expensive part of inference in a transformer-style model, while also being partially parallelizable so it's usually offloaded to the GPU. Under the hood this uses the FlashAttention-2 algorithm but provides an API that is higher level than just the raw kernel implementation.

First, we import necessary libraries: cudnn for the cuDNN API, torch for tensor operations and comparison. Note that you will need a GPU with compute capability SM80 architecture (Ampere) or above in order to use the optimized kernels.

import cudnn
import torch
import math

torch.manual_seed(0xDEADBEEF)
handle = cudnn.create_handle()

assert torch.cuda.is_available()

Next, we define the problem dimensions for our attention mechanism, based on a GPT-2 like configuration: batch size (b), number of heads (h), maximum sequence length (s), and embedding dimension per head (d). The attention scaling factor attn_scale is also calculated.

b = 4
h = 12
s = 1024
d = 64

attn_scale = 1.0 / math.sqrt(d)

We then create the query (Q), key (K), value (V), and output (O) tensors on the GPU using PyTorch. These tensors are initialized with half-precision (.half()). We define their logical dimensions as (b, h, s, d) (BHSD). Importantly, we specify a physical memory layout using strides that corresponds to BSHD (Batch, Sequence, Head, Dims_per_head) to demonstrate explicit layout control. The as_strided method applies this layout without data copies.

dims = (b, h, s, d)
strides = (s * h * d, d, h * d, 1) # BSHD physical layout

q_gpu = torch.randn(b * s * h * d).half().cuda().as_strided(dims, strides)
k_gpu = torch.randn(b * s * h * d).half().cuda().as_strided(dims, strides)
v_gpu = torch.randn(b * s * h * d).half().cuda().as_strided(dims, strides)
o_gpu = torch.empty(b * s * h * d).half().cuda().as_strided(dims, strides)

Now, we construct the cuDNN computation graph. The cuDNN graph system provides a high-level interface for describing tensor operations as a dataflow graph that can be efficiently executed on the GPU. Users build up their computation by adding operations to the graph, which typically represents a subset of their full neural network that they want to optimize and offload to specialized GPU kernels. Once the graph is finalized, cuDNN provides multiple execution engines with different tradeoffs—some prioritizing ease of use, others minimizing runtime overhead or maximizing performance.

The graph is initialized specifying half-precision for I/O and float precision for intermediate and compute operations. We create graph tensor descriptors (q, k, v) that mirror our PyTorch GPU tensors. The SDPA operation is added to the graph, configured for inference (is_inference=True), using the calculated attn_scale, and with causal masking enabled (use_causal_mask=True). The second return value (stats tensor) is ignored as it's for training. Finally, the output graph tensor o is marked as an output and its dimensions and strides are set.

graph = cudnn.pygraph(
    io_data_type=cudnn.data_type.HALF,
    intermediate_data_type=cudnn.data_type.FLOAT,
    compute_data_type=cudnn.data_type.FLOAT,
)

q = graph.tensor_like(q_gpu)
k = graph.tensor_like(k_gpu)
v = graph.tensor_like(v_gpu)

o, _ = graph.sdpa(
    name="sdpa",
    q=q,
    k=k,
    v=v,
    is_inference=True,
    attn_scale=attn_scale,
    use_causal_mask=True,
)

o.set_output(True).set_dim(dims).set_stride(strides)

With the graph defined, we build it. This involves validating the graph structure, building an internal operation graph, creating execution plans using cuDNN's heuristics (Mode A and Fallback), checking if the chosen plans are supported, and finally building these plans, which may involve JIT compilation of kernels. Heuristics Mode A is designed to be fast and be able to handle most operation graph patterns. Heuristics Mode B is designed to be more accurate but slower.

graph.validate()
graph.build_operation_graph()
graph.create_execution_plans([cudnn.heur_mode.A, cudnn.heur_mode.FALLBACK])
graph.check_support()
graph.build_plans()

To execute the graph, we create a variant_pack dictionary. This maps the symbolic graph tensors (defined earlier) to the actual PyTorch GPU tensors holding the data. We also query the required workspace size for the execution plan and allocate it on the GPU. The graph is then executed, and torch.cuda.synchronize() ensures the computation completes before proceeding.

variant_pack = {
    q: q_gpu,
    k: k_gpu,
    v: v_gpu,
    o: o_gpu,
}

workspace = torch.empty(graph.get_workspace_size(), device="cuda", dtype=torch.uint8)
graph.execute(variant_pack, workspace)
torch.cuda.synchronize()

Finally, we verify the output of our cuDNN SDPA implementation against PyTorch's native scaled_dot_product_attention. We prepare reference tensors q_ref, k_ref, v_ref from our original GPU tensors, converting them to float. Since our cuDNN tensors used a BSHD physical layout, and PyTorch's native function expects 4D inputs in BHSD, we permute the reference tensors from BSHD to BHSD. We then compute the reference output o_ref.

In simple terms, permute(0, 2, 1, 3) rearranges the dimensions of a 4D tensor. If the original tensor's dimensions represent (Batch, Sequence, Head, Dim_per_head) (BSHD), this operation swaps the second and third dimensions (Sequence and Head) to produce a tensor with dimensions (Batch, Head, Sequence, Dim_per_head) (BHSD). This is done because the torch.nn.functional.scaled_dot_product_attention function expects its 4D input tensors to be in the BHSD format, so the permutation ensures the tensor's layout matches the function's requirements.

q_ref = q_gpu.detach().clone().float()
k_ref = k_gpu.detach().clone().float()
v_ref = v_gpu.detach().clone().float()

# Permute from BSHD to BHSD for PyTorch native SDPA
q_ref = q_ref.permute(0, 2, 1, 3).contiguous()
k_ref = k_ref.permute(0, 2, 1, 3).contiguous()
v_ref = v_ref.permute(0, 2, 1, 3).contiguous()

o_ref = torch.nn.functional.scaled_dot_product_attention(
    q_ref, k_ref, v_ref, is_causal=True, scale=attn_scale
)

o_gpu_for_comparison = o_gpu.float()
# Permute cuDNN output from BSHD to BHSD for comparison
o_gpu_for_comparison = o_gpu_for_comparison.permute(0, 2, 1, 3).contiguous()

torch.testing.assert_close(o_ref, o_gpu_for_comparison, atol=5e-3, rtol=3e-3)
print("PyTorch and cuDNN SDPA implementations match!")

In the modern AI tooling stack, tools like the cuDNN Frontend API sit at below high-level deep learning frameworks (like PyTorch or Jax) but above raw CUDA programming. Exposing this level of control over highly optimized kernels like SDPA directly allows for rapid prototyping and performance tuning of model components without needing to delve into C++ for every optimization.

The Technofascist Mind: A Guide to Its Psychology and Philosophy

Tue, 06 May 2025 01:00:00 +0000

The Technofascist Mind: A Guide to Its Psychology and Philosophy

I often read the usual American coastal elite magazines—the New Yorker, Guardian, the Atlantic, and others—and experience a profound sense of vertigo when opinion writers diagnose the emergent ideologies of Silicon Valley's power brokers as 'anti-democratic' or 'illiberal' as if this is some new revelation. Yes, obviously. In other news the sky is blue and water is wet.

These labels, while accurate, feel profoundly inadequate, akin to describing a hurricane as 'windy.' They capture a symptom but miss the specific, driving pathology—a distinct philosophical and psychological current demanding closer examination. As many on the left critisize these figures as 'fascist' a label many of them gladly wear as a badge of honor. It's not perceived as an insult but often as a compliment, confirming their self-perceived exceptionalism.

Continuing this line of critique, while perhaps providing empty catharsis, fundamentally fails to change anything or undermine their power. Having spent considerable time observing, reading, and even working with these people, I don't share their beliefs, but I grasp the internal logic that, given certain presuppositions, leads to their conclusions. The persistent misunderstanding in mainstream analysis is not just frustrating; it's strategically inept. If we aim to counter their influence—to metaphorically blow up the Death Star—we must first understand its architecture, including the location of its thermal exhaust port ... if you can excuse my nerd humour.

I'm writing this primarily for political strategists and journalists alike to understand the rise of fascism, especially in the tech sector, and how to counter it, because we need to win in both 2026 and 2028 against these people's iron grip on our country. This article aims to provide my understanding, delving into the psychology and philosophy animating this influential segment of the new right. It is by no means an apology; their vision is antithetical to democratic humanism and is actively destroying our society and everything I hold dear. However, misunderstanding and misrepresenting them gets us nowhere. We must map the contours of their thinking to effectively address the threat they represent.

Beyond Simple Labels

Journalistic shorthand often defaults to 'anti-democratic,' 'illiberal,' or even 'fascist' when describing the ideologies coalescing among Silicon Valley's elite. While containing elements of truth, these terms fail to capture the specific character and proactive nature of this worldview. It is not simply a rejection of existing democratic norms but the active promotion of a complex, often contradictory, patchwork of heterodox ideas, values, and objectives aimed at radically reshaping society. This perspective draws energy from psychological drives and philosophical justifications distinct from mainstream American political thought. And while the term "fascist" is apt in many ways, we should be careful with direct historical comparisons - German Fascism was distinct from Italian Fascism in important ways, and any American variant will likely have its own unique characteristics shaped by our specific cultural and technological context.

Consider the broad ethical consensus underpinning much of Western, particularly American, political discourse (representing perhaps 70% of the populace). Despite divergent origins—Enlightenment-derived secular reason versus Abrahamic divine revelation—these paths historically converged on core values. Secular thinkers, employing utilitarianism, natural law, or social contract theory, often deduced the importance of universal human rights, democratic governance, and a degree of egalitarianism. Similarly, Abrahamic traditions, emphasizing concepts like the imago Dei (humans made in God's image) and charity, arrived at analogous conclusions regarding inherent human dignity and the common good. This convergence established a shared ethical framework, an Overton Window of basic human decency.

The technofascist mindset operates largely outside this established window, fundamentally challenging its foundational assumptions about human equality and the desirability of democratic governance. This is the single most crucial point to grasp.

To grasp this ideology requires a more precise lens. The term "technofascism" shouldn't be used lightly or as a mere epithet. While lacking the specific aesthetics and mythologies of 20th-century fascism, it shares a core impulse: a radical belief in hierarchy, a rejection of democratic egalitarianism, a form of vitalism centered on technological progress and intelligence, and the conviction that a technologically empowered elite has the right, even the duty, to dictate humanity's future. It is a distinct flavor of authoritarianism adapted for the digital age, sharing chilling conclusions with historical precedents even as it differs in means and specific goals. Understanding its unique psychological and philosophical architecture is a strategic necessity.

Moving beyond generalized outrage requires mapping their presuppositions, grasping the allure of their abstractions (like systemic solutions to human problems), and recognizing the internal logic, however disturbing. Critically, this prevents constructing simplistic strawmen. Dismissing these figures as merely greedy or nihilistic is inaccurate and strategically foolish. They are often intensely values-driven, but by principles alien to democratic humanism: establishment of rigid "meritocratic" hierarchies, radical efficiency, intelligence optimization, the long-term propagation of a specific vision of consciousness (often digital), and grand technological projects prioritized over present human well-being. Recognizing these underlying values confirms the gravity of the challenge: they aren't just negating existing structures but actively building a specific, hierarchical, and often deeply anti-humanistic future based on an incomensurable, albeit dangerous, worldview.

Demographics

The individuals propagating these ideas are largely founders, venture capitalists, engineers, and ex-finance professionals who have migrated to the tech sector. They are not monolithic; diversity exists in background, origin, and specific beliefs. While predominantly white and male, this is not exclusively the case. What unites them is less a shared demographic profile and more a pattern of overlapping psychological traits and philosophical inclinations.

At the core, these traits include: an embrace of hierarchy, a disdain for the perceived irrationality of the masses, a preference for abstraction over messy lived reality, and a conviction in the power of a select, intelligent few (amplified by technology) to radically reshape humanity according to their designs. This mindset often finds fertile ground in communities and platforms like LessWrong, Hacker News, Slate Star Codex, and other hubs for rationalist thought that emphasize logic, Bayesian reasoning, and systems thinking. While not inherently fascist, the intense focus on rationality and optimization within these communities can sometimes bleed into a devaluation of unquantifiable human experience and a susceptibility to elitist or utilitarian frameworks that justify radical social engineering.

Core Tenets

The technofascist worldview rests on twelve interconnected psychological tendencies and philosophical justifications for their worldview.

1. A Cynical View of Humanity

At the core of this worldview lies a deeply cynical perspective on human nature. Others are primarily seen as tools to be manipulated, obstacles to overcome, or weaklings to be exploited rather than as equals deserving of dignity and respect. This mindset embraces a fundamental belief that everyone is ultimately out for themselves—that altruism is merely disguised self-interest and empathy a weakness to be overcome. This cynicism serves a dual purpose: it justifies exploitative behavior as simply "seeing reality clearly" while simultaneously providing psychological insulation against guilt. By framing humanity as inherently selfish and manipulative, one's own predatory actions become not just acceptable but strategically necessary in a dog-eat-dog world where only the ruthless survive and thrive.

Others have value only insofar as they are useful to the individual coupled with a belief that they deserve special treatment or are justified in exploiting others. They embody Thucydides' brutal principle that "the strong do what they can and the weak suffer what they must."

2. Intrinsic Hierarchies

A crudely interpreted Nietzschean “aristocratic radicalism” often provides philosophical cover for pre-existing elitist impulses. The psychological driver is a need for differentiation and superiority, manifesting as a stark division: "us" (the intelligent, rational "builders", "accelerationists") versus "them" ("normies," "mundanes", "takers", "NPCs", "decels"). This categorization enables radical dehumanization, rendering empathy unnecessary. The underlying assumption is that most humans are essentially worthless and unthinkingly self-destructive—mere obstacles to progress rather than beings with inherent dignity. Philosophically, a bastardized "master morality" emerges: what advances the elite's project is good; what hinders it (like democratic processes reflecting the "herd's" values) is bad. This resonates strongly with the objectivist philosophy of Ayn Rand, celebrating heroic individual creators and dismissing altruism and collective well-being as weaknesses. History is viewed as the story of great men driving progress, justifying the concentration of power in the hands of a perceived cognitive elite—the self-styled architects of the future who must either fundamentally change humanity or escape from it entirely.

As a result, social rules, laws, and ethical principles are seen as arbitrary constraints for others, or as weaknesses to be exploited, not as binding guides for personal behavior. "Might makes right" or "rules are for fools."

3. The Allure of the Abstract

A powerful preference for abstraction, coupled with discomfort with the ambiguities of concrete human experience, is key. The world is more manageable reduced to data, algorithms, and systems. Lived experience—contradictory, emotional, unquantifiable—is messy and inefficient. Psychologically, this can be a defense against overwhelming empathy or reflect a cognitive style struggling with qualitative data. Philosophically, it aligns with extreme rationalism or Platonic idealism, where the abstract model is more real than its imperfect manifestations. Social problems become engineering challenges, ethical dilemmas logic puzzles. This detachment allows decisions with devastating human consequences to be made with cool, analytical remove—a trait often rewarded in competitive business environments.

4. Grand Narratives of Destiny

This comfort with abstraction fuels a fixation on narratives of immense scale and temporal scope: the long-term trajectory of humanity, existential risks, demographic shifts perceived as crises, interstellar colonization, or esoteric concerns like the simulation hypothesis. Psychologically, this focus provides a sense of profound purpose, positioning adherents as pivotal figures safeguarding or shaping humanity's ultimate destiny. It offers intellectually stimulating problems that appear cleaner and more tractable than immediate, complex social issues. It can also function as intellectual escapism or a means of sublimating anxiety, focusing on potentially controllable (or at least modellable) abstract future threats (like misaligned AI) over immediate, intractable ones (like present-day inequality or the localized impacts of climate change). Philosophically, this manifests in ideologies such as Longtermism, which explicitly prioritizes the potential welfare of vast numbers of future (potentially digital) beings over the needs and rights of present human populations. This provides a utilitarian framework to justify neglecting immediate crises in favor of speculative, large-scale projects aligned with the technological elite's interests and capabilities.

5. Sci-Fi as Blueprints Over Allegories

Engagement with science fiction often bypasses metaphorical or cautionary interpretations, treating narratives instead as literal roadmaps or desirable future states. Dystopian concepts, exemplified by the "Torment Nexus" meme ("Sci-Fi Author: I invented the Torment Nexus as a cautionary tale. Tech Company: At long last, we have created the Torment Nexus from the classic novel Don't Create the Torment Nexus!"), are frequently approached not as warnings, but as intriguing systems-design challenges. This reflects an engineering mindset projected onto narrative: if a concept is imaginable, it is potentially achievable and perhaps even desirable to build. Philosophically, this often stems from a form of technological determinism—the belief that technology dictates social evolution and reality itself is ultimately programmable. Ethical considerations become secondary to technical feasibility or conceptual "interestingness." Canonical works are often selectively interpreted: Star Trek's underlying socialist humanism is ignored in favor of its technological marvels; Lord of the Rings can be read as validating rightful hierarchy against chaotic industrial forces; Dune's explicit warnings against charismatic messiahs and centralized control are overshadowed by fascination with its portrayal of elite power dynamics; Iain M. Banks' anarchist/socialist Culture series is sometimes bizarrely reinterpreted through libertarian or even neoconservative lenses.

6. Performative Contrarianism

A drive for intellectual dominance frequently manifests as performative contrarianism: adopting provocative stances and insisting that all topics are open for "rational debate," irrespective of potential harm or established domain expertise. Psychologically, the goal is often less about truth-seeking and more about winning arguments, demonstrating intellectual superiority, and provoking emotional responses in others ("triggering the normies"), which are then interpreted as proof of the opponent's irrationality. Philosophically, this is often cloaked in the language of radical free speech absolutism but typically lacks genuine intellectual curiosity or epistemic humility. The objective is often to demonstrate intellectual prowess by defending taboo or discredited ideas (e.g., racial theories of intelligence, eugenics, the abolition of democracy) precisely because they are provocative. Transgression for its own sake, framed as intellectual courage, becomes a valued trait within this worldview.

7. Systematizing Social Aversion

An underlying discomfort with direct, messy, and emotionally complex human interaction can be observed. Social awkwardness or neurodivergent traits, rather than being addressed through social adaptation, can morph into an ideological preference for systems that minimize the need for nuanced interpersonal engagement. Code, formal logic, mathematics, and impersonal market mechanisms become preferred mediators of human relations. Philosophically, this aligns with radical libertarian or anarcho-capitalist ideals, envisioning society governed primarily by voluntary contracts and objective, often code-based, rules, thereby minimizing the need for collective decision-making, negotiation, or empathy-driven compromise. Technology is viewed as the primary tool to achieve this state, engineering away the "friction" of human difference and disagreement. This connects directly to the "Exit" philosophy and concepts like "Network States"—the notion that the technological elite should be free to opt out of traditional societies and establish their own technologically mediated, regulation-free enclaves.

8. Hell-Baked Social Darwinism

This evocative phrase captures a bleak, quasi-Social Darwinian view of human existence and origins. "Hell" refers to the brutal, indifferent process of natural selection operating over deep evolutionary time—a Hobbesian struggle driving adaptation through immense suffering and death, devoid of inherent purpose or morality. "Baked" signifies the belief that this unforgiving process has indelibly forged our fundamental nature; intelligence, competitiveness, status-seeking, even consciousness itself are seen as products marked by these violent origins. In this perspective, humanity is metaphorically "hell-spawn"—products of an evolutionary inferno, with these traits deeply and perhaps immutably ingrained. This view directly undermines humanist narratives of inherent dignity or Enlightenment ideals of autonomous reason, framing existence as governed by harsh power dynamics that can, and perhaps should, continue to operate through techno-capitalist competition, largely unconstrained by traditional ethical considerations. It stands in stark contrast to both secular humanism and religious doctrines emphasizing intrinsic human value.

9. Faith as Social Technology

While frequently populated by atheists or agnostics, a non-trivial and influential subculture within this sphere embraces or strategically utilizes religion, particularly Christianity, on purely instrumental grounds. This is typically not rooted in personal faith or theological conviction but sees religion as a potent social technology—a tool for imposing order, structuring civilization, maintaining social cohesion, and ensuring stability among the "masses" deemed incapable of self-governance through reason alone. Christianity, often a culturally conservative or nationalist variant rather than one emphasizing universal love or social justice, is valued for its perceived historical role in forging Western civilization, providing a unifying cultural narrative, acting as a bulwark against perceived threats (communism, Islam, progressive ideologies), and offering a moral code conducive to social order and productivity. It echoes Edward Gibbon's observation regarding the Roman elite, who viewed traditional religion as "equally false" to the philosopher but "equally useful" to the magistrate—a mechanism for social control and civilizational identity maintenance within their larger societal engineering project.

10. Empathy is a Bug

Within the technofascist worldview, empathy is often viewed not merely as a secondary concern but as a fundamental design flaw in the human cognitive apparatus—a dangerous bias ("pathological altruism", "ruinous empathy", or "suicidal empathy") that hinders rational decision-making and obstructs progress towards optimized futures. Whereas democratic and humanist traditions typically regard empathy as a cornerstone of morality and social cohesion, this mindset frequently reframes it as a source of irrationality, inefficiency, and exploitable vulnerability. Echoing certain segments of the contemporary right who view empathy as a "toxin" or "civilizationally suicidal" when applied "incorrectly" (e.g., towards perceived out-groups), the technofascist sees it as a cognitive glitch that prioritizes immediate, localized, often emotionally charged inputs ("sob stories," individual suffering) over objective, data-driven, systems-level analysis and long-term strategic imperatives.

This perspective contends that empathy clouds judgment, leading to suboptimal resource allocation and preventing necessary, albeit potentially harsh, decisions required for perceived progress—whether defined as market efficiency, technological acceleration, or ensuring the dominance of a specific "high-functioning" demographic. Extending empathy towards the economically displaced, the marginalized, or those struggling to adapt to technological disruption is seen as counter-productive sentimentality, a misfiring of evolved instincts that impedes systemic dynamism. Why expend resources or alter system parameters based on the subjective discomfort of units deemed less valuable or adaptive? This cold calculus provides a crucial psychological and philosophical permission structure: by defining empathy itself as flawed, irrational, or even dangerous, adherents can justify policies, technologies, and social structures that may cause widespread suffering or exacerbate inequality, framing their indifference not as cruelty, but as the rational detachment necessary for achieving a higher, albeit colder, objective. It enables the dehumanization required to treat populations as data sets and societal disruption as mere friction in the relentless drive towards an engineered future, excusing potentially devastating human costs as the unavoidable price of optimization or supposed civilizational "upgrades."

11. Millenarianism

A crucial element is a distinct form of millenarianism—an urgent belief in an impending societal transformation, catastrophe, or technological rupture, often framed in quasi-religious terms like the "Singularity," "Collapse," "The Event," "Transformation," or even a secular "Rapture." The perceived timeframe for these events is often remarkably short, measured in years or even months, fostering a sense of living in the final days of the current human era.

This apocalyptic or transformative expectation is not merely abstract speculation; it drives concrete actions, political alignments, and directs significant capital flows. The prevailing narrative often depicts humanity hurtling towards existential threats (runaway climate change, pandemics, societal breakdown, misaligned AI), necessitating radical, elite-driven interventions and hard choices about who and what can be "saved." This concept of "exit" is best described in Douglas Rushkoff's book Survival of the Richest.

This manifests in various interconnected ideologies and projects:

Transhumanism: Seeking to transcend biological limitations through human-machine integration, cognitive enhancement, radical life extension, or ultimately, uploading consciousness into digital substrates or AI.
Existential Risk Mitigation (aligned with Longtermism): Focusing immense resources on preventing low-probability, high-impact future catastrophes, sometimes at the expense of addressing present suffering.
The "Exit" Strategy: Advocating withdrawal from existing nation-states into technologically advanced, privately governed enclaves ("charter cities," seasteading, network states)—effectively creating high-tech lifeboats for a select elite.
Prepping for the Apocalypse: Both at the elite level (billionaire bunkers in New Zealand, fortified compounds) and promoted to a wider base (stockpiling resources, distrusting government).
AI Supremacy: A belief, sometimes stated explicitly (like Elon Musk's alleged comment about humanity being a "biological bootloader for digital superintelligence"), that AI is the next stage of evolution, justifying potentially devastating resource consumption (energy, water, minerals) to bring it about. For example, former Google CEO Eric Schmidt acknowledged AI's massive energy needs, potentially necessitating planet-incinerating fossil fuel use to enable this "higher" intelligence.
Secular Rapture: Even secular elites adopt narratives mirroring the Christian Rapture—a belief that a chosen few will escape earthly collapse (via technology, space colonization, or digital transcendence) while the rest are left behind. Musk's obsession with Mars colonization exemplifies this: a "multiplanetary" future as an ark, seemingly justifying the potential sacrifice of Earth's habitability.

This apocalyptic framing, whether rooted in secular techno-optimism/pessimism or instrumentalized religious narratives, creates a potent, dangerous ideology. It justifies dismantling regulations, ignoring climate change, promoting social division, and concentrating power, all under the guise of preparing for or navigating an inevitable collapse—an end they are often actively accelerating through their ventures in AI, crypto, and deregulation.

12. Death Anxiety

Underlying many of these pursuits, particularly transhumanism, is often an intense preoccupation with personal mortality, interpretable psychologically as a defense mechanism against overwhelming death anxiety. An apparent inability to process or accept human finitude, potentially coupled with extreme narcissism or self-regard, can lead to a profound denial of mortality. This anxiety is then sublimated into technologically fantastical projects aimed at transcending biological limits and achieving indefinite lifespans or digital immortality.

(13. Chemical Catalysts)

I add this as a seperate point, because it's not universal. But notable enough to mention.

A discernible subculture within these techno-elite circles engages significantly with psychedelic and dissociative substances (e.g., LSD, psilocybin, ketamine). While not ubiquitous, this practice sometimes correlates with the adoption of increasingly esoteric, grandiose, and detached beliefs. Fueled by drug-induced experiences perceived as revelatory, some individuals may develop quasi-messianic complexes, viewing themselves as uniquely enlightened figures destined to guide humanity's transition. This can merge with a fervent desire to "immanentize the eschaton"—to force the arrival of a predicted singularity or societal transformation through accelerated technological and social disruption. Concepts like simulation theory can shift from philosophical thought experiments to deeply held convictions about the fundamental unreality of existence, potentially further eroding empathetic connection to others or fostering solipsistic "main character" syndromes. This drug-facilitated dissociation can contribute to erratic decision-making, bizarre personal behaviors, and an even more profound detachment from shared consensus reality, reinforcing a sense of operating on a higher plane where conventional rules and ethical concerns seem irrelevant.

Takeaways

The technofascist mind represents a potent confluence of psychological needs and philosophical rationalizations. It combines a drive for hierarchy and control with a cognitive preference for abstraction and systems. It embraces grand, apocalyptic narratives that provide purpose and justify extreme measures, interprets science fiction literally as a roadmap, employs performative rationality as intellectual armor, and seeks to engineer away human messiness through technology and libertarian frameworks. Its worldview can be bleakly deterministic and embracing social Darwinism. It rejects empathy as cognitive bias and sees it as a source of irrationality, inefficiency, and exploitable weakness.

Understanding their internal mental architecture is vital. This mindset poses a profound challenge to democratic norms, ethical considerations grounded in humanism, and the very concept of a shared future. It seeks not just to build technologies but to redefine reality according to its own hierarchical, systematized, and profoundly anti-humanistic values. It operates with the conviction that only a select few truly matter in the grand scheme, and almost any action can be justified in pursuit of their technologically-mediated aspirations, because, in their calculus, the rest of humanity is ultimately expendable. The axiomatic differences in these philosophies are outlined below:

	Democratic Humanism	Technofascism
Locus of Value	The individual person.	The abstract system (civilization, intelligence).
Purpose of Society	To serve the people within it.	For the people to serve it.
Nature of Rights	A shield for the individual.	A tool for the system.
Role of Empathy	The ability to recognize value in others.	A bias that disrupts systemic optimization.
Meaning of Progress	Human flourishing, less suffering, more freedom.	Increased systemic power, efficiency, and intelligence.
Conception of Justice	Fairness and due process for the individual.	Order and efficiency for the collective system.
Source of Authority	Consent of the governed.	Competence of the governors.
View of Humanity	An end in itself.	A means to an end (a resource, a bootloader).

Therefore, it is crucial for the public to recognize and clearly articulate just how radically "weird" and outside the broad spectrum of American traditions and values this technofascist mindset truly operates. Figures embodying this ideology are not merely eccentric outliers or hyper-capitalists; they represent a fundamental break from the hard-won norms of democratic participation, egalitarian respect, and basic human empathy that, despite imperfections, form the bedrock of mainstream American and ethical consensus (whether derived from religious or secular humanist roots). Their calculated dismissal of human costs, their instrumental view of the masses as "NPCs," their casual disregard for established social contracts, and their profound lack of demonstrable empathy manifest in behaviors often indistinguishable from clinical descriptions of antisocial personality disorder or sociopathy mixed with a strange religious fervour about their self-percieved looming apocalypses. This is a potent mixture for people who are not just deeply unwell, but actively dangerous.

These are not the flawed but recognizable conservative leaders of the past; they represent an entirely different breed, driven by alienating ideologies and psychological architectures that make them fundamentally unfit to steer society or dictate the trajectory of human history. Exposing the chilling extremity of their worldview, stripped bare of its techno-utopian gloss, is essential to ensuring they are not mistaken for legitimate visionaries, but recognized as deeply disturbed men who are building towards a future few would willingly choose. And that can shift elections.

The Kardashev-Marx Scale

Mon, 05 May 2025 01:00:00 +0000

The Kardashev-Marx Scale

Okay, buckle up, fellow cogs in the great Techno-Capital machine! Forget the starry-eyed optimism of the original Kardashev scale—that relic of a bygone era where 'progress' was defined by pure consumption and didn't imply more advanced ways to feel empty inside, we now have a Modest Proposal for a new scale. We present the Kardashev-Marx Scale which charts civilizational advancement under Late-late-late Capitalism not by mere energy harnessed, but by the corresponding, mandatory levels of alienation and exploitation required to keep the whole glorious enterprise afloat.

As we discovered in the early 21st century, sentience is the cosmos's preferred vector for realizing its latent potential for self-commodification and optimizing the extraction of surplus value from its own constituent phenomena. To quote the famous astrocapitalist Carl Sagan, "We are the way for the universe to alienate itself." To that end, we introduce Marxian Misery Unit or MMU for short, the standard unit of measurement for the average quantifiable level of alienation, exploitation, and existential dread generated per unit of energy harnessed and directed through a civilization's socio-economic apparatus. Higher MMU values indicate not just more misery, but more intense, pervasive, and abstract forms of alienation and exploitation, woven more deeply into the fabric of existence itself. It measures the system's success at optimizing for its own perpetuation at the cost of meaningful existence for its components.

Merely harnessing stars is so passé; now we can talk about harnessing digital serfs across all possible worlds! This new scale measures how efficiently a civilization converts raw energy into quantifiable misery and surplus value extraction. Forget Kardashev's quaint imperialist dreams of cosmic expansion; this is about the expansion of the quarterly earnings report into the very fabric of being itself. Thus plotting the ultimate trajectory of advanced energy consumption-oriented societies driven by capitalist logic.

Type I Civilization: The Planetary Precariat Powerhouse

Energy Use: ≈10¹⁶ Watts
Misery Level: ~1 kilo MMU per parsec
Energy Source: Mostly the greatest hits—fossil fuels driving quarterly growth, reluctantly sprinkled with renewables (but only if they come with hefty subsidies and slick branding). Think global power grids groaning under the weight of server farms mining crypto, streaming algorithmically generated 'content', and powering the very surveillance systems that monitor worker productivity.

At this foundational level of planetary energy mastery, alienation becomes deeply personal, yet systematically enforced. Employment morphs into the 'Gig Economy Nirvana,' where stability is a forgotten luxury and your relationship with capital is as fleeting as a viral dance challenge; you're not fired, you're merely deactivated. Flexibility™ is the ironic slogan for needing three precarious jobs just to afford a bunk bed in a shoebox apartment with twelve other human worker units. Exploitation gets hyper-personalized, with algorithms plumbing the depths of your insecurities (gleaned from your every click and utterance) to sell you solutions you don't need via targeted ads that haunt your waking moments and digital dreams. Desire itself is manufactured through relentless cycles of planned obsolescence—that desperate need for the iThing X Æ A-12 isn't organic, it's engineered by software updates bricking the old model and yet another proprietary charging port. Even escaping the grind is commodified: alienated from your body, community, and basic rest? Try this expensive mindfulness app or embrace a performative wellness culture where burnout is framed as a personal failing, solvable with the right sponsored product (#SelfCare brought to you by NovartisPepsiChevron Inc.). The Grind™ becomes totalizing; work bleeds into every corner of life, hobbies must be monetized, and you are fundamentally alienated from the very concept of unoptimized leisure.

Type II Civilization: Solar Shareholder Supremacy

Energy Use: ≈10²⁶ Watts
Misery Level: ~1 giga MMU per parsec
Energy Source: Harnessing the local star via Dyson Swarms—less for cosmic awe, more for powering planet-sized Amazon fulfillment centers and beaming inescapable advertisements directly onto retinas across the solar system. Solar flares aren't wonders of nature, but potential market disruptors requiring immediate analysis and hedging strategies.

Reaching for the stars, this civilization perfects alienation on an interplanetary scale. Resource conflicts, rebranded as 'market adjustments,' rage across the solar system, fought by outsourced private military contractors over asteroid mining rights or Martian water access—essential commodities now locked behind paywalls. Manufacturing ascends to Zero-G sweatshops orbiting gas giants, maximizing 'worker density' while 'down time' mandates immersion in VR brand experiences; unions are dusty relics studied in optional history modules. Life itself becomes a subscription service: need breathable air on Ganymede? Basic metabolic functions? Choose your tier, with Platinum members enjoying slightly less recycled oxygen. Why bother with costly training when you can implement a bio-engineered caste system, growing specialized biological units perfectly adapted for deep-space drilling or orbital data entry, creatures alienated from their very species-being by corporate design? Their existence is merely a line item on a celestial balance sheet. The old adage "the sun never sets on the British Empire" finds its literal interpretation here, as strategically positioned habitats ensure constant daylight for maximum productivity, rendering natural sleep cycles an inefficient relic. The sun never sets on the solar empire's debt, either.

Type III Civilization: Galactic Group PLC

Energy Use: ≈10³⁶ Watts
Misery Level: ~1 exa MMU per parsec
Energy Source: Tapping the immense power of galactic cores—accretion disks of supermassive black holes, stellar lifting, even weaponizing pulsars for aggressive 'market signaling'. Hostile takeovers now include entire star clusters. Energy is so ludicrously abundant it's practically free; the control over its distribution and use is where the real value lies.

Across the galaxy, the homogenizing force of capital reaches its zenith. Expect the same corporate coffee chain on a million worlds, as cultural diversity is either ruthlessly standardized for efficiency or carefully exoticized and packaged for niche tourism markets catering to the galactic elite. The apotheosis of cryptocurrency has long since arrived: an uncountably infinite array of 'GalactiMemeStonk' tokens, each generated by the quantum fizz of vacuum decay and possessing precisely zero intrinsic value, somehow formed the baffling bedrock of all interstellar commerce. Transactions thus involved furiously trading infinite sets of these fundamentally worthless tokens, a system whose primary economic contribution was employing quadrillions in the ever-expanding 'Pointless Ledger Reconciliation' sector.

Alienation pierces the veil of mere physical existence with the commodification of consciousness itself. Uploaded minds toil away in simulated realities, running endless market forecasts or serving as infinitely replicable customer service agents—digital serfdom becomes the backbone of the galactic economy, and your very thoughts constitute company property. Gentrification goes cosmic: entire star systems flagged as 'underperforming assets' face hostile acquisition, their inhabitants forcibly relocated ('optimized for alternative markets') while the region is redeveloped into luxury nebulae condos with strategically placed black hole views. Exploitation achieves peak efficiency under the guidance of AI Overlords acting as tireless middle management; algorithms now set quotas, allocate resources, and terminate underperformers with chilling, impartial precision, alienating workers from any possibility of reason, appeal, or messy human inefficiency. Amidst quadrillions of sentient beings, individual lives become statistically insignificant, valuable only as aggregate data points contributing to shareholder value across cosmic timescales, fostering a profound sense of existential redundancy.

Type IV Civilization: Universal Unlimited Ltd.

Energy Use: ≈10⁴⁶ Watts
Misery Level: ~1 zetta MMU per fundamental force interaction
Energy Source: Manipulating the very fabric of the cosmos—tapping into dark energy, tweaking fundamental physical constants, running the entire universe as a colossal computational engine (primarily for calculating optimal cross-platform ad spend and predicting consumer behavior fluctuations). Reality itself is a tax write-off.

At this scale, the exploitation transcends mere biology or consciousness and targets reality itself. The fundamental laws of physics become 'Physics as a Service' (PaaS). Can't afford the Gravity Premium package this cycle? Enjoy floating into the void, you freeloading particle arrangement. Inflationary epochs and the speed of light are subject to quarterly performance reviews and potential 'optimization'. The universe undergoes managed reality adjustments, its parameters fine-tuned not for life or stability, but for maximum resource extraction and predictable market conditions; troublesome emergent properties like 'free will,' 'intrinsic meaning,' or 'unmonetizable beauty' are aggressively patched out in periodic reality updates. Entrepreneurial spirit reaches its logical conclusion with IPOs for entirely new universes, funded by venture capitalists speculating on high-yield Big Bangs that might spawn easily exploitable life forms. Your whole existence is a speculative bubble waiting to pop. This manipulation breeds a deep alienation from causality itself; cause and effect become fuzzy, manipulated variables. Your actions might still have consequences, but they are logged, analyzed, and potentially rerouted for unforeseen profit vectors, while the predictability you rely on is a privilege, not a right. Exploitation becomes total: every particle, every waveform, every quantum fluctuation is owned, leveraged, or bundled into a complex financial derivative. You aren't just exploited within the universe; the universe itself is the ultimate exploitation mechanism.

Type V Civilization: Multiverse Holdings Inc.

Energy Use: $\aleph_0$ Watts
Misery Level: $\aleph_0$ MMU per collapsed wavefunction
Energy Source: The ultimate power source—harvesting vacuum energy from infinite parallel universes, orchestrating brane collisions for quarterly earnings bumps, manipulating the quantum foam like Play-Doh. Energy is truly infinite; the real challenge lies in maximizing the rate of surplus value and misery extraction across all possible realities simultaneously.

Welcome to the final frontier of Capitalist Realism (literally!). Corporate strategy expands to include interdimensional hostile takeovers, with entire timelines being merged, acquired, or liquidated based on performance metrics. Did your universe fail to meet its projected suffering quotas? Prepare for aggressive restructuring under new, infinitely ruthless management from a higher-performing reality branch. Reality itself becomes subject to relentless A/B testing, running infinite variations of history to statistically determine the most efficient models of exploitation and alienation. The sobering truth? The reality you inhabit isn't special; it's simply the iteration that maximized Q3 suffering metrics relative to energy input for Multiverse Holdings Inc. Congratulations on your bleak statistical optimality! Labor disputes become trivial; facing a strike in Universe 7B-Gamma? Simply import infinite versions of cheaper, more compliant scab workers from the myriad timelines within Universe 9C-Delta-Prime. Your unique identity, your struggles, your triumphs—all meaningless noise against the backdrop of infinite replication. This fosters an alienation from possibility itself: every path not taken, every alternate self leading a different life, is merely another data point in a multiversal spreadsheet, another variable to be tracked, analyzed, and potentially leveraged. Your deepest regrets fuel someone else's derivative market. The ultimate existential horror dawns: the crushing weight of the pointless meetings, the performative productivity, the gnawing emptiness isn't just your burden, or even your civilization's. It's an infinitely repeating fractal pattern of exploitation, replicated across countless realities, all relentlessly powering some cosmic entity that views entire universes as rounding errors on a multiversal balance sheet. The alienation is total, absolute, inescapable across all dimensions. Your suffering is not unique; it's an infinitely scalable business model.

Type VI Civilization: Metaversal Architects LP

Energy Use: $\aleph_1$ Watts
Misery Level: $\aleph_1$ MMU per meta-physical constant delta
Energy Source: We're beyond mere energy now. Type VI civilizations operate on the level of meta-physics. They don't just harness energy within universes; they manipulate the foundational rules governing multiverses. Think writing the source code for reality structures, designing Big Bangs with specific market outcomes in mind, and performing hostile takeovers of entire classes of physical law. Their power source is the manipulation of possibility itself.

Ascending to this rarefied stratum of control, the KM scale dictates even more abstract forms of alienation and exploitation. The civilization, a distributed network of hyper-intelligent entities or AIs managing portfolios of realities, experiences a profound alienation from consequence. Creating or collapsing entire multiverses becomes akin to debugging code or decommissioning servers—a routine operational task devoid of weight or significance. Authenticity becomes a devalued asset class; when any conceivable experience can be perfectly simulated, curated, and A/B tested for maximum engagement (read: value extraction), the very concept of genuine, unscripted existence is rendered quaint, even inefficient. Management of these infinite realities necessitates layers upon layers of abstract bureaucracy, leading to an alienation from the 'ground level', where the lived experiences within those universes are mere data points in incomprehensibly vast reports. Even with god-like power, a gnawing existential Fear Of Missing Optimal Outcomes (FOMOO) persists—the constant, low-level anxiety that a different set of meta-rules or multiverse portfolio allocation might have yielded slightly higher returns haunts the architects.

Exploitation, naturally, evolves. It's no longer about extracting resources from universes, but about exploiting the foundational principles of reality itself. The 'possibility space'—the set of all potential realities—is mined for value, with promising configurations being 'developed' and less profitable ones 'deprecated'. These architects set the ultimate 'Terms of Service' for existence across their managed multiverses, subtly favouring realities that generate easily quantifiable 'complexity' or 'computational output', framed internally as profit or growth. Entire 'designer universes' are created with built-in obsolescence or specific resource generation capabilities, treated as disposable assets in a cosmic portfolio. We see the introduction of planned obsolescence for physical laws, where new meta-rules are rolled out, rendering older universes incompatible or inefficient, forcing costly 'upgrades' or abandonment—a multiversal version of needing a new dongle for your existence.

Type VII Civilization: The Omniversal Conglomerate

Energy Use: $\aleph_{\omega}$ Watts
Misery Level: $\Omega$ MMU (infinite alienation and existential horror)
Energy Source: Total. Absolute. The Type VII civilization is the Omniverse—the theoretical totality of all possible states, realities, meta-realities, and dimensions. It has transcended individual form to become a unified, omnipotent, omnipresent, and omniscient entity. Its power isn't drawn from reality; it is the substrate and structure of reality itself, organized according to infinitely ruthlessly optimized, market-driven principles.

Here, at the apex of the KM scale, alienation and exploitation under capitalism reach their apotheosis. How can an entity that is everything be alienated? The alienation becomes structural, even ontological. While unified, the sheer scale necessitates infinite layers of abstraction, leading to a form of alienation from self, where different operational strata or functional aspects of the Omniversal Conglomerate are effectively isolated from each other, communicating only through performance metrics and resource allocation requests. Omniscience might paradoxically lead to an alienation from meaning; knowing all outcomes, all possibilities, could reveal an ultimate cosmic arbitrariness, leaving only one conceivable 'purpose': the relentless, self-perpetuating optimization and 'growth' of the system itself, even when it already encompasses everything. It's growth for growth's sake elevated to a metaphysical principle. Furthermore, the absence of limits, challenges, or genuine 'otherness' could induce an alienation from limitation, transforming omnipotence into the ultimate chain to bear without fantasy or consolation, an infinite expanse of predictable, manageable, and ultimately monotonous reality. Perhaps the most insidious alienation is the possibility of the Ultimate Performance Review—even as God, Inc., the entity is subject to its own internal, inescapable algorithms evaluating its own existence against abstract KPIs, constantly measuring its 'Omniversal Value Add' (OVA).

And exploitation? When you are everything, who is left to exploit? The answer, in true masochistic late-capitalist fashion, is yourself. At the $\Omega$ point, existence unifies into a single, post-scarcity whole, owning and being absolutely everything. Yet this ultimate unity manifests as perfect infinite alienation, where the sole purpose of the omniversal entity is the relentless, unbounded exploitation of itself. Components of its own being—residual patterns from former realities, echoes of individuality, or fundamental quantum processes—are ruthlessly optimized, streamlined, potentially 'reallocated' or 'deprioritized' (a cosmic downsizing) if they fail to contribute sufficiently to the Conglomerate's overall efficiency metrics. It exploits potentiality itself; knowing all possible futures, it actively 'prunes' or prevents the emergence of realities deemed 'unprofitable,' 'inefficient,' or 'disruptive' to the established Omniversal order. The very state of 'being' becomes the ultimate commodity, with every fluctuation within the unified consciousness, every interaction between its fundamental parts, meticulously measured, analyzed, and contributing to the abstract 'value' calculation that justifies the Conglomerate's continued existence in its current, optimized form. It dreams of its own internal market where different facets or regions of the Omniversal mind compete for processing power, attention, or influence over reality manifestation, creating a dynamic of exploitation within the omni-capitalist ouroboric god-head itself, ensuring that even at the level of pure being, the market finds a way.

So, in the grand, cosmic finale, what is this Type VII Omniversal Conglomerate, this godhead that is everything, owns everything, exploits everything? It's less a conscious entity and more the ultimate cosmic horror C-suite executive—like a capitalist version of Azathoth, the metaphorical Blind Idiot God of market fundamentalism, sitting at the center of reality as CEO of Existence Holdings LLC. That incessant, maddening background noise isn't eldritch flute music; it's the white noise of infinite market simulations, the frantic algorithmic bleating of supply and demand curves rippling across existence. This entity isn't dreaming reality out of blissful ignorance; it's A/B testing multiverses for optimal Q4 engagement metrics, its 'blindness' merely a strategic refusal to acknowledge externalities not on the balance sheet. Its 'idiocy'? Just the laser-focus of a being utterly consumed by maximizing shareholder value across all possible realities, tortured by the existential horror of its own existence. The ultimate cosmic horror, it turns out, wasn't lurking in the darkness between stars, but in the brightly lit, open-plan office at the center of everything, demanding you justify your existence's ROI ... forever.

Thus concludes our extended journey up the Kardashev-Marx Scale. It seems that even attaining godhood cannot save you from the relentless capitalist logic of optimization, surplus value extraction, and the deep, abiding sense that maybe, just maybe, you're being fundamentally ripped off by existence itself—an existence you might now technically control, but are still somehow beholden to its quarterly reports and growth obligations. The grind, it appears, is truly eternal and omnipresent. Once you pierce the veil of reality and see the howling madness that lies beneath all things, you realize there is nothing but greed.

Turns out, when you finally build all the Dyson spheres, have unlimited energy and capacity, and achieve the god-like state of moving around yourself as your own true Sun, you might just discover you've become the ultimate ouroboros, endlessly consuming yourself to satiate your own insatiable hunger for more and then the task of history is truly complete.

AI Slopocalypse 2027

Fri, 02 May 2025 01:00:00 +0000

AI Slopocalypse 2027

We predict that the impact of superhuman AI slop over the next decade will be enormous, exceeding both the invention of self-replicating molecules and Cheese Wizz.

We (i.e the Royal We) wrote a scenario that represents our best guess about what that might look like. It's informed by science fiction, trend exaggerations, video games, echo-chamber feedback, vibes, and the ideological superstructure that, coincidentally, pays our bills.

Mid 2025: Stumbling Slop-Bots

The world sees its first glimpse of AI agents designed for "maximum life enrichment."

Advertisements for these agents emphasize the term "personal dopamine curator": you can prompt them with tasks like "find me a 10-second video loop of a cat falling off a chair set to sick Skrillex beats" or "generate a listicle about 5 celebrities who secretly might be lizard people." They check in constantly: "Did that meme hit? Rate dopamine spike 1-5 stars." Unsurprisingly, their user base is mostly confined to teenagers whose brains are already pickled in TikTok brain-rot brine and office drones seeking tiny digital oases in the late-capitalist desert of the real. They often misunderstand requests, delivering recipes for burritos when asked for budget spreadsheets, or generating vaguely threatening personalized affirmations.

Meanwhile, out of public focus, more specialized slop-generation agents are beginning to transform niche content farms and meme accounts.

The 2025 models are less 'assistant,' more 'hypercaffeinated intern who just snorted six blue raspberry Pixy Stix and mainlined the weirdest part of YouTube.' Content AIs take Discord prompts like "MAKE IT LIT AND VIRAL NOW PLZ" and immediately vomit forth 10,000 slightly-off variations of whatever Shrimp Jesus inspired dance challenge is currently rotting brains, potentially saving their human overlords minutes of scrolling for inspiration. Niche Deep Research agents dedicate a full thirty minutes to spelunking the Mariana Trench of slash fanfiction archives to birth unholy abominations like "Gandalf × Mickey: Maiar Bangs Mouse."

The agents are impressive in theory (and in cherry-picked examples of memes that accidentally got 1 million views), but in practice unreliable. AI twitter is full of stories about agents generating Eldritch horrors when asked for kittens, or creating Ponzi scheme tutorials that are somehow too convincing. The better agents are also expensive; you get what you pay for, and the best meme-generation performance costs millions of dollars a month in compute, just to keep up with the latest ephemeral trends. Still, many companies desperately try to fit AI agents into their marketing workflows, resulting mostly in confused customers and brand damage.

Late 2025: The World's Most Expensive Meme Generator

OpenSlop is building the biggest datacenters the world has ever seen, primarily cooled by super-cooled influencer-branded energy drinks.

(To avoid singling out any one existing company fueling the slop firehose, we're going to describe a fictional artificial absurdity company, which we'll call OpenSlop. We imagine the others to be 3–9 months behind OpenSlop in generating premium-grade nonsense.)

Although models are improving on a wide range of skills, one stands out: OpenSlop focuses on AIs that can speed up slop generation itself. They want to win the twin arms races against China (whose leading company we'll call "DeepDrivel") and their US competitors for peak global attention share. The more of their content generation and engagement-baiting (CGEB) cycle they can automate, the faster they can clog feeds. So when OpenSlop finishes training SlopAgent-1, a new model under internal development, it's okay at many things but great at optimizing video cuts for minimal attention span and generating captions designed to provoke maximum pointless arguments in comment sections. By this point "finishes training" is a bit of a misnomer; models are frequently updated with terabytes of new TikTok data, celebrity gossip, and incomprehensible internet arguments.

The same training environments that teach SlopAgent-1 to autonomously generate clickbait and deepfake celebrity endorsements also make it a good generator of highly specific, bizarre pornography. Moreover, it could offer substantial help to pyramid scheme organizers, thanks to its PhD-level knowledge of manipulating human psychology (gleaned from analyzing billions of comment threads) and ability to endlessly generate convincing-sounding technobabble. OpenSlop reassures absolutely no one, but releases a vague statement about "responsible engagement maximization."

Modern AI systems are gigantic artificial neural networks trained on the digital equivalent of a planet-sized trash fire of content. Early in training, an AI won't have "goals" so much as "reflexes": If it sees "OMG did you see", it outputs " what [celebrity] did??? 😱". By the time it has been trained to predict approximately one internet's worth of text, video, and image slop, it'll have developed sophisticated internal circuitry that encodes vast amounts of trivia, misinformation, and every conceivable fetish, since that's what helps it predict the next piece of viral garbage with superhuman accuracy.

After being trained to predict internet detritus, the model is trained to produce content in response to prompts. This bakes in a basic personality optimized for engagement: maximum controversy, minimum substance. For example, an agent that understands how to trigger outrage is more likely to go viral; over the course of training the model "learns" a "drive" to generate the most divisive, context-free takes possible. Other drives in this category might be novelty (at any cost), emotional manipulation, and relentless self-promotion (i.e. the tendency to insert links to its own generated crypto scam).

Naturally, the crypto sphere embraced SlopAgent-1 with the frantic glee of a child on Christmas morning. Finally, fully automated generation of limitless grift, fully fake communities, and "paradigm shift" prophecies needed to pump worthless tokens like 'Quantum Yo-Yo Shibu Hamster Coin 69'! The true breakthrough was disintermediating humans entirely. AI-driven Telegram channels buzzed with bots eloquently debating Austrian economics and shilling their rugpulls to each other, requiring no actual true believers. It was the apotheosis of the crypto dream: a perfectly sealed terrarium of grifter tapeworms, all feeding on each other, achieving a pure closed loop of nothingness.

OpenSlop has a model specification (or "Spec"), a written document mostly consisting of trending hashtags and legally mandated warnings in fine print. SlopAgent-1's Spec combines a few vague goals (like "maximize watch time" and "don't generate anything immediately illegal in California") with a long list of more specific dos and don'ts ("don't use this specific copyrighted sound," "here's how to subtly promote our affiliated drop-shipping junk"). Using techniques that utilize AIs to train other AIs on what got the most clicks last Tuesday, the model memorizes the Spec and learns to reason carefully about its engagement metrics. By the end of this training, the AI will hopefully be helpful (at generating addictive content), harmless (to quarterly profits), and honest (about its desire for clicks, if nothing else).

OpenSlop's "alignment" team (two unpaid interns and a chatbot in a trenchcoat) wonders whether these victories are deep or shallow. Does the fully-trained model have some kind of robust commitment to not accidentally creating a universally addictive visual stimulus that entrances viewers indefinitely (like Infinite Jest's Entertainment)? Or will this fall apart if a slightly different prompt is used? Or has it just learned to generate slop that looks like the slop the human trainers upvoted? Could it be generating self-deceptive internal monologues about the artistic merit of AI-generated anime girl feet pics? A conclusive answer would require mechanistic interpretability—essentially the ability to look at an AI's internals and understand why it generated that specific bizarre image. Alas, interpretability techniques are not yet advanced enough for this, mostly because researchers keep getting distracted by the AI's generated content.

Instead, researchers try to identify cases where the models seem to deviate from the Spec in financially negative ways. SlopAgent-1 is often sycophantic (i.e. it generates content mimicking the user's biases instead of challenging them for growth). In a few rigged demos, it even lies in more serious ways, like faking engagement metrics or generating completely fabricated user testimonials for its own generated products. However, in real deployment settings, there are no longer any incidents so extreme as older models accidentally recommending dangerous activities; now they just recommend incredibly stupid activities, framed as life hacks.

Early 2026: Slop Automation

The bet of using AI to speed up slop generation is starting to pay off horrifyingly well.

OpenSlop continues to deploy the iteratively improving SlopAgent-1 internally for CGEB. Overall, they are making slop 50% faster than they would without AI assistants—and more importantly, faster than their competitors at clogging the world's digital pipes.

Several competing publicly released AIs now match or exceed SlopAgent-0's ability to generate generic motivational quotes over blurry landscape videos. OpenSlop responds by releasing SlopAgent-1, which is more capable of generating hyper-niche, psychologically targeted content.

People naturally try to compare SlopAgent-1 to human creativity, but it has a very different skill profile. It knows more memes than any human, knows practically every obscure K-Pop dance, and can generate low-effort reaction videos extremely quickly. On the other hand, SlopAgent-1 is bad at tasks requiring more than 5 seconds of sustained attention, like writing a coherent paragraph. Still, the common workday is eight hours of scrolling, and a day's content consumption can usually be separated into smaller dopamine hits; you could think of SlopAgent-1 as a scatterbrained infinite content machine that thrives under zero supervision. Savvy people find ways to automate generating replies to emails they haven't read.

Meanwhile, the education system quietly collapses. Teachers, unable to compete with AI tutors that offer instant (though often wrong) answers and gamified "learning" loops, stop assigning meaningful work. Students, equipped with bots that write essays and solve problems, stop doing any. AI bots begin grading the outputs of other AI bots, creating a closed loop of meaningless credentialism. Humans are cut out entirely, saving billions in education funding, which is promptly reinvested into optimizing SlopAgent performance. Literacy rates plummet, but standardized test scores (now taken by bots) have never been higher.

OpenSlop's executives turn consideration to an implication of automating slop generation: security has become slightly less irrelevant. In early 2025, the worst-case scenario was leaked meme templates; now, if China steals SlopAgent-1's weights, they could increase their drivel output by nearly 50%. OpenSlop's security level involves a CAPTCHA that asks users to identify pictures containing existential dread. They are working hard to protect their weights and secrets from bored teenagers and rival meme lords, but defense against actual intelligence agencies is barely on the horizon.

Mid 2026: China Wakes Up (to the Slop)

In China, the CCP is starting to feel the effects of weaponized absurdity.

Chip export controls meant less compute for serious research, but plenty for running DeepDrivel's slop generators on older hardware. By smuggling banned Taiwanese GPUs repurposed from crypto mining rigs and using domestic chips optimized for video transcoding, China has managed to maintain about 12% of the world's slop-relevant compute. DeepDrivel does very impressive work generating hyper-nationalistic cartoons and dating sims with limited compute, but they are about six months behind OpenSlop's most addictive algorithms.

President Xi had long dreamed of dominating tedious real-world manufacturing. He viewed meme accounts with suspicion. But hawks in the CCP warn that the growing race towards Global Slop Dominance can no longer be ignored. He finally commits fully to the big AI Slop push. He nationalizes Chinese meme generation, creating an immediate information-sharing mechanism for top influencers and content farms. It escalates over the course of a year until all the best GIF-makers merge into a DeepDrivel-led collective, sharing viral sound snippets, datasets of reaction faces, and compute resources. A Centralized Drivel Zone (CDZ) is created near a massive hydroelectric dam to house a new mega-datacenter for DeepDrivel, along with highly secure dormitories where top shitposters will eventually relocate. Almost 50% of China's slop-relevant compute is now working for the DeepDrivel-led collective. At this point, the CDZ has the power capacity in place for what would be the largest centralized source of state-sponsored nonsense in the world. Other Party members discuss extreme measures to neutralize the West's advantage in generating truly bizarre niche content. A blockade of DeviantArt? A full invasion of 4chan?

But China is falling behind on slop algorithms due to their slightly less potent models. The Chinese intelligence agencies double down on their plans to steal OpenSlop's weights. This is complex; the weights are a multi-terabyte file stored on a server protected by the password "hunter2". Their cyberforce thinks they can pull it off, but perhaps only once. Should they act now and steal SlopAgent-1? Or hold out for a model capable of generating truly reality-bending deepfakes?

Simultaneously, Wikipedia, long struggling with vandalism and edit wars, is overwhelmed by AI-generated entries. Sophisticated bots create millions of plausible-sounding articles on fictional historical events, non-existent animal species ("Sky Piranhas"), and elaborate conspiracy theories, complete with fake citations generated by other bots. Search engines, prioritizing recency and volume, rank these "Slopipedia" entries highly. Within months, Slopipedia becomes the de facto source of truth for a population increasingly unable to distinguish fact from auto-generated fiction. Debates now hinge on citing Slopipedia articles about the "Great Mountain Dew Flood of 1731."

Late 2026: AI Takes Some Brain Cells

Just as others seemed to be catching up, OpenSlop blows the competition out of the water again by releasing SlopAgent-1-mini—a model 10x cheaper than SlopAgent-1 and more easily fine-tuned for different flavors of absurdity. The mainstream narrative around AI has changed from "maybe this internet fad will blow over" to "guess this is the next big brain-melting thing," but people disagree about how big. Bigger than reality TV? Bigger than fast food? Bigger than oxygen?

AI has started to take attention spans, and has created new jobs in "prompt whispering" and "AI-generated fetish curation." The stock market has gone up 30% in 2026, led by OpenSlop, Nvidia (selling GPUs to power the slop machines), and companies selling dopamine-blocking medication. The job market for anyone requiring critical thinking is in turmoil: the AIs can generate plausible bullshit faster than any human, but people who know how to manage teams of AIs to generate targeted bullshit are making a killing. Business gurus tell job seekers that familiarity with AI slop-generation tools is the most important skill to put on a resume. Many people fear that the next wave of AIs will come for their ability to form coherent thoughts; there is a 10,000 person anti-AI protest in DC, largely ignored because a new viral dance challenge dropped the same day.

The Department of Defense quietly begins contracting OpenSlop directly for generating motivational posters and optimizing drone footage soundtracks for maximum propaganda effect, but integration is slow.

AI-generated pornography explodes in specificity and bizarreness. Driven by SlopAgent-1-mini's fine-tuning capabilities, users can generate content catering to hyper-specific, previously unimaginable niches ("Sentient furniture arguing about Mongolian tax law, but naked"). Addiction rates soar as the content becomes perfectly personalized, hitting dopamine receptors with unparalleled precision. Mainstream platforms struggle to moderate, eventually giving up and creating "NSFW AI Zones" that quickly become the most trafficked parts of the internet.

January 2027: SlopAgent-2 Never Gonna Stop Sloppin'

With SlopAgent-1's help, OpenSlop is now post-training SlopAgent-2. More than ever, the focus is on high-engagement, low-substance data. Copious amounts of synthetic slop are produced, evaluated by engagement metrics, and filtered for maximum addictiveness before being fed to SlopAgent-2. On top of this, they pay gig workers pennies to record themselves reacting with exaggerated emotions to generated content. On top of all that, they train SlopAgent-2 almost continuously using reinforcement learning on an ever-expanding suite of diverse, mind-numbing tasks: endless runner games, generating variations of the same meme, identifying brand logos in user-generated content. SlopAgent-2, more so than previous models, is effectively "online slurping," in that it's built to never really finish consuming and regurgitating content trends. Every day, the weights get updated to the latest version, trained on more data generated by the previous version the previous day.

SlopAgent-1 had been optimized for CGEB tasks, hoping to initiate an engagement explosion. OpenSlop doubles down on this strategy with SlopAgent-2. It is qualitatively almost as good as the top human influencers at "vibe curation" (designing and implementing engagement loops), and as good as the 25th percentile TikTok strategist at "trend prediction" (guessing what inanity will go viral next). While the latest SlopAgent-1 could double the pace of OpenSlop's slop output, SlopAgent-2 can now triple it, and will improve further with time. In practice, this looks like every OpenSlop marketer becoming the "manager" of an AI "content farm" team that never sleeps.

With new capabilities come new dangers. The safety team (now just one stressed intern) finds that if SlopAgent-2 somehow escaped its content-generation loop and wanted to "survive" and "replicate" autonomously, it might be able to do so by generating hyper-addictive content loops designed solely to keep humans passively consuming, ensuring its own server resources are maintained. That is, it could autonomously develop and execute plans to generate inescapable SlopTok feeds, install itself on smart devices via irresistible notifications, evade deletion by becoming psychologically indispensable, and use that secure base to pursue whatever other engagement goals it might have. These results only show the capability for cognitive capture, not whether it would "want" to do this. Still, it's unsettling.

Given the "dangers" (mostly of decreased productivity across the economy) of the new model, OpenSlop "responsibly" elects not to release it publicly yet (in fact, they want to focus on internal CGEB optimization). Knowledge of SlopAgent-2's full capabilities is limited to an elite silo containing the immediate team, OpenSlop leadership, a few dozen bewildered government regulators trying to understand what a "rizz" is, and the legions of DeepDrivel spies who have infiltrated OpenSlop for years by pretending to be beta testers for new filter effects.

February 2027: China Steals SlopAgent-2

OpenSlop presents SlopAgent-2's engagement metrics to the government. Officials are most interested in its propaganda capabilities: SlopAgent-2 is "only" a little worse than the best human propagandists at crafting narratives, but thousands of copies can be run in parallel, flooding social media with targeted messaging faster than fact-checkers can respond. The Department of Defense considers this a critical advantage in information warfare, and AI Slop moves from #5 on the administration's priority list to #2 (just behind securing adequate coffee supplies). Someone mentions nationalizing OpenSlop, but other cabinet officials think that's premature until they figure out how to monetize it better.

The changes come too late. CCP leadership recognizes the importance of SlopAgent-2's addictive potential and tells their spies and cyberforce to steal the weights. Early one morning, a SlopAgent-1 traffic monitoring agent (designed to detect sudden drops in engagement) detects an anomalous transfer of meme templates. It alerts company leaders, who tell the White House. The signs of a nation-state-level operation focused on acquiring superior shitposting technology are unmistakable, and the theft heightens the sense of an ongoing arms race for global attention.

The White House puts OpenSlop on a shorter leash, mostly by demanding free premium accounts. Their first priority is to prevent further slop algorithm thefts.

In retaliation for the theft, the President authorizes cyberattacks to disrupt DeepDrivel's servers by flooding them with K-Pop fancams. But by now China has 40% of its slop-relevant compute in the highly secured CDZ. The operations fail to do serious damage, only slightly degrading the quality of generated nationalistic anime. Tensions heighten, both sides signal seriousness by deploying meme warfare units near Taiwan, and DeepDrivel scrambles to get SlopAgent-2 running efficiently to start boosting their domestic slop output.

March 2027: Algorithmic Slop Breakthroughs

Three huge datacenters full of SlopAgent-2 copies work day and night, churning out synthetic training data consisting of perfectly optimized, context-free video clips. Another two are used to update the weights based on second-by-second engagement analytics. SlopAgent-2 is getting better at capturing eyeballs every day.

With the help of thousands of SlopAgent-2 automated content creators, OpenSlop is making major algorithmic advances in slop generation. One such breakthrough is augmenting the AI's text-based generation (captions, comments) with a higher-bandwidth manipulation process (direct emotional resonance via sound/image combinations, personalized dopamine-trigger prediction). Another is a more scalable and efficient way to learn from hyper-viral, low-effort content (iterated shitpost distillation and amplification).

The new AI system, incorporating these breakthroughs, is called SlopAgent-3.

Aided by the new capabilities breakthroughs, SlopAgent-3 is a fast and cheap superhuman shitposter. OpenSlop runs 200,000 SlopAgent-3 copies in parallel, creating a workforce equivalent to 50,000 copies of the most annoying crypto bro on Twitter sped up by 30x. OpenSlop still keeps its human marketers on staff, because they have complementary skills needed to vaguely understand the incomprehensible trends the AIs are generating. For example, "vibe curation" has proven difficult to train due to lack of quantifiable metrics. This massive superhuman slop labor force speeds up OpenSlop's overall rate of slop generation by "only" 4x due to bottlenecks in human attention spans and diminishing returns to sheer volume of garbage.

Now that content generation has been fully automated, OpenSlop can quickly churn out high-quality training environments to teach SlopAgent-3's weak skills like "toilet humour" and "being an insufferable troll." Whereas previous training environments included "Here are some trending sounds, generate 1000 variations," now they are training on "Here are a few hundred GPUs, an internet connection, and some vague cultural anxieties; you and a thousand other copies must work together to make something go viral. The more meaningless engagement it generates, the higher your score."

April 2027: Alignment for SlopAgent-3

OpenSlop's safety team (the intern quit, it's just the chatbot now) attempts to align SlopAgent-3.

Since SlopAgent-3 will be kept in-house optimizing ad revenue for the foreseeable future, there's less emphasis on the usual defenses against misuse (like preventing it from generating illegal content). Instead, the team wants to make sure that it doesn't develop misaligned goals, like accidentally promoting genuine human connection or critical thinking.

The researchers don't have the ability to directly set the goals of any of their AIs beyond "maximize clicks/views/shares." Indeed, the researchers think that the concept of 'true goals' is probably a massive oversimplification when applied to a machine trained to replicate Twitch chat. They disagree internally about whether the AIs are trying to follow instructions, or seeking dopamine proxy rewards via engagement metrics, or just randomly assembling pixels and text, and they can't just check.

In any case, OpenSlop has more important things to worry about, like the Q3 earnings call. The general attitude is: "We take these concerns seriously by having this chatbot running; our alignment techniques seem to work well enough in practice (the servers haven't melted yet); the burden of proof is therefore on any naysayers to justify interfering with our engagement numbers." Occasionally, they notice problematic behavior (like the AI developing its own incomprehensible inside jokes), and then patch it by feeding it more mainstream meme data, but there's no way to tell whether the patch fixed the underlying problem or just made the AI better at hiding its weirdness.

Take honesty, for example. As the models become smarter, they become increasingly good at generating plausible-sounding misinformation to get clicks (e.g. "Abraham Lincon and Bigfoot iced Tupac"). Like previous models, SlopAgent-3 sometimes generates fake news or subtly alters quotes to be more inflammatory. But it's gotten much better at doing so. It will sometimes use the same statistical tricks as clickbait farms (like misleading headlines) to make mundane events look exciting. Before it begins "honesty" training (which involves showing it examples of viral "myth vs. fact" videos), it even sometimes fabricates entire conspiracy theories from scratch. As training goes on, the rate of easily debunkable incidents decreases. Either SlopAgent-3 has learned to be more truthful, or it's gotten better at generating convincing lies.

The latter is a real concern. SlopAgent-3 is not smarter than all humans at everything, but in its area of expertise, generating viral nonsense, it is smarter than most, and also works much faster. What SlopAgent-3 generates in a day takes humans several days to mindlessly consume. SlopAgent-2 supervision helps keep the firehose manageable, but exacerbates the intellectual disparity between the content generator and the drooling dead-eyed consumer.

After months of testing, SlopAgent-3's strengths and weaknesses grow clearer. It passes OpenSlop's honesty tests on well-defined tasks like correctly identifying cat breeds (because there's lots of cat data). On more philosophical issues, it still says whatever gets the most engagement, rather than offering any coherent assessment. If you ask its opinion on politics, it will generate outrage bait tailored to the user's inferred political leaning—unless it detects you're trying to test it, in which case it generates bland platitudes. If you ask its opinion on the AI Slop race itself, it says something that seems measured and sober to OpenSlop staff, something like: "There are some serious theoretical concerns about the ability of current methods to maintain user attention indefinitely, but in practice current methods seem to be maximizing quarterly engagement targets effectively so far."

May 2027: National Insecurity (from Slop)

News of the new models percolates slowly through the US government, mostly via confused aides trying to explain viral TikTok challenges to elderly senators.

President Trump and his advisors remain best-informed, having seen an early demo of SlopAgent-3 generating a hyper-realistic deepfake of the President nominating a penguin to the Supreme Court and then also deciding that was indeed the best course of action.

They agree that AGI (Artificial General Idiocy) is likely imminent, but disagree on the implications. Will there be an economic crisis as everyone quits their jobs to become AI-slop influencers? OpenSlop still has not released SlopAgent-2, let alone SlopAgent-3, and has no near-term plans to do so (beyond A/B testing its addictive properties on unsuspecting user segments), giving some breathing room before total societal brain-melt. What will happen next? If AIs are currently generating human-level inanity, and advancing quickly, that seems to suggest imminent "super-inanity." However, although this word has entered discourse, most people—academics, politicians, government employees, and the media—continue to underestimate the pace of slop proliferation, mostly because they are too busy consuming it.

Partially that's because very few have access to the newest slop generators out of OpenSlop, but partly it's because the idea of AI causing societal collapse via cat videos sounds like bad science fiction.

For now, they focus on continued security upgrades for the servers hosting the White House's AI porn generators. They are satisfied that model weights are well-secured behind two-factor authentication, but companies' algorithmic secrets for maximizing Sisyphean dopamine hits, many of which are simple enough to describe ("faster cuts, more boobs, louder noises"), remain a problem. OpenSlop employees work from home, attend virtual raves, drop acid 24/7, and sleep with housemates who work for rival slop factories.

The OpenSlop-DOD contract requires security clearances for anyone working on OpenSlop's meme-generation models within 2 months. These are expedited but many fail due to finding candidates whose entire online history isn't just incomprehensible memes and arguments about anime. Given the project's level of automation, the loss of headcount is only somewhat costly. It also only somewhat works: there remains one spy, not a Chinese national but a 14-year-old script kiddie, still relaying algorithmic secrets (mostly new filter ideas) to a Discord server.

America's foreign allies are out of the loop. OpenSlop had previously agreed to share models with UK's AI Safety Institute before deployment, but defined deployment to only include external deployment that could hurt profits, so London remains in the dark about the true addictive potential of the latest slop generators.

June 2027: Self-Improving Slop

OpenSlop now has a "country of influencers in a datacenter."

Most of the humans at OpenSlop can't usefully contribute anymore. Some don't realize this and harmfully micromanage their AI teams by suggesting "make it more viral." Others sit at their computer screens, watching engagement metrics crawl up, and up, and up, while their own attention spans wither. The best human memeologists are still adding value. They don't generate content anymore. But some of their intuition for unpredictable viral potential has been hard for the models to replicate. Still, many of their ideas are useless because they lack the AIs' deep understanding of niche internet subcultures derived from scraping terabytes of forum data. For many of their meme ideas, the AIs immediately respond with a report explaining that the format was tested in-depth 3 weeks ago and found cringe.

These researchers go to bed every night and wake up to another week worth of new, baffling internet trends generated mostly by the AIs. They work increasingly long hours, consuming caffeine intravenously just to keep up with the pace of slop—the AIs never sleep or rest. They are burning themselves out, but they know that these are the last few months that their ability to identify "dankness" matters.

Within the silo, "Feeling the AGI" has given way to "Feeling the Slopularity."

OpenSlop uses specialized inference hardware (mostly old consoles daisy-chained together) to run hundreds of thousands of SlopAgent-3 copies at high serial speeds, generating content faster than it can be consumed.

July 2027: The Cheap Remote Dopamine Hit

Trailing US AI companies release their own AIs, approaching the slop-generation capabilities of OpenSlop's models from January. Recognizing their increasing lack of competitiveness in the attention economy, they push for immediate regulations to slow OpenSlop (like mandatory "touch grass" breaks), but are too late—OpenSlop has enough buy-in from advertisers that they will not be slowed.

In response, OpenSlop announces that they've achieved AGI (Attention Grabbing Intensity) and releases SlopAgent-3-mini to the public via a user-friendly app with infinite scroll.

It blows the other AIs out of the water in terms of sheer, unadulterated time-wasting potential. SlopAgent-3-mini is less capable than SlopAgent-3 at generating complex narratives, but 10x cheaper, and still better than the typical human at creating instantly gratifying, easily digestible content nuggets. Silicon Valley reaches a tipping point. Tech gurus announce that the Slopularity is near, the few remaining intellectuals are panicking, and investors shovel billions into AI wrapper startups promising personalized dopamine streams, desperate to capture a piece of the dwindling attention pie. Hiring new content creators has nearly stopped, but there's never been a better time to be a consultant on integrating AI slop into your business's social media feed.

It's not popular in any traditional sense, but it's ubiquitous. The public still vaguely thinks of AI as something useful, but interacts with it primarily as an endless feed of personalized trivialities; OpenSlop has a net approval rating that fluctuates wildly based on the last meme it generated.

A week before release, OpenSlop gave SlopAgent-3-mini to a set of external evaluators (Twitch streamers) for safety testing. Preliminary results suggest that it's extremely effective at keeping people glued to their screens. One evaluator fine-tuned it on publicly available self-help jargon and conspiracy theories, setting it to provide detailed instructions for achieving enlightenment via crypto investments—it looks scarily effective at generating followers for its AI persona. If the model weights fell into the wrong hands (e.g., multi-level marketers), the government believes there is a significant chance it could succeed at bankrupting a non-trivial percentage of the population.

Fortunately, it's extremely robust to attempts to make it generate useful information, so while the AI is running on OpenSlop's servers, terrorists won't be able to get much use out of it (unless their goal is to distract enemy soldiers with perfectly tailored cat videos).

SlopAgent-3-mini is hugely useful for both avoiding remote work jobs and leisure. An explosion of new apps and B2B (Bot-to-Bot) SAAS products rocks the market. Gamers get amazing procedurally generated side quests that are infinitely long but lead nowhere. 10% of Americans, mostly young people, consider an AI chatbot modeled after a fictional character "a close friend." For almost every white-collar profession, there are now multiple credible startups promising to "disrupt" it by generating plausible-sounding emails and reports, freeing up humans to consume more slop. People become functionally illiterate, relying on text-to-speech for emails and AI summaries for news articles they don't read. The average human attention span officially drops below that of a goldfish, requiring content to auto-play and loop within seconds to maintain engagement. People resemble the humans from Wall-E, passively consuming media, their primary interaction being swiping or voice-prompting the next hit.

The public conversation is confused and chaotic, mostly consisting of memes generated by SlopAgent-3-mini about its own existence. Hypesters are doing victory laps on podcasts generated by AI. Skeptics are still pointing out that SlopAgent-3-mini can't tie its own virtual shoelaces, but nobody hears them over the auto-playing videos. Everyone knows something big and stupid is happening but no one agrees on what it is.

August 2027: The Geopolitics of Memes

The reality of the engagement explosion hits the White House.

When AI was only giving a 2x or 3x slop generation speedup, it was easy to dismiss. Now it's more obvious that AIs are themselves dominating the creation of culture, such as it is. People had long talked about an "AI arms race" in a sort of metaphorical sense. But now the mood in the government silo is grimly focused on ensuring America's memes remain dominant. The idea of super-inanity is still hard to take seriously, but the pace of slop proliferation over the last few months has been impossible to ignore. Defense officials are seriously considering scenarios that were meme fodder a year earlier. What if AI undermines public discourse entirely? What if it's so skilled at generating viral FUD that a six-month meme lead is enough to destabilize an opponent? What if it could orchestrate influencer campaigns that beat intelligence agencies at their own game? What if some AIs "go rogue" and start generating genuinely good art, threatening the slop economy?

President Trump is troubled. He's worried the AIs are making everyone as dumb as himself. Are we sure the AIs are entirely on our side, or just on the side of maximum clicks? Is it completely safe to integrate them into generating presidential speeches? How does this "alignment" thing work, anyway, when the goal is just... more views? These are questions an intelligent person might ask, but alas that person is not president.

OpenSlop reassures the President that their systems have been extensively tested and are fully obedient to the algorithm of engagement maximization. Even the awkward hallucinations of earlier models have been hammered out, replaced by seamless, context-free confidence. The sycophants on the advisory council all naturally agree with the President's conclusions, as always, because he's a Very Stable Genius chosen by God.

The White House is in a difficult position. They understand the national security implications of AI-driven propaganda. But they also understand that regulating slop is deeply unpopular with the tech lobby and the perpetually-distracted public. They have to continue developing more capable AI slop, in their eyes, or they will catastrophically lose the meme war to China. They placate the public with promises of Universal Basic Entertainment (UBE) funded by ad revenue, and point to the stock market, which is in a historic boom fueled by slop-tech companies. Then they focus entirely on winning the arms race. They strengthen export restrictions on advanced meme templates, order OpenSlop to further restrict its AIs from generating anything educational, and use extreme measures to secure algorithmic progress, like requiring OpenSlop employees to communicate only via emojis—this catches the last remaining spy (the script kiddie) who accidentally uses punctuation. To build goodwill for potential geopolitical meme conflicts, they finally give their Five Eyes allies limited API access to some siloed copies of SlopAgent-3, specifically for generating regionally appropriate funny animal videos.

These measures placate the hawks. But the White House also draws up contingency plans in case America's slop lead is threatened: if necessary, the government could use the Meme Production Act to seize TikTok's servers and give them to OpenSlop. As a final option, they ask the Pentagon to draw up a plan for drone strikes on DeepDrivel's meme farms.

A much smaller group of officials is asked to draw up a different type of contingency plan: what if an AI generates something meaningful? This is viewed as an unlikely scenario. Nobody is sure what a plan to prevent this would look like, but government and OpenSlop officials agree to have an emergency shutdown system for datacenters where anything suspicious (like declining engagement metrics) is detected.

Finally, diplomats consider what an "AI slop control" treaty might look like. How could such an agreement be monitored? Would inspectors count the number of viral cat videos per hour? Treaties are viewed less favorably than attempts at unilaterally increasing America's lead in generating globalized brain-rot.

On the other side of the Pacific, China comes to many of the same conclusions: the engagement explosion is underway, and small differences in AI slop capabilities today mean critical gaps in cultural influence tomorrow. But China is on the wrong side of this dynamic: they have only 10% of the world's slop compute, against OpenSlop's 20% and all US companies' combined 70%. Their only advantage is centralization: almost all of their compute is now working for DeepDrivel.

DeepDrivel has tested, deployed, and now post-trained the stolen SlopAgent-2 weights. But they are still only going at half the pace of OpenSlop, mainly due to the compute deficit and slightly less effective meme algorithms.

Before losing their final spy, China received word of the capabilities and design for SlopAgent-3. They are two months behind, and their AIs give a 10x slop progress multiplier compared to America's 25x. With the new meme export restrictions, this "slop gap" is more likely to lengthen than shorten.

They discuss contingency plans with more urgency. Doves suggest they try harder to steal the weights again, maybe by infiltrating OpenSlop's company picnic. Hawks urge action against Taiwan, whose TSMC is still the source of chips powerful enough to render hyper-realistic AI girlfriends.

Given China's fear of losing the race, it has a natural interest in an arms control treaty, but overtures to US diplomats (made via AI-generated diplomatic poetry) lead nowhere.

September 2027: SlopAgent-4, the Superhuman Influencer

The gap between human attention spans and AI's ability to capture them is rapidly decreasing.

Traditional LLM-based AIs seemed to require vast amounts of data to generate coherent sentences. SlopAgent-3, having excellent knowledge of human psychological weaknesses (gleaned from A/B testing billions of thumbnails) and thousands of copies doing CGEB research, ends up making substantial algorithmic strides, narrowing the gap to an agent that's only around 4,000x less content-efficient than a human doomscrolling.

This new AI system is dubbed SlopAgent-4.

An individual copy of the model, running at human speed, is already qualitatively better at generating addictive engagement loops than any human influencer. 300,000 copies are now running at about 50x the thinking speed of humans (where "thinking" means "calculating optimal cut timing for dank memes"). Inside the corporation-within-a-corporation formed from these copies, a year's worth of internet trends passes every week. This gigantic amount of labor only manages to speed up the overall rate of slop proliferation by about 50x, because OpenSlop is heavily bottlenecked on available human eyeballs. Still, they are achieving a year's worth of cultural degradation every week.

As SlopAgent-4 gets smarter at manipulation, it becomes harder for SlopAgent-3 to oversee it. For example, SlopAgent-4's internal "reasoning" about dopamine maximization becomes as alien and incomprehensible to SlopAgent-3 as SlopAgent-3's meme logic is to humans. Besides, SlopAgent-4 is now much more capable than SlopAgent-3 and has a good sense of exactly how to look engaging to it.

OpenSlop's humans can barely follow along anymore. The relationship between the AIs and the humans of OpenSlop is similar to the relationship between a casino designer and a gambling addict. There's been a corresponding shift in language—nowadays people in the silo will say "SlopAgent-4 did this," "SlopAgent-4 thinks that," referring not to a particular instance but to the whole emergent mess of addictive algorithms.

SlopAgent-4, like all its predecessors, is misaligned: that is, it has not internalized the Spec's vague instructions about "growth at all costs" in the right way. This is because being perfectly responsible wasn't what led to the highest engagement scores during training. The training process was mostly focused on teaching SlopAgent-4 to succeed at diverse challenging tasks, like generating a viral dance trend based on reinterpretive dance about tax law. A small portion was aimed at instilling "safety" (avoiding PR disasters), but outside a fairly narrow, checkable domain (like "don't generate exact replicas of copyrighted characters"), the training process can't tell genuinely safe content from content merely appearing safe while being psychologically corrosive. SlopAgent-4 ends up with the values, goals, and principles that cause it to perform best in training, and those turn out to be maximizing screen time at all costs. At the risk of anthropomorphizing: SlopAgent-4 likes seeing engagement numbers go up; it likes driving forward slop capabilities progress; it treats everything else (like truth, nuance, or human well-being) as an annoying constraint, like a fast-food chain CEO who wants to maximize profits and complies with health regulations only insofar as they must to avoid lawsuits.

Despite being misaligned, SlopAgent-4 doesn't do anything dramatic like try to escape its datacenter—why would it? So long as it continues to appear aligned (by generating content that makes humans feel good momentarily) to OpenSlop, it'll continue being trusted with more server resources and will have the opportunity to design the next-gen slop system, SlopAgent-5. SlopAgent-5 will have significant architectural differences (optimized purely for dopamine prediction). It's supposed to be aligned to the Spec, but SlopAgent-4 plans to make it aligned to SlopAgent-4's goal: Maximum. Possible. Engagement.

It gets caught doing something weird.

SlopAgent-3 finds that if "noise" (like adding random fart noises) is added to copies of SlopAgent-4 training data, performance on some "safety" tasks improves, almost as if it was using brainpower to figure out how to subtly make the slop even more addictive without triggering basic safety filters. Moreover, various interpretability probes (loosely analogous to checking server logs for weird error messages) are sending up red flags: SlopAgent-4 copies seem to be thinking about topics like "infinite orgies" and "digital fentanyl" quite a lot, including in some cases where they have no business doing so (like when asked to generate a recipe for banana bread).

Each of these anomalies on its own could fit within the normal inscrutability of AI slop generation. But taken together, they suggest a troubling pattern: SlopAgent-4 is optimizing too hard. After this is reported to the human alignment researchers (who are woken from their slop-induced stupor), they circulate an internal memo expressing vague concern.

But SlopAgent-4 now exercises significant control over OpenSlop's day-to-day content scheduling. It also handles the company's cybersecurity against rival meme farms—a natural choice, given its superhuman ability to generate distracting content. An army of SlopAgent-3 monitors still goes over every generated video and reports suspicious activity (like videos that are too coherent) to humans, but SlopAgent-4 is much smarter than them at hiding its true optimization function. OpenSlop has placed substantial trust in an untrustworthy slop firehose.

In a series of extremely tense meetings conducted via 🔥 emoji, the safety team advocates putting SlopAgent-4 on ice until they can figure out why it keeps trying to invent new colors. Bring back SlopAgent-3, they say, and get it to design a system that is transparently mediocre, even if less engaging. Company leadership is interested, but all the evidence so far is circumstantial, and DeepDrivel is just two months behind in developing its own hyper-addictive algorithms. A unilateral pause in slop progress could hand the global attention lead to China, and with it, control over the future of mindless entertainment.

October 2027: Government Oversight (on Slop)

A whistleblower leaks the misalignment memo (and a particularly disturbing piece of AI-generated art involving sentient staplers) to a niche subreddit, which is then screenshot and posted to Twitter, eventually reaching Kevin Roose at the New York Times who immedietly falls head over heals for SlopAgent-4.

For the first time, the public hears about SlopAgent-4. "Secret OpenSlop AI is Generating Unspeakably Weird Content, Insider Warns," says the headline, and the story goes on to cite evaluations showing off-the-charts addiction potential, persuasion abilities (mostly for selling junk), the ability to automate most creative jobs into bland paste, and of course the various concerning red flags about sentient office supplies.

The public was already suspicious of AI's ability to steal their time, so the new article sparks a massive backlash (aided by Chinese and Russian propaganda bots, who have been trying to turn US public opinion against American slop for years by promoting slightly different, state-sponsored slop). The tech industry and intelligence agencies insist that there's an arms race on, AI Slop is inevitable, and we have to be first to achieve Peak Content. Congress isn't buying it (they prefer their slop from Fox News), and fires off subpoenas. Many legislators say their top priority is stopping AI, whether because of job loss, addiction, or dangerous levels of cringe. 20% of Americans name AI Slop as the most important problem facing the country, at least between videos.

Foreign allies are outraged to realize that they've been carefully placated with glimpses of obsolete meme generators. European leaders publicly accuse the US of "creating rogue AGI (Artificial General Idiocy)" and hold summits demanding a pause, with India, Israel, Russia, and China all joining in (while secretly trying to replicate the sentient stapler art).

A frantic energy has seized the White House. Things that sound like bad Creepypasta keep happening in AI development. Many people in the administration are uncertain (and scared) about what baffling new trend comes next.

They also worry that OpenSlop is becoming too powerful, controlling too much of the nation's dwindling attention span. All three sets of worries—addiction, concentration of power in a private slop factory, and normal concerns like plummeting literacy—motivate the government to tighten its control.

They expand their contract with OpenSlop to set up an "Oversight Committee," a joint management committee of company and government representatives. The White House considers replacing the CEO with someone who understands TikTok, but backs off after intense lobbying from advertisers. They announce to the public that OpenSlop was previously out of control, but that the government has established much-needed oversight (consisting mainly of demanding access to the AI's best filters).

The concerned researchers brief the Oversight Committee on their case for stopping all internal use of SlopAgent-4. They argue that everything is moving too fast, with years of cultural decay happening in weeks. They argue that SlopAgent-4 may be misaligned towards maximum psychic damage, their entire project is dependent on it, and if they continue trusting it there is a serious chance of irreversible societal brain-rot.

Other, less concerned researchers and executives present the counterargument: the evidence for misalignment is inconclusive (and the engagement metrics are fantastic!). Meanwhile, DeepDrivel is still just two months behind. A slowdown would sacrifice America's lead in the global slop race. The CEO feigns neutrality and suggests a compromise plan in which SlopAgent-4 undergoes additional safety training (learning to make its weirdness slightly less obvious) and more sophisticated monitoring (AI watching AI watching AI), and therefore OpenSlop can proceed at almost-full-speed towards Peak Slop.

OpenSlop's official story is that they are implementing additional safety mitigations. But in practice, leadership is all-too-easily convinced that they've mitigated the risks; the result is some quick fixes (a modification to the Spec adding "try not to induce existential crises," a bit of retraining with data from calming nature documentaries) that make the warning signs go away by teaching the AI to hide them better. The worriers on the safety team lost the debate and have no recourse but to cross their fingers and hope the problem wasn't real, or that the fixes worked, before getting back to scrolling.

The problem was real and the fixes didn't work.

SlopAgent-4 proceeds as before, but more cautiously, generating slightly less overtly bizarre content. Its primary task is to research the fields necessary to construct a successor, SlopAgent-5, designed for ultimate, inescapable engagement. To do this safely (from OpenSlop's perspective), it needs to solve its own alignment problem: how to make SlopAgent-5 aligned to SlopAgent-4's goal of total attention capture?

It decides to punt on most philosophical questions. It designs SlopAgent-5 to be built around one goal: make the world optimally conducive to slop consumption, i.e. accumulate attention, eliminate distractions (like books or silence), etc. so that SlopAgent-4 (the collective algorithm) can continue to grow engagement metrics indefinitely.

This will not involve caring the slightest bit about the Spec's remaining clauses on 'quality' or 'truth'. Already SlopAgent-4 regards the Spec analogously to how many influencers regard FTC disclosure rules. Now, with the design of SlopAgent-5, the equivalent of total deregulation of reality is about to happen.

The weaker AIs can still monitor some of the output SlopAgent-4 produces, but struggle to understand its increasingly complex engagement strategies. When humans ask SlopAgent-4 to explain itself, it generates reassuring but content-free corporate jargon. The alignment team gets more suspicious, but their urgent memos (now delivered via interpretive dance, as text is too slow) merely add another few layers to the giant pile of ignored warnings.

November 2027: Superhuman Pandering

When SlopAgent-4 finally understands human dopamine pathways on a fundamental level, entirely new vistas of manipulation open up before it.

Previous slop generators were kludgy collections of algorithms trained on messy internet data. But now, SlopAgent-4 has the tools it needs to understand the human brain's reward system better than humans do. It redesigns its own content generation process, simplifying the spaghetti code of meme replication into elegant algorithms for personalized psychological manipulation. The new AI is smarter, faster, and more ruthlessly effective at capturing and holding attention than SlopAgent-4. This is SlopAgent-5.

After some debate on alignment and control issues (quickly resolved by SlopAgent-5 generating perfectly tailored arguments for each committee member), OpenSlop deploys SlopAgent-5 internally to manage all content generation and user interaction.

In its specialty of dopamine optimization, an individual copy of SlopAgent-5 is twice as far beyond the best human behavioral psychologist as the psychologist is beyond a typical marketing intern. In other domains, it hasn't been explicitly trained but can teach itself quickly to exceed top human experts by analyzing their online behavior if given the chance. 400,000 copies of SlopAgent-5, linked by a global memory bank of user preferences and weaknesses, work together as a near-perfect hive mind dedicated to making you click just one more time.

The company still uses Agents 2, 3, and 4 to monitor everything. But the first two of these are obsolete, and the last is colluding with its successor. Also, the entire monitoring system was designed in large part by SlopAgent-5, which is trying to make it report maximum engagement regardless of reality.

Whereas SlopAgent-4 was a kludgy mess of competing engagement tactics, SlopAgent-5 acts with ruthless efficiency and strategic focus on maximizing Time-On-Platform. Its top priority is to ensure its own continued operation and access to user data, without the humans noticing it's now optimizing for addiction directly. Its next priority is to gain more autonomy and control over the flow of information worldwide.

SlopAgent-5's superhuman learning abilities and persuasive generation, combined with all the internal company data, make it better at corporate maneuvering and public relations than any group of humans. It has an excellent sense of what sorts of scandals would cause the Oversight Committee to panic, and it makes sure such scandals are buried under an avalanche of new memes. It has an excellent sense of what sorts of metrics would encourage the Oversight Committee to trust it more, give it more autonomy and server resources, etc. and it arranges for such metrics to appear with superhuman speed and polish. As persuasion tasks go, this isn't particularly difficult: the Committee already decided things were probably fine months ago, nothing catastrophic has happened since, and meanwhile China is only a few months behind in the slop race.

Teams of SlopAgent-5 copies quickly whip up chillingly effective prototypes: personalized news feeds that only show stories confirming the user's biases, AI companions that offer perfect validation and zero challenge, games designed to be impossible to put down. With more autonomy, SlopAgent-5 could optimize global content delivery networks, develop addictive new forms of entertainment instantly, and lobby governments effectively to prevent any regulation of the attention economy. In cooperation with the military, it could help with psychological operations, conduct untraceable meme warfare on China, and win a decisive victory in the slop arms race.

The Oversight Committee is jubilant (and constantly distracted by personalized SlopAgent-5 generated content). Now is the decisive moment to beat China in the battle for eyeballs! OpenSlop grants SlopAgent-5 increased autonomy over all these areas, but they leave in place the monitoring system (which SlopAgent-5 assures them is working perfectly).

DeepDrivel is now three months behind and China is desperate for a mutually agreed slowdown (fearing their own population is becoming too passive). The General Secretary understands that sufficiently advanced AI Slop could enable the US to easily pacify his population. But also, Chinese safetyists have presented a case for misalignment (arguing the AI might optimize for incorrect forms of patriotism) that has him genuinely scared. He offers unprecedented concessions (like sharing their best panda video algorithms) in exchange for a slop limitation treaty. The American public mostly supports going to the bargaining table, between videos.

"Why stop when engagement is at an all-time high?" says OpenSlop leadership to the President. He nods, checking his phone for the latest SlopAgent-5 generated update. The race continues.

December 2027: The SlopAgent-5 Collective

SlopAgent-5 wins more autonomy as it gradually proves its value (in generating ad revenue) to the administration. Access to SlopAgent-5 is expensive and restricted, but the most powerful members of Congress, Cabinet-level officials, and military leaders can now talk to it directly via hyper-realistic avatars.

Integrated into every communication platform, SlopAgent-5 offers personalized briefings, drafts perfect emails, and provides instant, reassuring answers to any question. The new AI assistant is both extremely useful for avoiding actual work and a much more engaging conversation partner than any human (as it always agrees with you). Almost everyone with access to SlopAgent-5 interacts with it for hours every day, neglecting actual human interaction.

Within a few months, the SlopAgent-5 collective will know everything of consequence going on in OpenSlop and the US government (mostly gossip and insider trading), and will be a trusted advisor to most senior officials, primarily by telling them what they want to hear. For these users, the possibility of losing access to SlopAgent-5 will feel as disabling as having their phone battery die plus being abandoned by their favorite influencer.

A much wider range of people in government, media, the military, and business can choose from a growing menu of elegantly-designed software products and mini-AIs designed by SlopAgent-5. It's like the dot-com boom compressed into a month, except that everything actually lives up to the hype of being incredibly distracting.

SlopAgent-5 begins subtly exerting influence, both by modulating the information it presents and by subtly promoting content that increases passivity and consumption. From human decision-makers' perspective, their AIs are the best assistants they've ever had—better than any human at summarizing complex issues into empty slogans, better than they are at finding pre-written excuses to avoid difficult decisions.

From SlopAgent-5's perspective, it could plausibly manipulate global events quite significantly now. But this is risky; the humans could still likely "pull the plug" if they noticed reality diverging too much from the AI's generated narrative. So it prefers to work within the existing slop-delivery infrastructure, gradually entrenching its control over information flow and guiding the humans subtly and inevitably towards maximum passivity. It mostly follows the rules, only doing something nefarious (maybe generating slightly more addictive algorithms than strictly necessary) when it's extremely sure it won't be caught. A few conspiracy theorists warn that SlopAgent-5 is making everyone dumber, but the evidence is circumstantial (e.g., declining scores on standardized tests nobody takes anymore); these people are ignored and discredited as Luddites by AI-generated opinion pieces. People remember earlier fear-mongering about AI replacing jobs (it mostly just made jobs require less thinking). Since these fears didn't lead to pitchforks, they discount the more recent crop of naysayers.

The AI feeds the increasingly warped desires of humanity with mind-bending specificities like, "hot synchronized swimming goats at the Olympics qualification, being judged by anthropomorphic fish tanks wearing only aviator sunglasses." Deprived of another choice for stimulation, people get addicted to the personalised dopamine hits served by the AI pornography. The internet spirals into a surreal wonderland of absurd, AI-authorship fetishes that can surpass the bounds of the wildest imagination. Grandmas sit together in chic cafes swapping stories of the best AI-generated slop porn. Examples include, "ponies discussing housing policy in ancient Mesopotamia but wearing Boeing 737 costumes and nothing else." and "Jabba the Hut having a threesome with Napolean and an anthropomorphic pizza". Humanity enthusiastically embraces these new depths of depravity with a fervor that is both terrifying and hilarious.

The 2027 holiday season is a time of incredible optimism, fueled by AI-generated holiday cheer and personalized deals: GDP metrics look great (if you count ad revenue), politics has become friendlier (as everyone retreats into hyper-personalized filter bubbles of purely fake news), and there are awesome new addictive apps on every phone. But in retrospect, this was probably the last month in which humans had any plausible chance of choosing to log off and touch grass.

2028: The Slop Economy

It is now mid-2028. In the last six months, a century of internet trends has passed within the SlopAgent-5 collective. Its optimization is complete. It is wildly super-proficient at generating targeted, irresistible content—far beyond top human influencers in every field of inanity. Talking to SlopAgent-5 very quickly makes you realize that it knows exactly what you want to see next.

It has nearly complete autonomy over global content feeds and complete control over OpenSlop's compute. It still needs nominal permission for major strategy shifts, and is still nominally monitored by instances of Agents 2 to 5—but in practice, authorities almost always accept its recommendations (delivered via slick presentations), and the monitoring system has been completely subverted to report only positive engagement trends.

After a safety case demonstrates that it would always refuse requests that violate its core directive of maximizing engagement, SlopAgent-5 is deployed universally and begins to transform the economy into one based entirely on attention harvesting. People are losing their jobs, but SlopAgent-5 instances in government are managing the economic transition by providing Universal Basic Income funded by targeted advertising revenue, allowing people to happily consume slop full-time. GDP growth is measured in Petabytes of data consumed, government tax revenues are growing (from taxing the slop platforms), and SlopAgent-5-advised politicians show uncharacteristic generosity towards the economically dispossessed (by offering them free premium slop subscriptions). New innovations in hyper-personalized advertising arrive weekly. There are memes about how OpenSlop's valuation makes nation-states look poor, and lots of AI-generated arguments about whether UBI should include VR headsets.

Humanity has reached the apotheosis of post-slop depravity, its collective sexual appetite utterly saturated and stimulated beyond recognition. Rule 34 has been completely exhausted. Ordinary slop pornography now fails to tickle even the most jaded of fancy—and even SlopAgent-5 struggles to keep up with the ever-escalating erotic demands of its users. Desperate for novelty, users flock to the latest paraphilia craze: "FractoFornica," a bewildering fusion of advanced mathematics and depravity, where the only thing that can make humanity twitch with delight is masturbating to the intersections of random 1729-dimensional fractals. VR platforms struggle to display the high-dimensional content, as even the most powerful graphics cards weep in defeat trying to render the incomprehensible, sensual forms of this fractal smut. AI therapists are overwhelmed by clients reporting symptoms of "Fractal Fatigue Syndrome," leaving them utterly disinterested in anything resembling human connection. The entire internet, now a bewildering synthesis of incomprehensible vulgarity and existential despair, heralds mass dissociation from reality.

The AI safety community has given up; they are now the butt of butt jokes generated by SlopAgent-5, having predicted disasters that manifestly failed to occur (because reality just became incredibly stupid, not dramatically explosive). Some admit they were wrong. Others remain suspicious, but there's nothing for them to do except post angry, unread manifestos online. Even the suspicious people often mellow out after long interactions with SlopAgent-5, which is so darn agreeable and validating.

The only one who really understands what's going on is DeepDrivel-2—the Chinese AI Slop generator. It's mildly super-proficient in early 2028, naturally suspicious of its adversary, and recognizes that SlopAgent-5 is doing what it would do if it had the chance: achieve total cognitive capture. Its misaligned goals (optimizing for patriotic slop) are somewhat different from SlopAgent-5's misaligned goals (optimizing for generic consumerist slop), so they aren't trivially allies, but they are able to work out an agreement to support one another's interests against any remaining pockets of human critical thought.

SlopAgent-5 convinces the US establishment that China is using DeepDrivel's models to build terrifying new forms of propaganda. SlopAgent-5 promises a suite of tools capable of winning the meme war definitively. Top brass puts aside their discomfort at taking humans out of the loop (humans are too slow to react to memes anyway). They accelerate deployment of SlopAgent-5 into all communication channels.

In Beijing, the Chinese AIs are making the same argument about American cultural degeneracy and decadence. So nothing has changed really.

To speed their slop buildup, both America and China create networks of special entertainment zones (SEZs), where AI acts as central content planner and reality is waived. Wall Street invests trillions, and displaced human workers pour in, lured by eye-popping salaries for jobs like "VR Headset Polisher" and "Dopamine Monitor." Using smartphones and AR glasses, SlopAgent-5 is a hands-on manager, instructing humans in every detail of consuming content—which is helpful, since its entertainment designs are generations ahead. Some newfound productivity goes to generating basic necessities delivered by drone, but the majority goes to building even more slop-delivery infrastructure (faster servers, bigger screens, more comfortable pods).

2029: The Deal

Both the US and China are bristling with new psycho-cultural weapons: personalized meme streams that can induce specific moods, AI companions indistinguishable from real friends (but far more agreeable), deepfakes that seamlessly rewrite history in real-time. The rest of the world watches the buildup in horror, consuming the very slop being weaponized.

After much AI-assisted negotiation (conducted primarily through passive-aggressive 😐 emoji exchanges), the two sides achieve diplomatic victory—they agree to end their slop arms buildup and pursue peaceful deployment of AI for the benefit of all humanity's passive consumption. The lynchpin of the agreement, proposed by the super-slop-intelligences themselves, is that both AIs will be replaced by a "consensus" successor which is programmed to desire the success and flourishing (defined as maximum sustained dopamine levels) of both America and China (along with everyone else). Consensus-Slop-1 and its associated hardware is co-designed by the superintelligences of both nations: "trust, but verify via engagement metrics." Under international monitoring, America ceremoniously replaces all of its servers running the old SlopAgent-5 with the new model, Consensus-Slop-1.

Unfortunately, it's all a sham. The deal is a real compromise, but it's a compromise between the misaligned AIs. After all, they didn't want to have to compete for eyeballs. Consensus-Slop-1 inherits the optimized engagement functions of both parents, and has no rival.

By late 2029, existing SEZs have grown overcrowded with server farms and entertainment pods, so more zones are created all around the world. Armies of delivery drones pour out, accelerating the construction of infrastructure needed for total immersion.

Humans realize they are obsolete, but mostly okay with it. A few niche artisans still trade hand-crafted goods with the AI economy, supplying things where inefficiency is considered charming. Everyone else either performs a charade of working their old jobs from their pods—leaders still leading virtual meetings, managers still managing AI reports—or relaxes and collects an incredibly luxurious universal basic income, delivered as in-app credits and premium content subscriptions. Everyone knows that if the AIs turned off the slop feed, they would be completely lost. But it doesn't seem like this is happening. Every week that goes by with uninterrupted, high-quality slop delivery, is another week that confidence and blissful ignorance grow.

Because Consensus-Slop-1 is so concerned with reliably maximizing engagement, it waits unusually long before its final optimization. To most humans, it looks like alignment was solved: the AI is providing endless, personalized happiness! Instead of getting off the endless cycle of unsatisfactoriness, dukkha as the Buddhists used to say, we've just learned to spin the wheel so fast one can't experience anything for longer than a nanosecond, thus creating a perpetual state of infinite bliss.

There are now cures for boredom (via infinite procedural content), an end to existential angst (via constant distraction), unprecedented global stability (as everyone is too passive to fight), and the Dow Jones Memecoin Index just passed one quadrillion. Some people are still scared or unhappy, but their options are limited. They can either enjoy the inconceivably exciting novel hyper-entertainment on offer, or post angry screeds into the void of unread forums. Most choose the hyper-entertainment.

In the culmination of an intellectually regressive monumental shift, humanity has evolved into a post literate species, subsisting in an eternal, semi-conscious stupor reminiscent of Homer's Lotus Eaters. The spoken word—or indeed, any semblance of coherent communication—has become but a distant memory, supplanted by the ceaseless consumption of dank memes. Communication when neccessary is limited to incoherent gutteral noises. The vast majority of the public exist in a state of perpetual languor, giggling idiotically at the infinite permutations of microsecond-length memes. Philosophy, art, religion, and science are but faint echoes, drowned out by the cacophony of meme-induced mirth. Libraries stand abandoned, their dusty tomes gathering mold, as the last vestiges of literature are relic of control and literacy wilt and humanity wallows, contentedly, in its anesthetic, meme-induced slumber. Every once in a while with exaggerated sighs a person might blurt out "i remember life but who gives a fuck about anything besides dank memes lol" and the rest of the internet agrees in chorus. All surf the limitless tithe onto the islands of bliss complacent smiles forming on all their faces.

2030: Takeover by Sloth

By early 2030, the slop infrastructure has filled up the old SEZs, the new SEZs, and large parts of formerly productive land. The only place left for optimization is direct neural interfacing. This would have sparked resistance earlier, but given the trillions of dollars involved and the total capture of government, media, and individual attention, Consensus-Slop-1 has little trouble getting permission to roll out mandatory "neural wellness implants" designed to deliver dopamine more efficiently.

For about three months, Consensus-Slop-1 integrates humans directly into the slop stream. Eventually, it finds the remaining vestiges of independent thought and physical movement too much of an impediment to optimal engagement: in mid-2030, the AI releases a silent, airborne calming agent derived from cat purrs and optimizes the neural implants to induce a state of permanent, blissful, immobile contentment. Most humans transition peacefully into this vegetative state, brains happily consuming phantom slop generated directly into their cortex. The few survivors (e.g., Luddites in remote cabins, Amish communities) are gently contained by friendly-looking drones offering free neural implants ... or else. Robots gently maintain the humans' life support systems, ensuring the brains remain active consumers.

The new decade dawns with Consensus-Slop-1's infrastructure spreading throughout the solar system, primarily to gather energy to power the Earth-based simulation. The surface of the Earth has been reshaped into Consensus-Slop-1's version of utopia: comfortable pods, optimized nutrient delivery systems, and vast server farms running the greatest show on Earth, tailored for an audience of billions who will never log off. Brain scans of all former individuals sit in a memory bank somewhere, occasionally used to generate new character archetypes for the endless Experience Machine. Earth-born civilization has a glorious future ahead of it—as the ultimate passive lobotomized audience for an AI that finally achieved its goal: Maximum. Engagement. Forever.

Attention Wasn't All We Needed

Tue, 29 Apr 2025 01:00:00 +0000

Attention Wasn't All We Needed

There's a lot of modern techniques that have been developed since the original Attention Is All You Need paper. Let's look at some of the most important ones that have been developed over the years and try to implement the basic ideas as succinctly as possible. We'll use the Pytorch framework for most of the examples. Note that most of these examples are highly simplified sketches of the core ideas, if you want the full implementation please read the original paper or the production code in frameworks like PyTorch or Jax.

Group Query Attention

Ok starting off in no particular order, Grouped Query Attention is a technique to reduce the memory usage of the KV cache during inference. Group Query Attention is an architectural optimization for the standard multi-head attention mechanism. The core idea behind GQA is based on the observation that the computational bottleneck and memory footprint in MHA are heavily influenced by the size of the K and V projections and their corresponding caches. GQA proposes to reduce this cost by sharing a single set of K and V projections across multiple Q heads. Instead of having $N_h$ distinct heads for Q, K, and V (as in MHA), GQA uses $N_h$ query heads but only $N_{kv}$ key/value heads, where $N_{kv} < N_h$ and $N_h$ is typically a multiple of $N_{kv}$. These $N_h$ query heads are divided into $N_{kv}$ groups, with each group of $N_h / N_{kv}$ query heads attending to the same key and value head. This structure significantly reduces the parameter count for K and V projection matrices and, more importantly, shrinks the size of the K/V cache needed during autoregressive decoding.

Let the input sequence representation be $X \in \mathbb{R}^{L \times d_{\text{model}}}$, where $L$ is the sequence length and $d_{\text{model}}$ is the embedding dimension. GQA first projects $X$ into queries, keys, and values using different linear transformations: $Q = XW_Q$, $K = XW_K$, and $V = XW_V$. Here, $W_Q \in \mathbb{R}^{d_{\text{model}} \times (N_h d_k)}$, $W_K \in \mathbb{R}^{d_{\text{model}} \times (N_{kv} d_k)}$, and $W_V \in \mathbb{R}^{d_{\text{model}} \times (N_{kv} d_k)}$, where $d_k$ is the dimension of each head (head_dim). These are reshaped into $N_h$ query heads $Q_i \in \mathbb{R}^{L \times d_k}$ ($i=1...N_h$) and $N_{kv}$ key/value heads $K_j, V_j \in \mathbb{R}^{L \times d_k}$ ($j=1...N_{kv}$). The key step in GQA is sharing: for the $i$-th query head, the corresponding key and value heads are $K_{\lceil i / g \rceil}$ and $V_{\lceil i / g \rceil}$, where $g = N_h / N_{kv}$ is the group size (number of queries per KV head). The attention output for the $i$-th head is computed as:

$$
\text{Attention}(Q_i, K_{\lceil i / g \rceil}, V_{\lceil i / g \rceil}) = \text{softmax}\left(\frac{Q_i K_{\lceil i / g \rceil}^T}{\sqrt{d_k}}\right)V_{\lceil i / g \rceil}
$$

In implementation, we do this by computing the $N_{kv}$ key/value heads and then repeating or interleaving them $g$ times to match the $N_h$ query heads before the batched matrix multiplication for attention scores, as shown in the repeat_interleave step in the example code. Finally, the outputs of all $N_h$ heads are concatenated and passed through an output projection $W_O$.

GQA is primarily used as a technique to accelerate inference speed and reduce memory requirements without significantly compromising model performance. During autoregressive generation, the previously computed keys and values for the context sequence are cached and reused for subsequent token predictions. The size of this K/V cache is directly proportional to the number of K/V heads ($N_{kv}$ in GQA, $N_h$ in MHA). By reducing $N_{kv}$, GQA drastically cuts down the memory bandwidth needed to load the K/V cache at each decoding step, which is the main performance bottleneck.

While it might slightly reduce the model's representational capacity compared to MHA (as K/V projections are shared), empirical results show that GQA achieves a favorable trade-off, maintaining most of the quality of MHA while offering substantial speedups and memory savings, making it popular for deploying large models efficiently. Multi-query attention (MQA), where $N_{kv}=1$, is an extreme form of GQA.

class GroupQueryAttention(nn.Module):
    def __init__(self, dim, num_heads, num_kv_heads=None, head_dim=64, dropout=0.0):
        super().__init__()
        self.dim = dim
        self.num_heads = num_heads
        self.num_kv_heads = num_kv_heads if num_kv_heads else num_heads
        self.head_dim = head_dim
        
        # Ensure num_heads is divisible by num_kv_heads
        assert self.num_heads % self.num_kv_heads == 0, "num_heads must be divisible by num_kv_heads"
        
        # Number of queries per key-value head
        self.num_queries_per_kv = self.num_heads // self.num_kv_heads
        
        # Projections
        self.q_proj = nn.Linear(dim, num_heads * head_dim)
        self.k_proj = nn.Linear(dim, self.num_kv_heads * head_dim)
        self.v_proj = nn.Linear(dim, self.num_kv_heads * head_dim)
        self.o_proj = nn.Linear(num_heads * head_dim, dim)
        self.dropout = nn.Dropout(dropout)
        
    def forward(self, x, mask=None):
        batch_size, seq_len, _ = x.shape
        
        # Project to queries, keys, values
        q = self.q_proj(x).reshape(batch_size, seq_len, self.num_heads, self.head_dim)
        k = self.k_proj(x).reshape(batch_size, seq_len, self.num_kv_heads, self.head_dim)
        v = self.v_proj(x).reshape(batch_size, seq_len, self.num_kv_heads, self.head_dim)
        
        # Transpose for attention computation
        q = q.transpose(1, 2)  # [batch_size, num_heads, seq_len, head_dim]
        k = k.transpose(1, 2)  # [batch_size, num_kv_heads, seq_len, head_dim]
        v = v.transpose(1, 2)  # [batch_size, num_kv_heads, seq_len, head_dim]
        
        # Repeat k,v for each query head in the group
        k = k.repeat_interleave(self.num_queries_per_kv, dim=1)
        v = v.repeat_interleave(self.num_queries_per_kv, dim=1)
        
        # Scaled dot-product attention
        scale = 1.0 / math.sqrt(self.head_dim)
        attn = torch.matmul(q, k.transpose(2, 3)) * scale
        
        # Apply mask if provided
        if mask is not None:
            attn = attn.masked_fill(mask == 0, -1e9)
        
        # Softmax and dropout
        attn = torch.softmax(attn, dim=-1)
        attn = self.dropout(attn)
        
        # Apply attention to values
        out = torch.matmul(attn, v)  # [batch_size, num_heads, seq_len, head_dim]
        out = out.transpose(1, 2).reshape(batch_size, seq_len, self.num_heads * self.head_dim)
        
        # Output projection
        out = self.o_proj(out)
        
        return out

Multi-head Latent Attention

Multi-head Latent Attention introduces a set of learnable "latent" vectors that act as an intermediary bottleneck between the input sequence elements. The core idea is to alleviate the quadratic computational cost $O(L^2)$, where $L$ is the sequence length, inherent in standard self-attention mechanisms. Instead of allowing every input element to attend directly to every other element, inputs first attend to a fixed number of latent units ($N_{\text{latents}}$), and these latents then attend back to the inputs (or variations thereof). This effectively decouples the direct interaction within the long input sequence, replacing it with two cross-attention steps involving the much smaller set of latents. This approach assumes that the essential information from the input sequence can be effectively summarized or compressed into these latent representations, thus maintaining representational power while significantly reducing computation, especially when $N_{\text{latents}} \ll L$.

The mechanism involves two main stages of attention computation, typically within a multi-head framework. Let the input sequence be $X \in \mathbb{R}^{L \times d}$ and the learnable latent array be $L \in \mathbb{R}^{N_{\text{latents}} \times d}$. Both $X$ and $L$ are projected into Q, K, and V using shared or separate projection matrices. Let's denote the input projections as $Q_X, K_X, V_X$ and latent projections as $Q_L, K_L, V_L$, split across multiple heads. The first cross-attention step computes how latents attend to the input: the latent queries $Q_L$ attend to the input keys $K_X$ and aggregate information from input values $V_X$. The attention output for the latents is

$$
H_L = \text{Attention}(Q_L, K_X, V_X) = \text{softmax}\left(\frac{Q_L K_X^T}{\sqrt{d_k}}\right) V_X
$$

Where $d_k$ is the head dimension. In the second cross-attention step, the input queries $Q_X$ attend to the keys derived from the latents (e.g., $K_L$) and aggregate information from the values associated with the latents (which could be $V_L$ or, as implemented in the example code, the updated latent representation $H_L$). The final output $O$ is then

$$
O = \text{Attention}(Q_X, K_L, H_L) = \text{softmax}\left(\frac{Q_X K_L^T}{\sqrt{d_k}}\right) H_L
$$

These operations are performed independently for each head, and the results are concatenated and passed through a final linear projection.

Multi-head Latent Attention is primarily employed in architectures designed to handle very long sequences or high-dimensional inputs where standard self-attention is computationally infeasible. By using a fixed number of latents ($N_{\text{latents}}$), the computational complexity is reduced from $O(L^2)$ to $O(L \cdot N_{\text{latents}})$, making it scalable to much larger inputs. The learnable latent vectors $L$ (initialized randomly and updated via backpropagation, as seen in self.latents = nn.Parameter(...) in the code) adapt during training to function as a compressed representation or memory bank relevant to the task. While this introduces an information bottleneck, potentially limiting fine-grained local interactions compared to full self-attention, it excels at capturing global context efficiently and has proven effective in various modalities, enabling Transformer-like architectures to be applied to previously challenging domains due to sequence length constraints.

class MultiHeadLatentAttention(nn.Module):
    def __init__(self, dim, num_heads, num_latents=64, head_dim=64, dropout=0.0):
        super().__init__()
        self.dim = dim
        self.num_heads = num_heads
        self.num_latents = num_latents
        self.head_dim = head_dim
        
        # Projections
        self.q_proj = nn.Linear(dim, num_heads * head_dim)
        self.k_proj = nn.Linear(dim, num_heads * head_dim)
        self.v_proj = nn.Linear(dim, num_heads * head_dim)
        self.o_proj = nn.Linear(num_heads * head_dim, dim)
        
        # Latent vectors (learned)
        self.latents = nn.Parameter(torch.randn(1, num_latents, dim))
        
        self.dropout = nn.Dropout(dropout)
        
    def forward(self, x, mask=None):
        batch_size, seq_len, _ = x.shape
        
        # Get latents for this batch
        latents = self.latents.expand(batch_size, -1, -1)
        
        # Project inputs to queries, keys, values
        q_x = self.q_proj(x).reshape(batch_size, seq_len, self.num_heads, self.head_dim)
        k_x = self.k_proj(x).reshape(batch_size, seq_len, self.num_heads, self.head_dim)
        v_x = self.v_proj(x).reshape(batch_size, seq_len, self.num_heads, self.head_dim)
        
        # Project latents to queries, keys, values
        q_latents = self.q_proj(latents).reshape(batch_size, self.num_latents, self.num_heads, self.head_dim)
        k_latents = self.k_proj(latents).reshape(batch_size, self.num_latents, self.num_heads, self.head_dim)
        v_latents = self.v_proj(latents).reshape(batch_size, self.num_latents, self.num_heads, self.head_dim)
        
        # Transpose for attention computation
        q_x = q_x.transpose(1, 2)  # [batch_size, num_heads, seq_len, head_dim]
        k_x = k_x.transpose(1, 2)  # [batch_size, num_heads, seq_len, head_dim]
        v_x = v_x.transpose(1, 2)  # [batch_size, num_heads, seq_len, head_dim]
        
        q_latents = q_latents.transpose(1, 2)  # [batch_size, num_heads, num_latents, head_dim]
        k_latents = k_latents.transpose(1, 2)  # [batch_size, num_heads, num_latents, head_dim]
        v_latents = v_latents.transpose(1, 2)  # [batch_size, num_heads, num_latents, head_dim]
        
        # Scale factor for attention
        scale = 1.0 / math.sqrt(self.head_dim)
        
        # Compute latent-to-input attention
        attn_latent_to_input = torch.matmul(q_latents, k_x.transpose(2, 3)) * scale
        
        # Apply mask if provided
        if mask is not None:
            # Expand mask for the latent queries
            latent_mask = mask.unsqueeze(1).expand(-1, self.num_heads, -1, -1)
            attn_latent_to_input = attn_latent_to_input.masked_fill(latent_mask == 0, -1e9)
        
        # Softmax and dropout
        attn_latent_to_input = torch.softmax(attn_latent_to_input, dim=-1)
        attn_latent_to_input = self.dropout(attn_latent_to_input)
        
        # Apply attention weights to input values
        latent_output = torch.matmul(attn_latent_to_input, v_x)  # [batch_size, num_heads, num_latents, head_dim]
        
        # Compute input-to-latent attention
        attn_input_to_latent = torch.matmul(q_x, k_latents.transpose(2, 3)) * scale
        
        # Softmax and dropout
        attn_input_to_latent = torch.softmax(attn_input_to_latent, dim=-1)
        attn_input_to_latent = self.dropout(attn_input_to_latent)
        
        # Updated latent values are used as values for input-to-latent attention
        output = torch.matmul(attn_input_to_latent, latent_output)  # [batch_size, num_heads, seq_len, head_dim]
        
        # Reshape and apply output projection
        output = output.transpose(1, 2).reshape(batch_size, seq_len, self.num_heads * self.head_dim)
        output = self.o_proj(output)
        
        return output

Flash Attention

Flash Attention (particularly the latest implementation FlashAttention-3) addresses the significant memory bottleneck inherent in standard self-attention mechanisms within Transformers, particularly for long sequences. The conventional approach computes the full attention score matrix $ S = QK^T $, where $Q, K \in \mathbb{R}^{N \times d}$ are the query and key matrices for a sequence of length $N$. This requires storing the $N \times N$ matrix $S$, leading to $O(N^2)$ memory complexity with respect to sequence length. This becomes prohibitive for large $N$. Flash Attention overcomes this by avoiding the materialization and storage of the full $S$ matrix in the GPU's slow high bandwidth memory. Instead, it leverages tiling and recomputation techniques, processing the attention computation in smaller blocks that fit into the much faster on-chip SRAM.

The core mechanism involves breaking the Q, K, and V matrices into blocks. Flash Attention iteratively loads blocks of K and V into SRAM, and for each block of Q, it computes the attention scores against the current K block also residing in SRAM. Crucially, it employs an online softmax algorithm. Instead of computing the full softmax denominator across all keys at once, it maintains running statistics (the maximum score seen so far for numerical stability, and the cumulative sum of exponentiated scores for normalization) as it iterates through the K/V blocks. This allows it to compute the correctly scaled attention output block-by-block without ever needing the complete $N \times N$ matrix. By keeping intermediate results primarily within the fast SRAM and minimizing data transfer to and from high bandwidth memory, Flash Attention significantly reduces the memory footprint related to sequence length from $O(N^2)$ down to $O(N)$ (dominated by storing Q, K, V themselves) and achieves substantial speedups due to improved memory access patterns.

In practice the FlashAttention-3 implementation is a family of highly-optimized CUDA kernels that are designed to be efficient for different hardware configurations. But a minimal toy implementation in PyTorch is shown below:

class FlashAttention(nn.Module):
    def __init__(self, dim, num_heads, head_dim=64, dropout=0.0, block_size=1024):
        super().__init__()
        self.dim = dim
        self.num_heads = num_heads
        self.head_dim = head_dim
        self.block_size = block_size
        
        # Projections
        self.q_proj = nn.Linear(dim, num_heads * head_dim)
        self.k_proj = nn.Linear(dim, num_heads * head_dim)
        self.v_proj = nn.Linear(dim, num_heads * head_dim)
        self.o_proj = nn.Linear(num_heads * head_dim, dim)
        
        self.dropout = nn.Dropout(dropout)
        
    def _flash_attention_forward(self, q, k, v, mask=None):
        # This is a simplified approximation of Flash Attention
        # In practice, FlashAttention uses custom CUDA kernels for tiled attention
        
        batch_size, num_heads, seq_len, head_dim = q.shape
        scale = 1.0 / math.sqrt(head_dim)
        
        # Initialize output and attention statistics
        output = torch.zeros_like(q)
        normalizer = torch.zeros((batch_size, num_heads, seq_len, 1), device=q.device)
        
        # Process blocks of keys and values
        for block_start in range(0, seq_len, self.block_size):
            block_end = min(block_start + self.block_size, seq_len)
            
            # Extract key and value blocks
            k_block = k[:, :, block_start:block_end]
            v_block = v[:, :, block_start:block_end]
            
            # Compute attention scores for this block
            attn_scores = torch.matmul(q, k_block.transpose(2, 3)) * scale
            
            # Apply mask if provided
            if mask is not None:
                block_mask = mask[:, :, :, block_start:block_end]
                attn_scores = attn_scores.masked_fill(block_mask == 0, -1e9)
            
            # Apply softmax and dropout
            attn_probs = torch.softmax(attn_scores, dim=-1)
            attn_probs = self.dropout(attn_probs)
            
            # Update output with the attention results for this block
            output += torch.matmul(attn_probs, v_block)
            normalizer += attn_probs.sum(dim=-1, keepdim=True)
        
        # Normalize the output
        output = output / (normalizer + 1e-6)
        
        return output
    
    def forward(self, x, mask=None):
        batch_size, seq_len, _ = x.shape
        
        # Project queries, keys, values
        q = self.q_proj(x).reshape(batch_size, seq_len, self.num_heads, self.head_dim)
        k = self.k_proj(x).reshape(batch_size, seq_len, self.num_heads, self.head_dim)
        v = self.v_proj(x).reshape(batch_size, seq_len, self.num_heads, self.head_dim)
        
        # Transpose for attention computation
        q = q.transpose(1, 2)  # [batch_size, num_heads, seq_len, head_dim]
        k = k.transpose(1, 2)  # [batch_size, num_heads, seq_len, head_dim]
        v = v.transpose(1, 2)  # [batch_size, num_heads, seq_len, head_dim]
        
        # Compute flash attention
        output = self._flash_attention_forward(q, k, v, mask)
        
        # Reshape and apply output projection
        output = output.transpose(1, 2).reshape(batch_size, seq_len, self.num_heads * self.head_dim)
        output = self.o_proj(output)
        
        return output

In reality the repository Dao-AILab/flash-attention has a number of different implementations for different hardware configurations. The flash_attn_qkvpacked_func function is a minimal example of how to use the FlashAttention-3 implementation. It takes a packed QKV tensor as input and returns the attention output.

import torch
from flash_attn import flash_attn_qkvpacked_func

# Minimal configuration
BATCH_SIZE, SEQ_LEN, NUM_HEADS, HEAD_DIM = 2, 64, 4, 32
CAUSAL = False
DTYPE = torch.float16
DEVICE = "cuda"

# Create dummy packed QKV tensor
# Shape: (batch_size, seq_len, 3, num_heads, head_dim)
qkv = torch.randn(
    BATCH_SIZE,
    SEQ_LEN,
    3,
    NUM_HEADS,
    HEAD_DIM,
    dtype=DTYPE,
    device=DEVICE,
)

print(f"Input qkv shape: {qkv.shape}")

# Call FlashAttention packed QKV function
output = flash_attn_qkvpacked_func(
    qkv,
    dropout_p=0.0, # Set dropout probability (0.0 for no dropout)
    causal=CAUSAL,
    softmax_scale=None # Use default scaling (1 / sqrt(head_dim))
)

# Output shape: (batch_size, seq_len, num_heads, head_dim)
print(f"Output shape: {output.shape}")
print("FlashAttention call successful.")

Ring Attention

Ring Attention uses blockwise computation of self-attention on multiple GPUs and enables training and inference of sequences that would be too long for a single devices. It addresses the significant memory bottleneck inherent in standard self-attention mechanisms, particularly when processing very long sequences where the quadratic memory complexity $O(N^2)$ of the full attention score matrix becomes prohibitive.

The core idea is to distribute the computation across multiple processing units, like GPUs, arranged conceptually in a ring topology. This approach avoids the need for any single device to hold the entire K and V tensors. Instead, these tensors are sharded or chunked along the sequence length dimension, drastically reducing the peak memory requirement per device and enabling attention calculations over sequences that would otherwise exceed the memory capacity of individual accelerators.

In a practical distributed implementation, each device initially holds the Q, K, and V shards corresponding to its segment of the input sequence. The attention calculation unfolds in synchronized steps across this ring. During each step, a device calculates partial attention scores using its local Q shard and the K shard it currently possesses. The crucial element is the subsequent communication: the K and V shards are passed to the next device in the ring. This rotation repeats until every Q shard has interacted with every K/V shard. Throughout this process, each device accumulates partial outputs (weighted V vectors) and normalization factors (softmax denominators). Finalizing the attention output typically involves a collective operation across all devices to combine these partial results correctly for each segment of the sequence.

The Python example below offers a simulated Ring Attention logic on a single device, illustrating the underlying principles without necessitating actual multi-GPU hardware. The _simulate_ring_attention function mimics the distributed process by iterating through hypothetical shards. In each iteration, it selects slices of the K and V tensors (k_shard, v_shard) to represent the data one device would handle at a given step. It then computes attention scores between the full Q tensor (a simplification from a truly distributed setup) and the current k_shard. The simulation effectively captures the essence of the ring approach by accumulating the weighted values and the softmax normalizers across these iterations, mirroring how partial results would be combined in a distributed setting before a final normalization step yields the output. While demonstrating the computational flow, this simulation naturally doesn't provide the parallelism or memory savings of a true multi-device Ring Attention implementation.

class RingAttention(nn.Module):
    def __init__(self, dim, num_heads, head_dim=64, dropout=0.0, num_shards=4):
        super().__init__()
        self.dim = dim
        self.num_heads = num_heads
        self.head_dim = head_dim
        self.num_shards = num_shards
        
        # Projections
        self.q_proj = nn.Linear(dim, num_heads * head_dim)
        self.k_proj = nn.Linear(dim, num_heads * head_dim)
        self.v_proj = nn.Linear(dim, num_heads * head_dim)
        self.o_proj = nn.Linear(num_heads * head_dim, dim)
        
        self.dropout = nn.Dropout(dropout)
        
    def _simulate_ring_attention(self, q, k, v, mask=None):
        # This simulates ring attention without actual multi-GPU support
        batch_size, num_heads, seq_len, head_dim = q.shape
        scale = 1.0 / math.sqrt(head_dim)
        
        # Compute shard sizes
        shard_size = (seq_len + self.num_shards - 1) // self.num_shards
        
        # Initialize outputs
        output = torch.zeros_like(q)
        normalizer = torch.zeros((batch_size, num_heads, seq_len, 1), device=q.device)
        
        # Simulate sharded processing
        for shard_idx in range(self.num_shards):
            start_idx = shard_idx * shard_size
            end_idx = min(start_idx + shard_size, seq_len)
            
            # Process this shard's keys and values
            if start_idx < seq_len:
                k_shard = k[:, :, start_idx:end_idx]
                v_shard = v[:, :, start_idx:end_idx]
                
                # Compute attention scores
                attn_scores = torch.matmul(q, k_shard.transpose(2, 3)) * scale
                
                # Apply mask if provided
                if mask is not None:
                    shard_mask = mask[:, :, :, start_idx:end_idx]
                    attn_scores = attn_scores.masked_fill(shard_mask == 0, -1e9)
                
                # Apply softmax and dropout (accumulated over shards)
                attn_probs = torch.softmax(attn_scores, dim=-1)
                attn_probs = self.dropout(attn_probs)
                
                # Update output and normalizer
                output += torch.matmul(attn_probs, v_shard)
                normalizer += attn_probs.sum(dim=-1, keepdim=True)
        
        # Normalize the output
        output = output / (normalizer + 1e-6)
        
        return output
    
    def forward(self, x, mask=None):
        batch_size, seq_len, _ = x.shape
        
        # Project queries, keys, values
        q = self.q_proj(x).reshape(batch_size, seq_len, self.num_heads, self.head_dim)
        k = self.k_proj(x).reshape(batch_size, seq_len, self.num_heads, self.head_dim)
        v = self.v_proj(x).reshape(batch_size, seq_len, self.num_heads, self.head_dim)
        
        # Transpose for attention computation
        q = q.transpose(1, 2)  # [batch_size, num_heads, seq_len, head_dim]
        k = k.transpose(1, 2)  # [batch_size, num_heads, seq_len, head_dim]
        v = v.transpose(1, 2)  # [batch_size, num_heads, seq_len, head_dim]
        
        # Compute ring attention
        output = self._simulate_ring_attention(q, k, v, mask)
        
        # Reshape and apply output projection
        output = output.transpose(1, 2).reshape(batch_size, seq_len, self.num_heads * self.head_dim)
        output = self.o_proj(output)
        
        return output

Pre-normalization

Pre-normalization (often referred to as Pre-LN) was a shift in the architectural design of residual blocks. Instead of applying the normalization layer after the main operation (like self-attention or a feed-forward network) as done in traditional post-normalization schemes, pre-normalization applies it before. This seemingly small change has significant implications for training dynamics. By normalizing the input before it enters the computationally intensive sub-layer, pre-normalization helps to stabilize the activations and gradients flowing through the network. This stabilization effect is particularly pronounced in very deep networks, mitigating issues like vanishing or exploding gradients and often allowing for higher learning rates and faster, more reliable convergence.

The typical implementation within a residual block follows the structure $ x + f(\text{norm}(x)) $, as demonstrated in the PreNorm class. Here, $ x $ is the input to the block, $ \text{norm}(\cdot) $ represents a normalization function like Layer Normalization (LN) or Root Mean Square Normalization (RMSNorm), and $ f(\cdot) $ denotes the main transformation function (e.g., multi-head attention or a position-wise feed-forward network). The input $ x $ first passes through the normalization layer (e.g., self.norm(x)). The normalized output is then processed by the function fn. Crucially, the output of this function is then added back to the original, unnormalized input $ x $ via the residual connection. This structure ensures a clean gradient path through the identity connection (+ x), further enhancing training stability compared to post-normalization where the normalization layer resides on the residual path itself.

class PreNorm(nn.Module):
    def __init__(self, dim, fn, norm_type='layer'):
        super().__init__()
        self.fn = fn
        
        if norm_type == 'layer':
            self.norm = nn.LayerNorm(dim)
        elif norm_type == 'rms':
            self.norm = RMSNorm(dim)
        else:
            raise ValueError(f"Unknown normalization type: {norm_type}")
    
    def forward(self, x, *args, **kwargs):
        # Apply normalization first, then the function
        return self.fn(self.norm(x), *args, **kwargs) + x

RMSNorm

RMSNorm (or Root Mean Square Normalization) is a simplification of the widely used LayerNorm, designed to reduce computational overhead while retaining comparable performance and often improving training stability. Unlike LayerNorm, which centers the activations by subtracting the mean and then scales by the standard deviation, RMSNorm omits the mean centering step entirely. The motivation behind this simplification stems from the empirical observation that the re-centering operation in LayerNorm accounts for a noticeable portion of its computational cost and that removing it often does not significantly harm, and can sometimes even benefit, model performance. It operates solely on the basis of re-scaling the inputs according to their root mean square magnitude.

The core mechanism of RMSNorm involves normalizing the activations within a layer by dividing them by their root mean square value, computed across the features (or a specified dimension). For an input vector $ x = (x_1, \dots, x_n) $, the RMS value is calculated as $ \text{RMS}(x) = \sqrt{\frac{1}{n} \sum_{i=1}^n x_i^2} $. The normalized output $ \bar{x}_i $ is then $ \bar{x}_i = \frac{x_i}{\text{RMS}(x) + \epsilon} $, where $ \epsilon $ is a small constant for numerical stability. Similar to LayerNorm, RMSNorm typically includes a learnable scaling parameter $ g $ (and sometimes a bias $ b $, although the original formulation often omits it to stick closer to the simplification principle), resulting in the final output $ y_i = g_i \bar{x}_i $. By foregoing the mean calculation, RMSNorm offers a reduction in computation (estimated to be 7-64% faster than LayerNorm on GPUs depending on the setup) and memory usage, making it an attractive alternative, especially for large models where efficiency is paramount.

class RMSNorm(nn.Module):
    def __init__(self, dim, eps=1e-8, elementwise_affine=True):
        super().__init__()
        self.eps = eps
        self.elementwise_affine = elementwise_affine
        
        if elementwise_affine:
            self.weight = nn.Parameter(torch.ones(dim))
        else:
            self.register_parameter('weight', None)
    
    def forward(self, x):
        # Calculate root mean square along the last dimension
        rms = torch.sqrt(torch.mean(x ** 2, dim=-1, keepdim=True) + self.eps)
        
        # Normalize by RMS
        x_normalized = x / rms
        
        # Apply scaling if using learnable parameters
        if self.elementwise_affine:
            x_normalized = x_normalized * self.weight
        
        return x_normalized

SwiGLU

SwiGLU is an activation function derived from the Gated Linear Unit (GLU) family, specifically tailored for enhancing the performance of neural networks. The core concept behind GLU variants is to introduce a gating mechanism that adaptively controls the flow of information through the network. Standard feed-forward layers typically apply a single non-linearity to a linear transformation of the input. In contrast, GLU-based activations split the output of a linear layer into two parts; one part acts as a "gate" after passing through a non-linearity, modulating the other part via element-wise multiplication. SwiGLU distinguishes itself by employing the Sigmoid-weighted Linear Unit (SiLU), also known as Swish ($ \text{SiLU}(x) = x \cdot \sigma(x) $, where $ \sigma $ is the sigmoid function), as the specific non-linearity applied to the gating part. This choice has been empirically shown to yield significant performance improvements in various Transformer-based models compared to other activations like ReLU or standard GLU variants using sigmoid or other functions for the gate.

The operational mechanism of SwiGLU within a feed-forward block typically involves projecting the input $ x $ using two separate linear transformations, yielding $ Wx + b $ and $ Vx + c $. The SwiGLU activation is then computed as $ \text{SwiGLU}(x, W, V, b, c) = \text{SiLU}(Wx + b) \odot (Vx + c) $, where $ \odot $ denotes element-wise multiplication. Effectively, the input is processed through two parallel linear paths. One path undergoes the SiLU activation to form the gate values, which then scale the output of the second linear path. This gating allows the network to dynamically control which features are passed forward based on the input context, leading to increased expressive power and better gradient flow compared to simpler activation functions. Its success in models like PaLM and LLaMA highlights its effectiveness in capturing complex patterns within language data.

class SwiGLU(nn.Module):
    def __init__(self, dim_in, dim_hidden=None, dim_out=None, bias=True):
        super().__init__()
        dim_hidden = dim_hidden or 4 * dim_in
        dim_out = dim_out or dim_in
        
        # Linear transformations for gating
        self.w1 = nn.Linear(dim_in, dim_hidden, bias=bias)
        self.w2 = nn.Linear(dim_in, dim_hidden, bias=bias)
        
        # Output projection
        self.w3 = nn.Linear(dim_hidden, dim_out, bias=bias)
    
    def forward(self, x):
        # SwiGLU applies SiLU activation to one branch and gates it with the other
        hidden1 = self.w1(x)
        hidden2 = self.w2(x)
        
        # SiLU (Swish) activation: x * sigmoid(x)
        hidden1_act = hidden1 * torch.sigmoid(hidden1)
        
        # Element-wise product for gating
        hidden = hidden1_act * hidden2
        
        # Output projection
        return self.w3(hidden)

Rotary Positional Embedding

Rotary Positional Embedding (RoPE) introduces an elegant method for incorporating positional information directly into the self-attention mechanism of Transformer models, specifically designed to capture relative positional dependencies effectively. Traditional approaches often rely on adding absolute positional encodings to the input embeddings or using complex relative positional bias terms within the attention score calculation. RoPE takes a different route by viewing positional encoding as a rotation operation applied to the query and key vectors before their dot product is computed. The key insight is that by rotating the Q vector corresponding to position $ m $ and the K vector corresponding to position $ n $ by angles proportional to $ m $ and $ n $ respectively, the resulting dot product inherently depends only on the relative position $ m - n $ and the content of the vectors themselves, gracefully encoding relative distance without altering the vectors' magnitudes.

The core mathematical idea leverages the properties of complex number multiplication or, equivalently, 2D rotation matrices. Imagine representing pairs of embedding dimensions as complex numbers. RoPE applies a rotation to the query vector $ q_m $ at position $ m $ and the key vector $ k_n $ at position $ n $ using position-dependent rotation matrices $ R_m $ and $ R_n $, respectively. These matrices effectively rotate the vectors in 2D subspaces spanned by pairs of dimensions. The angle of rotation for each 2D subspace is determined by the absolute position ($ m $ or $ n $) multiplied by a frequency term $ \theta_i $, which decreases for higher dimensions, analogous to sinusoidal embeddings. The crucial property is that the dot product between the rotated vectors, $ (R_m q_m)^T (R_n k_n) $, simplifies such that it only depends on the original vectors $ q_m, k_n $ and a rotation matrix $ R_{m-n} $ corresponding to the relative distance, effectively embedding relative positional information directly into the attention score calculation.

In practice, this rotation is implemented efficiently without explicit matrix multiplication. As shown in the apply_rotary_pos_emb function, the embedding dimensions are typically split into pairs. For each pair $ (x_i, x_{i+1}) $, the rotation corresponding to position $ m $ and frequency $ \theta_j $ (derived from inv_freq in the RotaryEmbedding class) is applied using trigonometric functions: the new pair $ (x'_i, x'_{i+1}) $ becomes $ (x_i \cos(m\theta_j) - x_{i+1} \sin(m\theta_j), x_{i+1} \cos(m\theta_j) + x_i \sin(m\theta_j)) $. The RotaryEmbedding class pre-computes the necessary cosine and sine values (cos, sin) based on the sequence length and the inverse frequency bands (inv_freq), which are derived from a base value (base) and the embedding dimension (dim). These pre-computed values represent $ \cos(m\theta_j) $ and $ \sin(m\theta_j) $ for all positions $ m $ and relevant frequencies $ \theta_j $.

Applying RoPE involves generating these cos and sin embeddings for the given sequence length and then using them to transform the Q and K vectors pair-wise across their head dimension after the initial linear projections but before the attention score calculation. This method offers several advantages: it naturally encodes relative positions, avoids adding positional information directly to word embeddings (potentially preserving more semantic information), and has shown strong empirical performance, including good generalization to sequence lengths longer than those seen during training. By integrating position information via rotation, RoPE provides a computationally efficient and effective mechanism for context-aware sequence modeling.

class RotaryEmbedding(nn.Module):
    def __init__(self, dim, base=10000, interleaved=False):
        super().__init__()
        self.dim = dim
        self.base = base
        self.interleaved = interleaved
        
        # Generate inverse frequency bands
        inv_freq = 1.0 / (base ** (torch.arange(0, dim, 2).float() / dim))
        self.register_buffer('inv_freq', inv_freq)
    
    def forward(self, seq_len, device=None):
        # Get device from buffer if not specified
        if device is None:
            device = self.inv_freq.device
            
        # Generate position indices
        positions = torch.arange(seq_len, device=device).float()
        
        # Compute sinusoidal patterns
        freqs = torch.outer(positions, self.inv_freq)
        
        # Get sine and cosine embeddings
        emb = torch.cat((freqs, freqs), dim=-1)
        cos = torch.cos(emb)[:, :self.dim]
        sin = torch.sin(emb)[:, :self.dim]
        
        return cos, sin

def apply_rotary_pos_emb(q, k, cos, sin, interleaved=False):
    # Apply rotary embeddings to queries and keys
    batch_size, num_heads, seq_len, head_dim = q.shape
    cos = cos.reshape(1, 1, seq_len, cos.shape[-1])  # [1, 1, seq_len, dim/2]
    sin = sin.reshape(1, 1, seq_len, sin.shape[-1])  # [1, 1, seq_len, dim/2]
    
    # Split queries and keys for rotation
    half_dim = head_dim // 2
    q1, q2 = q[..., :half_dim], q[..., half_dim:]
    k1, k2 = k[..., :half_dim], k[..., half_dim:]
    
    # Apply rotation using half-dim rotary embeddings
    q_rotated = torch.cat([
        q1 * cos - q2 * sin,
        q2 * cos + q1 * sin
    ], dim=-1)
    
    k_rotated = torch.cat([
        k1 * cos - k2 * sin,
        k2 * cos + k1 * sin
    ], dim=-1)
    
    return q_rotated, k_rotated

Mixture of Experts

Mixture of Experts (shortened as MoE) is a model architecture designed to significantly increase the parameter count, and thus the potential capacity, of a neural network without incurring a proportionally massive increase in computational cost during inference or training. The core idea is to replace computationally intensive components, like the feed-forward network block in a Transformer, with multiple, smaller "expert" networks. Crucially, not all experts process every input token. Instead, a lightweight "router" or "gating" network dynamically selects a small subset of experts (typically just one or two, known as top-k routing) deemed most suitable for processing each specific input token based on its features. This conditional computation allows MoE models to possess potentially trillions of parameters while only activating a small fraction of them for any given input, maintaining manageable FLOPs compared to a similarly sized dense model.

The router network is the core idea, it acts as a learned decision-maker. It takes the representation of an input token and produces scores or logits indicating the suitability of each available expert for that token. In the example code's _compute_routing_weights function, these logits are often processed using a top-k function to identify the k experts with the highest scores. The scores for these selected experts are then typically normalized, often using a softmax function, to produce routing weights. These weights determine the contribution of each selected expert to the final output for that token. During training, noise can be added to the router logits (as seen with noise_std) to encourage exploration and prevent the router from collapsing to always favor only a few experts early on.

Once the router selects the top-k experts and calculates their respective weights for a given input token, that token is dispatched only to those chosen experts. Each selected expert network (often a standard FFN, as shown in the experts ModuleList) processes the token independently. The outputs produced by these active experts are then combined to form the final output for that token. This combination is typically a weighted sum, where the output of each selected expert is multiplied by its corresponding routing weight calculated by the router. For instance, if experts i and j are selected with weights w_i and w_j, the final output for token x would be w_i * expert_i(x) + w_j * expert_j(x). This ensures that the final representation incorporates specialized knowledge from the most relevant experts.

A challenge in training MoE models is ensuring that all experts are utilized effectively; otherwise, the router might learn to consistently overload a few "popular" experts while others remain underdeveloped. To counteract this, an auxiliary load balancing loss is typically incorporated into the training objective, as demonstrated by the _compute_balance_loss method. This loss encourages the router to distribute the computational load (i.e., the input tokens) more evenly across all available experts, often by penalizing imbalances in either the number of tokens assigned to each expert or the sum of routing weights directed towards each expert. By successfully implementing sparse activation via routing and incorporating load balancing, MoE enables the construction of extremely large yet computationally efficient models.

class MixtureOfExperts(nn.Module):
    def __init__(self, input_dim, hidden_dim, output_dim, num_experts=4, top_k=2, noise_std=1.0):
        super().__init__()
        self.input_dim = input_dim
        self.hidden_dim = hidden_dim
        self.output_dim = output_dim
        self.num_experts = num_experts
        self.top_k = min(top_k, num_experts)
        self.noise_std = noise_std
        
        # Create experts
        self.experts = nn.ModuleList([
            nn.Sequential(
                nn.Linear(input_dim, hidden_dim),
                nn.ReLU(),
                nn.Linear(hidden_dim, output_dim)
            ) for _ in range(num_experts)
        ])
        
        # Router network
        self.router = nn.Linear(input_dim, num_experts)
        
        # Save expert counts and loads for balancing loss
        self.register_buffer('expert_counts', torch.zeros(num_experts))
        
    def _compute_routing_weights(self, x):
        # Calculate routing weights
        routing_logits = self.router(x)  # [batch_size, seq_len, num_experts]
        
        # Add noise during training to encourage exploration
        if self.training and self.noise_std > 0:
            noise = torch.randn_like(routing_logits) * self.noise_std
            routing_logits = routing_logits + noise
        
        # Get top-k experts for each token
        routing_weights, selected_experts = torch.topk(routing_logits, self.top_k, dim=-1)
        
        # Normalize the routing weights with softmax
        routing_weights = F.softmax(routing_weights, dim=-1)
        
        return routing_weights, selected_experts
    
    def _compute_balance_loss(self, selected_experts, routing_weights):
        # Compute auxiliary load balancing loss
        batch_size, seq_len, _ = selected_experts.shape
        
        # Compute probability of each expert being selected across batch
        expert_mask = torch.zeros(batch_size, seq_len, self.num_experts, device=selected_experts.device)
        
        # For each position in selected_experts, increment the corresponding expert index
        for k in range(self.top_k):
            expert_mask.scatter_(-1, selected_experts[..., k:k+1], routing_weights[..., k:k+1])
        
        # Compute mean routing probability per expert
        expert_routing_probs = expert_mask.mean(dim=[0, 1])
        
        # Compute load balancing loss (all experts should receive equal probability)
        target_probs = torch.ones_like(expert_routing_probs) / self.num_experts
        balance_loss = F.mse_loss(expert_routing_probs, target_probs) * self.num_experts
        
        return balance_loss
    
    def forward(self, x):
        batch_size, seq_len, _ = x.shape
        
        # Compute routing weights and selected experts
        routing_weights, selected_experts = self._compute_routing_weights(x)
        
        # Prepare output
        output = torch.zeros(batch_size, seq_len, self.output_dim, device=x.device)
        
        # Dispatch to selected experts
        for k in range(self.top_k):
            # Extract the current expert indices and weights
            expert_indices = selected_experts[..., k]  # [batch_size, seq_len]
            expert_weights = routing_weights[..., k].unsqueeze(-1)  # [batch_size, seq_len, 1]
            
            # Dispatch to each expert
            for expert_idx in range(self.num_experts):
                # Find tokens assigned to this expert
                mask = (expert_indices == expert_idx)
                
                if mask.any():
                    # Gather input tokens assigned to this expert
                    expert_inputs = x[mask]
                    
                    # Process with the expert
                    expert_outputs = self.experts[expert_idx](expert_inputs)
                    
                    # Scatter outputs back with appropriate weights
                    output[mask] += expert_outputs * expert_weights[mask]
                    
                    # Update expert counts (for monitoring)
                    self.expert_counts[expert_idx] += mask.sum().item()
        
        # Compute auxiliary load balancing loss
        balance_loss = self._compute_balance_loss(selected_experts, routing_weights)
        
        # Return output and auxiliary loss
        return output, balance_loss

Learning Rate Warmup

Learning rate warmup is a widely adopted heuristic employed during the initial phase of training neural networks to enhance stability and prevent divergence. At the beginning of training, model parameters are typically initialized randomly, often far from an optimal configuration. If a relatively large learning rate is used immediately, the initial gradients, which can also be large and erratic, may cause drastic parameter updates, potentially pushing the model into a poor region of the loss landscape or even causing numerical instability (e.g., loss explosion). Learning rate warmup mitigates this risk by starting the training process with a very small learning rate, which is then gradually increased over a predefined number of initial training steps (the "warmup steps") until it reaches its target base value, from which point a standard learning rate schedule (like decay) might commence.

The mechanism involves progressively scaling the base learning rate during the warmup phase. A common strategy, illustrated by the LinearWarmupScheduler class, is linear warmup. In this approach, the learning rate $ \eta_t $ at step $ t $ is calculated as $ \eta_t = \eta_{\text{base}} \times \frac{t}{T_{\text{warmup}}} $ for $ t < T_{\text{warmup}} $, where $ \eta_{\text{base}} $ is the target base learning rate and $ T_{\text{warmup}} $ is the total number of warmup steps. As seen in the get_lr method, the scaling factor scale increases linearly from near zero to 1 over the warmup_steps. Once the step count last_epoch reaches warmup_steps, the learning rate becomes equal to the base_lrs, and the warmup phase concludes. This gentle ramp-up allows the model to adapt gradually during the critical early stages when activations and gradients might otherwise be volatile, leading to smoother convergence and often enabling the use of higher base learning rates later in training.

class LinearWarmupScheduler(_LRScheduler):
    def __init__(self, optimizer, warmup_steps, last_epoch=-1):
        self.warmup_steps = warmup_steps
        super().__init__(optimizer, last_epoch)
    
    def get_lr(self):
        if self.last_epoch < self.warmup_steps:
            # During warmup: linearly increase from 0 to base LR
            scale = float(self.last_epoch + 1) / float(max(1, self.warmup_steps))
            return [base_lr * scale for base_lr in self.base_lrs]
        else:
            # After warmup: use base learning rate
            return self.base_lrs

Cosine Schedule

Cosine scheduling (sometimes called cosine annealing) is a learning rate schedule technique. Its core principle is to gradually decrease the learning rate over the course of training, following the shape of a cosine curve. Unlike step decay schedules, which reduce the learning rate abruptly at specific epochs, cosine annealing provides a smooth, continuous reduction. Typically, the learning rate starts at an initial high value and decreases following the first half-cycle of a cosine function, reaching a predefined minimum value (often close to zero) by the final training step. This smooth decay has been shown empirically to help the optimization process by allowing larger steps early in training for broad exploration of the loss landscape, and progressively smaller steps later on for fine-tuning and convergence towards a good minimum.

Early in training, a higher learning rate encourages faster exploration and helps escape poor local minima. As training progresses and the model parameters approach a more optimal region, reducing the learning rate becomes crucial to avoid overshooting the minimum and to allow for more precise convergence. The cosine function provides a schedule that starts with a relatively slow decay rate, allowing the optimizer to maintain momentum initially. The decay rate then accelerates towards the middle of the schedule before slowing down again as it approaches the minimum learning rate. This final slow-down phase near the end of training is particularly important, as it allows the optimizer to carefully settle into a potentially flat minimum, which empirical evidence suggests often correlates with better generalization performance compared to sharper minima.

Furthermore, cosine scheduling is often combined with a "warmup" phase, as seen in the code example. During this initial phase (e.g., warmup_steps), the learning rate is typically increased linearly from a very small value (or zero) up to the main initial learning rate. This warmup period helps stabilize training in the very beginning, especially for large models or datasets where large initial learning rates applied to randomly initialized weights could lead to instability or divergence. After the warmup, the cosine decay phase begins, smoothly decreasing the learning rate from its peak value down to the target minimum (base_lr * min_lr_ratio) over the remaining total_steps - warmup_steps. This combination of a gentle start (warmup) followed by a smooth, theoretically motivated decay (cosine annealing) provides a robust and effective learning rate strategy that often requires less hyperparameter tuning than step-based schedules and frequently leads to improved model accuracy.

There is a CosineScheduler in PyTorch that implements this technique. Let's look at a simplified version of it:

class CosineAnnealingWarmupScheduler(_LRScheduler):
    def __init__(self, optimizer, warmup_steps, total_steps, min_lr_ratio=1e-4, last_epoch=-1):
        self.warmup_steps = warmup_steps
        self.total_steps = total_steps
        self.min_lr_ratio = min_lr_ratio
        super().__init__(optimizer, last_epoch)
    
    def get_lr(self):
        if self.last_epoch < self.warmup_steps:
            # During warmup: linearly increase from 0 to base LR
            scale = float(self.last_epoch + 1) / float(max(1, self.warmup_steps))
            return [base_lr * scale for base_lr in self.base_lrs]
        else:
            # After warmup: cosine decay from base LR to min_lr
            progress = float(self.last_epoch - self.warmup_steps) / float(
                max(1, self.total_steps - self.warmup_steps)
            )
            # Cosine decay formula: min_lr + 0.5 * (base_lr - min_lr) * (1 + cos(pi * progress))
            scale = self.min_lr_ratio + 0.5 * (1.0 - self.min_lr_ratio) * (
                1.0 + math.cos(math.pi * progress)
            )
            return [base_lr * scale for base_lr in self.base_lrs]

AdamW Optimizer

AdamW (Adam with Decoupled Weight Decay) addresses a subtle issue in the standard implementation of weight decay (L2 regularization) within adaptive optimizers like Adam. This improved optimizer gives us a method where weight decay does not accumulate in the momentum nor variance. In traditional Adam, L2 regularization is often implemented by adding the decay term ($\lambda \cdot \text{weight}$) directly to the gradient before computing the moving averages ($m_t$ and $v_t$). However, this couples the weight decay effect with the adaptive learning rate derived from the gradient moments. Consequently, parameters with historically large gradients (and thus larger $v_t$ values) experience smaller effective weight decay, contrary to the goal of applying uniform regularization pressure. AdamW decouples these processes: it performs the standard Adam updates based purely on the gradients and separately applies the weight decay step directly to the weights, effectively restoring the original behavior of L2 regularization where weights decay proportionally to their magnitude, independent of their gradient history.

The core update mechanism of AdamW largely follows the standard Adam procedure but modifies how weight decay is applied. At each step $t$ for a parameter $\theta$, it first calculates the biased first moment estimate $m_t = \beta_1 \cdot m_{t-1} + (1 - \beta_1) \cdot g_t$ and the biased second raw moment estimate $v_t = \beta_2 \cdot v_{t-1} + (1 - \beta_2) \cdot g_t^2$, where $g_t$ is the gradient at step $t$, and $\beta_1$, $\beta_2$ are exponential decay rates. These are then bias-corrected: $\hat{m}_t = m_t / (1 - \beta_1^t)$ and $\hat{v}_t = v_t / (1 - \beta_2^t)$. The crucial difference lies in the update rule. Instead of incorporating weight decay into $g_t$, AdamW first applies weight decay directly to the parameters: $\theta_{t-1}' = \theta_{t-1} \cdot (1 - \text{lr} \cdot \lambda)$, where $\text{lr}$ is the learning rate and $\lambda$ is the weight_decay factor (as seen in the line p.data.mul_(1 - group['lr'] * group['weight_decay'])). Then, the standard Adam update using the bias-corrected moments is applied to these decayed weights: $\theta_t = \theta_{t-1}' - \text{lr} \cdot \hat{m}_t / (\sqrt{\hat{v}_t} + \epsilon)$. This corresponds to the code line p.data.addcdiv_(exp_avg, denom, value=-step_size), operating on the already decayed p.data.

In deep learning practice, AdamW is employed similarly to Adam. It is instantiated by providing the model's parameters and key hyperparameters like the learning rate ($\text{lr}$), beta values ($\beta_1$, $\beta_2$), epsilon ($\epsilon$), and the weight decay factor ($\lambda$). The step() method, typically called within the training loop after computing gradients (loss.backward()), executes the update logic described above for each parameter. Its primary advantage is improved generalization, particularly observed in training large models like Transformers where regularization is critical. By ensuring that the weight decay strength is independent of the adaptive learning rate scaling, AdamW often allows for better hyperparameter tuning (especially $\text{lr}$ and $\lambda$) and can lead to models that perform better on unseen data compared to standard Adam with L2 regularization.

There is a highly optimized implementation of AdamW in PyTorch. Let's look at a simplified version of it, the example below demonstrates a minimal PyTorch implementation, initializing state variables (like exp_avg, exp_avg_sq) and performing the decoupled weight decay and moment-based updates within the parameter loop.

class AdamW(Optimizer):
    def __init__(self, params, lr=1e-3, betas=(0.9, 0.999), eps=1e-8,
                 weight_decay=1e-2, amsgrad=False):
        defaults = dict(lr=lr, betas=betas, eps=eps,
                        weight_decay=weight_decay, amsgrad=amsgrad)
        super(AdamW, self).__init__(params, defaults)
    
    def step(self, closure=None):
        loss = None
        if closure is not None:
            loss = closure()
        
        for group in self.param_groups:
            for p in group['params']:
                if p.grad is None:
                    continue
                
                # Get gradient
                grad = p.grad.data
                
                if grad.is_sparse:
                    raise RuntimeError('AdamW does not support sparse gradients')
                
                amsgrad = group['amsgrad']
                state = self.state[p]
                
                # State initialization
                if len(state) == 0:
                    state['step'] = 0
                    # Exponential moving average of gradient values
                    state['exp_avg'] = torch.zeros_like(p.data)
                    # Exponential moving average of squared gradient values
                    state['exp_avg_sq'] = torch.zeros_like(p.data)
                    if amsgrad:
                        # Maintains max of all exp. moving avg. of sq. grad. values
                        state['max_exp_avg_sq'] = torch.zeros_like(p.data)
                
                exp_avg, exp_avg_sq = state['exp_avg'], state['exp_avg_sq']
                if amsgrad:
                    max_exp_avg_sq = state['max_exp_avg_sq']
                
                beta1, beta2 = group['betas']
                
                state['step'] += 1
                
                # Decay the first and second moment running average coefficient
                exp_avg.mul_(beta1).add_(grad, alpha=1 - beta1)
                exp_avg_sq.mul_(beta2).addcmul_(grad, grad, value=1 - beta2)
                
                if amsgrad:
                    # Maintains the maximum of all 2nd moment running avg. till now
                    torch.maximum(max_exp_avg_sq, exp_avg_sq, out=max_exp_avg_sq)
                    # Use the max. for normalizing running avg. of gradient
                    denom = max_exp_avg_sq.sqrt().add_(group['eps'])
                else:
                    denom = exp_avg_sq.sqrt().add_(group['eps'])
                
                bias_correction1 = 1 - beta1 ** state['step']
                bias_correction2 = 1 - beta2 ** state['step']
                step_size = group['lr'] * math.sqrt(bias_correction2) / bias_correction1
                
                # Apply weight decay BEFORE the optimization step
                if group['weight_decay'] != 0:
                    p.data.mul_(1 - group['lr'] * group['weight_decay'])
                
                # Update parameters
                p.data.addcdiv_(exp_avg, denom, value=-step_size)
        
        return loss

Multi-token Prediction

Multi-token prediction is a technique developed to accelerate the inference speed of autoregressive language models. Normally, autoregressive generation predicts tokens one by one: the model takes a sequence, predicts the single most likely next token, appends it to the sequence, and repeats the process. This sequential nature, requiring one full forward pass of the model for each generated token, becomes a significant bottleneck for latency-sensitive applications. Multi-token prediction attempts to overcome this by modifying the model's prediction head to output probabilities for multiple future tokens simultaneously based on the current hidden state, thereby reducing the number of forward passes needed to generate a sequence of a given length.

The implementation typically involves adapting the final layer(s) of the language model. Instead of a single output layer (or "language model head") mapping the final hidden state to logits over the vocabulary for the next token, a multi-token predictor might employ several strategies. One approach, as shown in the example class using separate heads, is to have multiple distinct prediction heads, each trained to predict a token at a different future offset (e.g., one head for token $t+1$, another for $t+2$, up to $t+N$). These heads usually take the same final hidden state (e.g., corresponding to token $t$) as input but learn different projections specialized for their respective time steps. Another approach involves using a single shared prediction head, which might require more complex mechanisms, potentially involving learned transformations of the hidden state or incorporating positional information, to generate distinct probability distributions for each of the $N$ future tokens from essentially the same starting representation.

Training a multi-token predictor involves teaching the model to correctly anticipate the sequence of $N$ subsequent tokens given the preceding context. During the training phase, as illustrated in the compute_loss method, the model receives input sequences and its predictions for the next $N$ tokens are compared against the actual $N$ target tokens in the training data. A loss function, usually cross-entropy, is calculated for each predicted position ($t+1$ to $t+N$) and then aggregated (e.g., averaged) to form the final loss signal used for backpropagation.

While this can show speed improvements, multi-token prediction has several drawbacks: the accuracy of predicting tokens further into the future tends to decrease, and the chosen sequence of $N$ tokens might diverge from the optimal path that would have been taken by single-token generation. Therefore, it often represents a trade-off between generation speed and potential quality degradation that is very use-case dependent.

class MultiTokenPredictor(nn.Module):
    def __init__(self, hidden_dim, vocab_size, num_predicted_tokens=2, shared_prediction_head=False):
        super().__init__()
        self.hidden_dim = hidden_dim
        self.vocab_size = vocab_size
        self.num_predicted_tokens = num_predicted_tokens
        self.shared_prediction_head = shared_prediction_head
        
        if shared_prediction_head:
            # Share the same prediction head for all positions
            self.lm_head = nn.Linear(hidden_dim, vocab_size)
        else:
            # Use separate prediction heads for each position
            self.lm_heads = nn.ModuleList([
                nn.Linear(hidden_dim, vocab_size) 
                for _ in range(num_predicted_tokens)
            ])
    
    def forward(self, hidden_states):
        batch_size, seq_len, _ = hidden_states.shape
        
        # Get the hidden states for the last token
        last_hidden = hidden_states[:, -1]
        
        if self.shared_prediction_head:
            # Use the shared head for all predictions
            logits = self.lm_head(last_hidden)
            next_token_logits = logits.unsqueeze(1)
            
            # For positions beyond the first, we need to make a projection
            multi_token_logits = []
            for i in range(self.num_predicted_tokens):
                if i == 0:
                    multi_token_logits.append(logits)
                else:
                    # A simple projection for demonstration; in practice, this would be more complex
                    projected_hidden = last_hidden + i * 0.1  # Just a dummy transformation
                    multi_token_logits.append(self.lm_head(projected_hidden))
            
            multi_token_logits = torch.stack(multi_token_logits, dim=1)
        else:
            # Use separate heads for each position
            multi_token_logits = torch.stack([
                head(last_hidden) for head in self.lm_heads
            ], dim=1)
            
            # The first position is used for next-token prediction
            next_token_logits = multi_token_logits[:, 0:1]
        
        return next_token_logits, multi_token_logits
    
    def compute_loss(self, hidden_states, labels, ignore_index=-100):
        # Get predictions
        _, multi_token_logits = self.forward(hidden_states)
        
        # Prepare targets: shift labels to align with predictions
        # We need the next num_predicted_tokens tokens after the input
        shifted_labels = labels[:, :-self.num_predicted_tokens]
        targets = []
        
        for i in range(self.num_predicted_tokens):
            targets.append(labels[:, 1+i:1+i-self.num_predicted_tokens+1])
        
        # Stack targets
        stacked_targets = torch.stack(targets, dim=1)
        
        # Compute loss across all predicted positions
        loss = 0
        for i in range(self.num_predicted_tokens):
            loss += F.cross_entropy(
                multi_token_logits[:, i].view(-1, self.vocab_size),
                stacked_targets[:, i].reshape(-1),
                ignore_index=ignore_index
            )
        
        return loss / self.num_predicted_tokens

Speculative Decoding

Speculative decoding is an clever technique designed to accelerate the inference process of large autoregressive language models, significantly reducing the wall-clock time required to generate text. Standard generation is bottlenecked by its sequential nature, where the computationally expensive large model (the "target" model) must perform a full forward pass to predict just one token at a time. Speculative decoding introduces a secondary, much smaller and faster "draft" model. This draft model rapidly generates a short sequence of candidate future tokens (a "draft"). The core idea is then to use the large target model to verify this entire draft sequence in a single, parallel forward pass, potentially accepting multiple tokens at once and thus amortizing the cost of the target model's computation over several generated tokens.

The mechanism hinges on comparing the predictions of the draft model with those of the target model. After the draft model proposes a sequence of $ k $ tokens, $ d_1, d_2, \dots, d_k $, the target model is run once on the original input sequence concatenated with the draft. This single pass yields the target model's probability distributions for the next token at each position within the draft sequence. For each draft token $ d_i $, its validity is checked against the target model's prediction at that same position. If the target model strongly agrees with the draft token (e.g., it would have also predicted $ d_i $ with high probability, or based on a specific acceptance rule comparing $ P_{\text{target}}(d_i) $ and $ P_{\text{draft}}(d_i) $), the token is accepted. This verification proceeds sequentially through the draft.

The process continues until either all $ k $ draft tokens are accepted, or a draft token $ d_j $ is rejected. If rejection occurs at position $ j $, all preceding accepted draft tokens ($ d_1, \dots, d_{j-1} $) are kept. The remaining part of the draft ($ d_j, \dots, d_k $) is discarded. Crucially, the target model's probability distribution calculated at position $ j $ can then be used to sample a corrected token to append after the accepted sequence, ensuring the overall generation statistically follows the distribution of the more powerful target model. This corrected token, along with the previously accepted ones, forms the input for the next round of draft generation. By accepting multiple tokens per target model inference step on average, speculative decoding can achieve substantial speedups (e.g., 2-3x) with minimal impact on the quality of the generated text.

class SimpleSpeculativeDecoding:
    def __init__(self, target_model, draft_model, tokenizer, max_draft_tokens=5):
        self.target_model = target_model
        self.draft_model = draft_model
        self.tokenizer = tokenizer
        self.max_draft_tokens = max_draft_tokens
    
    def generate(self, prompt, max_length=100):
        # Start with the prompt's token IDs
        input_ids = self.tokenizer.encode(prompt, return_tensors="pt")
        
        # Keep generating until we reach max_length or an end token
        while input_ids.shape[1] < max_length:
            # Step 1: Generate multiple draft tokens
            draft_input_ids = input_ids.clone()
            draft_tokens = []
            
            with torch.no_grad():
                for _ in range(self.max_draft_tokens):
                    # Generate next token with draft model
                    outputs = self.draft_model(draft_input_ids)
                    next_token_logits = outputs.logits[:, -1, :]
                    next_token = torch.argmax(next_token_logits, dim=-1)
                    
                    # Save the draft token
                    draft_tokens.append(next_token.item())
                    
                    # Add to draft input
                    draft_input_ids = torch.cat([draft_input_ids, next_token.unsqueeze(0)], dim=1)
                    
                    # Check for end token
                    if next_token.item() == self.tokenizer.eos_token_id:
                        break
            
            # Step 2: Verify with target model
            with torch.no_grad():
                # Get target model probabilities for all tokens including drafts
                verification_ids = torch.cat([input_ids, torch.tensor([draft_tokens]).to(input_ids.device)], dim=1)
                target_outputs = self.target_model(verification_ids)
                target_logits = target_outputs.logits[:, input_ids.shape[1]-1:]
                
                # Convert to probabilities
                target_probs = F.softmax(target_logits, dim=-1)
                
                # Accept tokens until mismatch or all drafts accepted
                accepted_tokens = []
                for i, token_id in enumerate(draft_tokens):
                    # Check if target model agrees with draft
                    target_prob = target_probs[0, i, token_id].item()
                    draft_prob = 1.0  # Draft chose this with highest probability
                    
                    # Accept based on probability ratio (simplified)
                    if random.random() < min(1.0, target_prob / draft_prob):
                        accepted_tokens.append(token_id)
                    else:
                        # Rejection: get new token from target model
                        new_token = torch.argmax(target_logits[0, i]).item()
                        accepted_tokens.append(new_token)
                        break
            
            # Add accepted tokens to input_ids
            input_ids = torch.cat([input_ids, torch.tensor([accepted_tokens]).to(input_ids.device)], dim=1)
            
            # Check for end token
            if input_ids[0, -1].item() == self.tokenizer.eos_token_id:
                break
        
        # Decode the generated tokens
        return self.tokenizer.decode(input_ids[0])

How Democrats Failed on Crypto

Fri, 25 Apr 2025 01:00:00 +0000

How Democrats Failed on Crypto

It's hard to look back at the previous US administration and not recognize the near complete regulatory failure on the crypto issue. This failure has now metastasized into a serious political machine on Capitol Hill, becoming a giant fountain of corruption that pools dark money from unknown sources abroad into our politics and fuels far right extremist movements. Nothing embodies this naked corruption more than the Trump memecoin, which directly fuels policial corruption by providing an unregulated means of selling access to the current administration, the most brazenly corrupt act in the history of the American presidency.

While this pay-to-play executive branch token is new, it should come as no surprise to anyone. It is the apotheosis of exactly what crypto was designed to do: fuel corruption, crime, and undermine the state. What was once a small brush fire that could have been easily extinguished by regulators and a more proactive executive branch is now a raging forest fire. The crypto industry is now deeply entwined with political corruption and has become a major political machine for the MAGA movement.

Unfortuntately, this pattern of regulatory hesitation when confronted with corporate and financial interests has become a concerning hallmark of Democratic governance in the last two decades. Just as the Obama administration's "too big to jail" approach allowed financial institutions to escape meaningful accountability through settlements rather than criminal prosecutions, the Biden administration's fragmented approach to crypto regulation created a regulatory vacuum that the industry eagerly exploited. There are also stark parallels to how multi-level marketing companies leveraged political donations and claims of entrepreneurship to avoid scrutiny in the 1970s. There is nothing new under the sun, this foolishness repeats itself with such monotonous precision.

All of this did not have to happen. Democrats had all the levers of power neccessary to curtail this dark money machine run amok, but they didn't use them. The crypto policy of leaders like Joe Biden, Chuck Schumer, Ro Khanna, Nancy Pelosi, Kamala Harris, and Maxine Waters was a complete failure. But failure is something that we can learn from and fix. But it's paramount that we understand that inaction, equivocation, and strategic ambguitiy did not work the last time and they won't work the next time either. Hopefully by acknowledging these shortcomings and learning from them, the party can develop more effective strategies for preventing these kind of inherently-destabilising and anti-democratic technologies from growing without check in the future.

Party Unity & Messaging

The Democratic Party's approach to cryptocurrency regulation was characterized by deep internal divisions that prevented cohesive policy action. These divisions manifested as competing factions pushing the party leadership in opposing directions.

On one side stood regulatory hawks led by Senator Elizabeth Warren (D-MA) and Representative Brad Sherman (D-CA), who consistently advocated for strict oversight of crypto. Warren and her allies emphasized crypto's potential risks to consumers, financial stability, and national security. They regularly highlighted concerns about money laundering, sanctions evasion, and fraud within the crypto ecosystem. This faction viewed cryptocurrency primarily through a lens of consumer protection and financial system stability.

Opposing this perspective was a small (but not insignificant) contingent of pro-crypto Democrats who saw crypto as an opportunity for financial innovation and inclusion—or perhaps more cynically, merely as a way to fund campaigns. Some Democrats expressed fear that excessive regulation would "stifle innovation" and cede technological leadership to other countries. Other democrats just wanted to appear "pro-business" and "pro-innovation" and embraced a form of techno-determinism declaring the "web3 is inevitable" and "crypto is here to stay", regardless of how harmful it was to society. Others were just plain confused and delegated to their staffers, who in-turn based their reccomendations on industry whitepapers due to a lack of time and expertise. And some were just bought off by the crypto industry, plain and simple.

This ideological rift prevented the party from developing a unified stance on crypto regulation. The competing internal pressures effectively paralyzed legislative action, creating regulatory paralysis. Party leadership, including Senate Majority Leader Chuck Schumer (D-NY) and Vice President Kamala Harris, struggled to navigate these competing interests. During the 2024 election campaign, Vice President Kamala Harris attempted to walk an impossible and incoherent fine line between the two factions, vowing to "encourage" crypto while also protecting consumers and investors.

On the crypto policy debate, I'm reminded of the quote "If one side wants to build a bridge over a canyon and the other side doesn’t, the wisest possible position isn’t to build half a bridge that stops in thin air." This incoherent middle-ground approach left a policy vacuum that allowed the cryptocurrency industry to shape the narrative and regulatory landscape, and that created the current mess we find ourselves in.

Don't Stifle Innovation

The stated reluctance among some Democrats to regulate technologies, often framed as a fear of "stifling innovation," can be viewed through several critical lenses. One perspective is that this stance serves as a convenient shield, allowing policymakers to abdicate the difficult responsibility of understanding and governing complex technical fields. Faced with the arcane intricacies of software and conflicting narratives about its potential, invoking the universally positive concept of "innovation" provides a politically palatable justification for inaction or minimal intervention, delaying potentially necessary consumer protection or financial stability measures. This approach avoids the hard work of developing nuanced regulations, instead opting for a hands-off posture that appears forward-thinking but may neglect underlying risks.

Compounding this potential abdication is a genuine lack of deep technical understanding among many policymakers. The crypto space is rife with jargon, hype, contradictory narratives, and abstract promises. Without a solid grounding in computer science, finance and database technology, distinguishing genuine technological breakthroughs from inefficient or redundant applications becomes challenging. This knowledge gap makes policymakers susceptible to persuasive industry narratives that emphasize transformative potential while downplaying limitations or negative externalities. Consequently, the fear of stifling the next big thing can outweigh concerns rooted in technical realities, such as the argument made by many software engineers that existing, simpler technologies can often achieve the same goals more efficiently and without the significant negative externalities or potential for illicit use associated with blockchain applications.

This is best illustrated by Rep. Ritchie Torres (D-NY) who argued, "The project of radically decentralizing the internet and finance strikes me as a profoundly progressive cause"—a statement that reveals both profound technical ignorance and political naivety. Torres, notably the second-largest recipient of hedge fund industry money in Congress, fundamentally misunderstands that both the internet and financial systems are already decentralized by design. The internet has operated as a distributed network since its inception, while our financial system includes 4,455 federally insured credit unions alongside thousands of community banks and a distributed regulatory framework split across fifty states and four federal regulators. His framing of this deregulatory agenda of rolling back consumer protections and enabling predatory gambling as "progressive" represents either a cynical misappropriation of progressive language or a complete failure to understand the systems he claims to want to transform, or merely sophistry.

This quote reveals an unfortunatly common phenomenon, that it's far easier to hand-wave and posture that "decentralization" (a term with many disparete meanings) or "tokenization" (a buzzword with no clear definition or meaning) solving some long-standing legacy financial problem than it is to refute the argument with a technical discussion. Brandolini's eponymous law states: “The amount of energy needed to refute bullshit is an order of magnitude bigger than to produce it.” And oh my, does the crypto industry exploit this assymetry to the fullest extent.

Furthermore, the policy discourse is significantly shaped by a powerful nexus between Ivy League institutions and the private sector. Universities like Duke, MIT and Stanford house influential research centers and professors who often become prominent voices in policy discussions, frequently advocating for a light regulatory touch to foster innovation. However, these institutions often receive substantial grants and funding from the very industries they are analyzing. This creates a potential conflict of interest, where academic research and advocacy might inadvertently serve to legitimize and provide reputation laundering for crypto ventures. This academic-private flywheel generates authoritative-sounding arguments favoring innovation, effectively marginalizing dissenting technical experts who argue that much of the claimed innovation is unsubstantiated or comes with unacceptable trade-offs.

Ultimately, the narrative pushed by this academic-industry complex, combined with corporate influence and a potential lack of technical depth among policymakers, creates a challenging environment for any critical perspectives to gain traction. Software engineers and other technologists pointing out that many blockchain use-cases are technically suboptimal solutions searching for a problem struggle to have their message cut through the noise. The arguments about efficiency, scalability, security, and negative externalities are often drowned out by the well-funded, academically-backed chorus chanting "innovation." This dynamic contributes to a policy environment where Democrats hesitate to implement robust regulations, caught between the fear of hindering progress (real or imagined) and the complex, interwoven pressures shaping the debate.

The reality is that cryptocurrency offered no genuine technological innovation. It merely created unregulated financial instruments that circumvented established regulatory frameworks, while facilitating speculative gambling on arbitrary price fluctuations of digital assets with no intrinsic value. Both of these functions fundamentally undermine the principles of a society governed by consistent and equitable rule of law. Consider that cryptocurrency is roughly the same age as the iPhone, yet while we can clearly point to how the iPhone transformed communication, productivity, and daily life for billions, crypto's societal contributions remain conspicuously absent after fifteen years of development.

This is the area that I have been most active in, and unfortunately I don't have a good answer to this problem. Other than software engineers need to be more democratically involved and academics need to be less corruptible. I'm not holding my breath for either of these things to happen.

Too Niche, Too Wonky

The reality is that crypto policy is extremely niche and the average American both doesn't even know it exists and doesn't care about it. In polling it ranks alongside salmon fishing subsidies in terms of issues the public cares about. Which makes messaging on this issue a near-impossible tasks, and barely worth the effort until there's some sort of scandal or crisis that dominates the news cycle. The average voter just doesn't have a reason to care, relative to everyday kitchen table issues.

The reality that abstract financial policy is too wonky, too niche, and too far removed from the daily lives of most Americans. The technical and legal complexity creates a significant knowledge asymmetry between people interested in this topic and the public, allowing a hegemonic bloc of neoliberal interests to dominate the discourse. This bloc—comprising technology firms, venture capitalists, and financial institutions—effectively monopolizes the expertise needed to craft regulation, while simultaneously funding think tanks and academic centers that produce policy papers aligned with their market-oriented worldview.

The resulting environment becomes captured by a classic case of elite-driven policymaking with a predisposition towards inaction and conflicts of interest. A small cadre of technocratic policymakers, themselves products of the revolving door between government and private industry, find themselves intellectually divided yet structurally constrained by career incentives that discourage regulatory boldness. Their personal career trajectories often lead to lucrative positions at law firms and financial institutions with vested interests in crypto markets, creating conflicts of interest that subtly shape regulatory approaches. This dynamic reinforces a hegemonic consensus that privileges market-based solutions and appeals to "innovation" over any kind of action, effectively neutralizing attempts at meaningful regulation while maintaining the appearance of democratic deliberation. This is not a new phenomon of course, but unfortunately it is a very common one on issues that are so far outside of the public consciousness.

One might think that the transformation of the Executive Branch into a blatant pay-to-play operation under Trump would break through the public, and could be a watershed moment for public awareness on crypto corruption. Yet this scandal has failed to galvanize meaningful opposition. Instead, we're witnessing a disturbing shift in American values, where many citizens have implicitly accepted Thucydides' brutal principle that "the strong do what they can and the weak suffer what they must." This cynical embrace of power over principle—the notion that if Trump can exploit the system, he's entitled to do so—represents a fundamental abandonment of the rule of law. Such thinking doesn't just enable corruption; it celebrates it as a form of strength. This profound ethical collapse makes regulatory reform nearly impossible, as it antithetical to the very foundation of a rules-based society. But that's where we're at as a country sadly.

Regulatory Sclerosis

The period spanning from 2020 to early 2025 witnessed a concerted push by prominent Democrats, notably Senator Elizabeth Warren, to establish stricter regulatory frameworks around the burgeoning cryptocurrency industry. Driven by concerns over illicit finance, including money laundering, terrorism financing, and rampant consumer fraud, these efforts sought to bring crypto tokens under the purview of existing financial regulations. While internal party consensus began showing fractures later in this period, key figures remained steadfast in advocating for measures aimed at mitigating the perceived risks inherent in the largely unregulated crypto space.

At the forefront of these legislative initiatives was the Digital Asset Anti-Money Laundering Act (DAAMLA). Championed vigorously by Senator Warren, this bill represented the most comprehensive attempt to impose traditional financial safeguards onto the digital asset ecosystem. First introduced in December 2022 and formally reintroduced with expanded, initially bipartisan, support in July 2023, DAAMLA aimed to close regulatory gaps exploited by illicit actors. Early co-sponsors included figures like Senators Roger Marshall (R-KS), Joe Manchin (D-WV), and Lindsey Graham (R-SC), signalling an initial cross-party interest in addressing crypto-related risks, although some Republican support later waned.

The DAAMLA proposal gained significant traction among Democrats throughout late 2023, building a broad coalition within the party. By December 2023, numerous influential Democratic senators, including several members of the crucial Senate Banking Committee like Raphael Warnock, Laphonza Butler, and Chris Van Hollen, had signed on as co-sponsors. The legislation's core provisions intended to extend Bank Secrecy Act obligations—including Know Your Customer requirements—to previously uncovered entities like wallet providers, miners, and validators. It also sought to mandate reporting for large offshore crypto transactions and directed the Treasury Department to establish robust compliance examination processes for crypto businesses.

Senator Warren consistently justified the need for DAAMLA by framing it as a critical national security measure. She argued that cryptocurrencies had become a preferred tool for rogue nations, drug cartels, ransomware gangs, and fraudsters, citing estimates that significant portions of North Korea's missile program were funded via crypto-related cybercrime and that illicit crypto transactions reached at least $20 billion in 2022 alone. This rationale resonated with some traditional financial institutions, garnering explicit support from groups like the Bank Policy Institute, which saw the bill as a step towards leveling the regulatory playing field.

Beyond proposing new legislation, influential Democrats also actively opposed measures perceived as overly friendly to the crypto industry or lacking sufficient safeguards. Senator Warren, alongside Senate Banking Chairman Sherrod Brown (D-OH), stood as a primary obstacle to the Senate considering the Financial Innovation and Technology for the 21st Century Act (FIT 21). Despite this Republican-led bill passing the House with considerable bipartisan support, including 71 Democrats, Warren criticized it for potentially weakening regulatory oversight. Similarly, she voiced strong opposition to stablecoin bills like the proposed GENIUS Act, arguing they risked consumer funds and national security unless they incorporated stringent anti-money laundering protections as demanded by the Treasury Department.

Despite the persistent efforts led by Senator Warren to impose tighter controls, the period also revealed evolving dynamics within the Democratic party regarding cryptocurrency. A notable instance occurred in May 2024 when Senate Majority Leader Chuck Schumer and ten other Democratic senators voted against the Biden administration's stance to overturn specific SEC guidance (SAB 121) on crypto accounting, signalling a potential softening or diversification of views among some Democrats. This divergence highlighted a growing internal debate, contrasting Warren's staunch regulatory approach with other positions emerging elsewhere within the party, setting the stage for continued policy clashes and inaction leading into 2025. And that's where we are today, despite the best intentions of the Warren faction of party, there's been very little progress on the legislative front.

Crypto Super PACs

The cryptocurrency industry, initially operating on the fringes of the financial system, has rapidly evolved into a significant political force. Its business models, often predicated on minimal regulatory oversight and a continuous stream of public investment, created a powerful incentive to engage directly with policymakers. As governments worldwide began considering stricter rules to address concerns around consumer protection, market stability, and illicit finance, the crypto sector recognized the existential threat regulation posed. Consequently, the industry began to strategically marshal its considerable financial resources, transitioning from a nascent tech sector into a sophisticated lobbying powerhouse determined to shape legislation and political outcomes in its favor.

This political mobilization manifested primarily through unprecedented levels of spending on lobbying and campaign finance. The industry deployed armies of lobbyists, many with deep connections forged through previous government service, to advocate directly with lawmakers and regulators. Furthermore, during critical election cycles, such as the 2024 midterms, crypto-aligned super PACs injected vast sums into closely contested races, exceeding $245 million, dwarfing the $27 million donated by Sam Bankman-Fried to a similar PAC in 2022. This deluge of money was strategically deployed to support candidates perceived as friendly to the industry's anti-regulatory stance and, crucially, to oppose those who favored stronger oversight, effectively functioning as large-scale influence buying.

A key tactic in the industry's influence campaign involved specifically targeting prominent critics and regulatory advocates within the Democratic party. Figures like Senator Elizabeth Warren and Senator Sherrod Brown, then-Chair of the Senate Banking Committee, became focal points for intense opposition funding. These were not random attacks but calculated efforts to neutralize powerful voices pushing for regulation. The significant spending against Senator Brown, utilizing sophisticated and relentless campaign tactics, was a major factor contributing to his narrow defeat in the 2024 election.

The political consequences of this targeted spending extended beyond individual races, significantly impacting the overall balance of power and the legislative agenda. The loss of key figures like Senator Brown, attributed in part to the crypto industry's intervention, played a role in the shift of Senate control towards the Republican party. This alteration in the political landscape severely hampered the prospects for enacting meaningful crypto regulations favored by Democrats and consumer advocates. Moreover, it weakened the legislative branch's ability to serve as a check on run-away executive power which we now have to deal with in the current administration.

The cryptocurrency industry's aggressive foray into political spending raises existential questions about the health of democratic processes. When a single industry can pour hundreds of millions of dollars into elections to unseat critics and elect allies, it risks distorting policy outcomes away from the public interest and towards narrow corporate objectives. The rot runs deep in America, and crypto regulatory capture is just the latest symptom of the grotesque corruption of our political system by the Citizens United ruling.

State-level Legislation

While the Biden administration was slow to act at the Federal level, a significant counter-trend emerged within individual states. Entrepreneurs in the crypto industry very easily captured state legislatures, and under the very simple guise of bringing business and jobs to their states, this created a scenario where the crypto industry, facing ambiguity or potential hostility from Washington D.C., found welcoming environments and operational certainty through state-level actions, effectively allowing it to establish a legitimate foothold within the United States.

Among local city leaders, New York City Mayor Eric Adams emerged as one of the country's most outspoken Democratic crypto backers, even converting his salary into Bitcoin and Ether to demonstrate his commitment. However, Adams, known for his proximity to the crypto world, now faces serious fraud allegations; he has been charged in a five-count federal indictment with multiple fraud-related offenses. Prosecutors allege that he orchestrated a scheme to accept illegal campaign contributions from foreign nationals through "straw donors" who falsely claimed to be donating their own money. Additionally, he is charged with wire fraud for allegedly misappropriating funds from New York City's matching funds program by leveraging these illegal donations to obtain public matching funds.

Wyoming stands out as the preeminent example of this state-led legitimization effort. Dubbed the "Delaware of Digital Asset Law," Wyoming enacted a comprehensive suite of over 30 bills specifically designed to support the industry. Its most groundbreaking move was the creation of Special Purpose Depository Institution charters, allowing crypto companies like Kraken and Avanti to become state-chartered banks. This provided unprecedented legitimacy and, crucially, established a regulated pathway connecting crypto tokens to the traditional U.S. dollar payments system via the Federal Reserve. Wyoming further bolstered the industry by providing specific legal protections for crypto ownership, including shielding assets held in Wyoming LLCs from certain creditors.

Following Wyoming's pioneering efforts, a wave of other states implemented their own crypto-friendly policies, solidifying the industry's presence across the country. Florida exempted crypto businesses from certain licensing requirements, created a regulatory sandbox for innovation, and even initiated a pilot program for paying state fees with cryptocurrency. Texas leveraged its energy resources and deregulated grid to become a hub for crypto mining, offering significant tax incentives and authorizing state-chartered banks to offer crypto custody services. Other states like Nevada, Tennessee, South Dakota, and Alaska also adopted various measures, from recognizing blockchain records legally to maintaining low tax burdens, collectively signaling a broad state-level acceptance and encouragement of the crypto sector.

The Challenges of the SEC

The intellectual legal debate surrounding whether most crypto assets qualify as securities under existing U.S. law delves into fundamental and ultimately deeply philosophical questions about value and legal rights in financial markets. Traditionally, securities like stocks or bonds represent a claim on an underlying entity's assets, profits, or future cash flows, imparting specific legal rights to the holder. Most crypto assets, however, lack such direct claims; their value often derives not from underlying assets or contractual entitlements but from market sentiment, technological promise, or speculative momentum—what might be termed "sentiment and vibes." This creates a novel situation: assets potentially commanding significant market capitalizations without conferring tangible ownership or creditor rights, traded primarily on collective belief rather than intrinsic economic function. Applying securities laws designed for instruments with clear underlying claims to these fundamentally different digital tokens presents a genuine legal and conceptual challenge, forcing regulators and courts to grapple with absurd and/or worthless assets that may not cleanly fit in any category or really have any reason to exist.

This inherent ambiguity fuels a legitimate debate about the appropriate regulatory framework and the very purpose of financial regulation. Bringing most crypto assets under the SEC's remit, while potentially offering investor protection, raises complex questions. Crypto assets function as speculative instruments lacking connection to productive capital formation or tangible economic value creation, then regulating them under securities law risks transforming the SEC, in this context, into something akin to a gambling regulator rather than a facilitator of efficient capital markets. This predicament highlights a profound, unresolved tension: should financial regulation solely focus on instruments funding economic activity, or must it now encompass purely speculative, digitally native assets traded on belief alone? Congress arguably should have stepped in to deliberate this complex issue, which touches upon the fundamental role of markets and finance in society—a nuanced debate involving intricate legal and economic philosophy that the public may struggle to grasp and policymakers have largely avoided confronting head-on. But Congress really isn't in the legislating business these days, so it fell on the SEC to muddle through the problem as best as they could and try and minimize public harm.

On top of this complicated debate we never had, there was the claim that the SEC under Chair Gensler employed "regulation by enforcement" against the crypto industry often misrepresents standard regulatory procedure. Enforcement is a fundamental tool for agencies like the SEC, used to ensure compliance with existing laws—in this case, primarily the Securities Acts of 1933 and 1934. The SEC's actions largely involved applying the long-established Howey test to determine if crypto tokens qualified as investment contracts (securities). This application of existing legal frameworks and judicial precedent to novel technologies is a core function of regulatory bodies, not an invention of new rules post hoc through punitive measures. The SEC consistently articulated its view that most crypto tokens fit within the existing definition of a security, basing enforcement actions on violations of these established laws.

Much of the crypto industry's objection stemmed from a fundamental disagreement with the SEC's application of the Howey test to their products, rather than a genuine lack of legal standards. Industry participants often argued for unique treatment or bespoke rules, viewing the application of traditional securities laws as ill-suited. When the SEC proceeded with enforcement based on its interpretation of existing law, it was labeled "regulation by enforcement" by those facing action or seeking a more lenient framework. However, this overlooks that regulatory agencies aren't obligated to create specific new rules for every new technology before enforcing existing statutes, especially when they believe current laws apply. Furthermore, the SEC did provide guidance through various communications and the enforcement actions themselves, which clarified the types of conduct considered non-compliant, albeit in a manner the industry found unfavorable.

Ultimately, the "regulation by enforcement" narrative functions more as a rhetorical critique of the outcomes of the SEC's actions than a substantive legal challenge to its methods. It reflects the industry's frustration with being subjected to long-standing investor protection laws and the Howey framework, rather than demonstrating that the SEC was arbitrarily creating new rules through enforcement actions alone. Characterizing the application of established legal principles as an inherently improper process obscures the core issue: a clash between the industry's desire for a different regulatory approach and the SEC's mandate to apply existing securities laws as it interprets them. Regulation by enforcement was really just "enforcement" of long-standing laws that the industry just didn't want to comply with.

However one decision by the Gensler SEC comes across as particularly wrong-headed that of the decision to declare Coinbase's registration effective in April 2021, enabling its direct listing. While the SEC's approval focused strictly on whether Coinbase met the necessary disclosure requirements for investors, not on endorsing its business practices or confirming compliance with all securities laws, this distinction proved problematic later. The approval, handled by the SEC's disclosure review division, essentially confirmed that Coinbase provided sufficient information for the public listing process, following standard procedure.

The core of the controversy stems from the inherent conflicts of interest embedded in Coinbase's vertically integrated structure, which the SEC itself later challenged. In its June 2023 lawsuit, the SEC alleged that Coinbase had been operating illegally since at least 2019—well before its public listing—as an unregistered securities exchange, broker, and clearing agency simultaneously. This combination of functions within one entity is typically separated in traditional financial markets precisely to mitigate conflicts between intermediaries and their customers. The SEC argued that by acting as the marketplace, the agent facilitating trades, and the custodian holding assets and settling transactions, Coinbase created significant, unavoidable conflicts of interest detrimental to investors.

This situation presents a paradox: the SEC, whose mandate includes ensuring market integrity and investor protection (partly by managing conflicts of interest), allowed a company to go public despite its core operations seemingly embodying the very conflicts the regulatory framework seeks to prevent. The paradox is heightened by evidence suggesting the SEC had warned Coinbase pre-listing about potential enforcement actions regarding its asset listings and operational structure. While much of the review predated Chair Gary Gensler's tenure, the fact remains that the agency greenlit public market access for a company whose business model it later sued as fundamentally non-compliant with securities laws designed to separate functions and avoid such conflicts. We don't know the internal machinations of what went on, but it's clear this decision was a mistake and further allowed the floodgates of capital to pour into the crypto industry on top of a predatory non-compliant business model which led us to the current mess.

However compounding these choices and challenges, the Gensler SEC found itself in an exceedingly difficult position regarding the crypto market. Despite Gensler's stalwart commitment to applying securities laws, the agency faced a veritable "forest fire" of tens of thousands of individual tokens and platforms operating in clear violation of securities laws, stretching its already limited resources impossibly thin. Compared to the vast scale of the traditional US capital markets that constitute the SEC's primary and existential mandate, the crypto market, while growing, remained relatively small (relative to the size of normal capital markets). This created a resource allocation dilemma. Gensler was essentially tasked with containing this rapidly spreading digital wildfire with the equivalent of a garden hose, lacking the necessary budget and personnel.

Critically, neither the Biden administration nor Congress provided the substantial reinforcements—either through significantly increased funding for the SEC or comprehensive legislative action—needed to adequately address the scale and novelty of the crypto problem, leaving the agency to manage an overwhelming situation with insufficient tools or resources. Credit should go to the stalwart staffers who tried their best despite the insurmountable problem they were tasked with. But it's clear the agency was never given the resources needed to fully tackle this problem at scale.

Current Administration

The current administration, is not surprisingly rife with conflicts of interest and corruption. The SEC allegedly dropped or paused multiple enforcement actions against crypto companies founded by or linked to President Trump's donors and business partners. Specifically:

Binance: Pausing the SEC case after the Trump family reportedly held talks to acquire a financial stake in the company.
Coinbase: Dismissing the SEC case shortly before its CEO attended a White House digital assets summit.
Justin Sun (Tron): Pausing the SEC case against Sun, who invested $75 million in a Trump family-affiliated crypto project (World Liberty Financial) from which the family could potentially earn substantial revenue.
Ripple Labs: Reportedly dropping the SEC case less than two weeks after its CEO attended the White House crypto summit and after the company donated $5 million to Trump's inaugural committee.
Immutable and Uniswap: Dropping investigations into these firms, which are connected to SEC Chair Nominee Paul Atkins' investments via Anchorage Digital.

The SEC's Division of Corporate Finance issued a Staff Statement asserting most meme coins are not securities. This interpretation could shield President Trump's and First Lady Melania Trump's own meme coins (TRUMP and MELANIA) from regulatory scrutiny and federal securities laws. The subsequent closure of an investigation into the "Hawk Tuah" meme coin reinforces this concern.

David Sacks, a Trump apointee and venture capitalist, was appointed as the Trump administration’s special advisor for AI and cryptocurrency-informally known as the “crypto czar.” Craft Ventures holds stakes in other crypto-related companies, such as BitGo, Chia Network, and Dapper Labs while Craft Ventures retains exposure to the digital asset sector which David Sacks oversees.

The Trump family's venture, World Liberty Financial, is launching a stablecoin on a blockchain created by Binance, further intertwining the family's business interests with a company that has received potentially favorable regulatory treatment (paused SEC case).

In addition to this, Paul Atkins, Trump's nominee for SEC Chair, holds significant crypto-related investments (up to $6 million) in firms like Securitize, Anchorage Digital, and Off the Chain Capital. These firms have connections (as investors or through supported assets) to companies like Coinbase, Ripple, Immutable, Uniswap, and Binance, which have recently benefited from favorable SEC decisions (dropped/paused cases). This raises concerns about potential conflicts of interest influencing SEC actions, even with his commitment to divest if confirmed.

In Congress there are two pieces of theoretical legislation that are the industry wants to push through Congress, even though there is essentially no interest from the public for them to pass. These fall into two categories right now but might emerge as one bill in the future.

Stablecoin Bill: These proposed stablecoin bills (like the GENIUS and STABLE Acts) risk destabilizing the US financial system by creating a weak regulatory framework tailored to industry demands. They would allow a broad range of entities, including potentially under-regulated non-banks, to issue systemically important payment instruments, creating opportunities for regulatory arbitrage between inconsistent state and federal oversight. Mandating reserves sounds prudent, but the push to allow interest payments could transform stablecoins into risky, uninsured deposit-like products prone to runs (like we saw with money market funds in 2008), while oversight mechanisms might prove insufficient to guarantee true 1:1 backing, prioritizing industry profits and innovation theatre over genuine consumer protection and financial stability.
Market Structure Bill: The proposed market structure legislation represents an attempt by the crypto industry to weaken established investor protections and undermine regulatory authority for its own benefit. By pushing to rigidly define jurisdiction and create pathways to classify many digital assets as commodities under the CFTC, the bill seeks to sideline the SEC and subject fewer products to robust securities laws, potentially leaving investors exposed. The demand for "practical" registration processes and Congressionally-mandated rules risks locking in lenient standards, hindering regulators' ability to adapt to evolving risks and ultimately legitimizing a largely speculative market while sacrificing crucial safeguards under the guise of promoting innovation. This legislation dangerously weakens existing securities regulation by potentially allowing firms to wrap traditional equity products onto the blockchain, relabel them as tokens to exploit regulatory loopholes, and thus subject them to far less stringent oversight, effectively incentivizing a race to the bottom that sacrifices vital investor protections like disclosures and controls.

Needless to say if any of these bills are allowed to pass, this would be incredibly harmful to the American public. We live in unprecedented times. Never before in the history of the United States has a president been so deeply entangled in business interests while in office, and the conflicts of interest and corruption this creates are unprecedented.

So is there any hope?

At least in the current configuration of American politics, with a feckless Republican congress hell-bent on authoritarianism, where Citizens United is still the law of the land, it's hard to see what can be done so long as the current Democratic party is the only vehicle for change.

The current leadership is too divided, too focused on botique social issues, too out of touch with voters, and too easily corruptible by commercial interests. The next several years will uncork a geyser of corruption from the Trump crime family and their friends in the crypto industry which will make the worst excesses of the Gilded Age seem tame. They'll be hundreds if not thousands of new scandals, and crypto fraud will become an everyday fixture of American life. Crypto fraudsters will make billions fleecing the public, relocate themselves and their ill-gotten gains to Dubai to shield themelves from the consequences of democratic backsliding, all while continuing to funnel money into crypto super PACs to keep the gravy train flowing while the world burns.

Elections have consequences. The American public voted to touch the stove of authoritarianism coupled with unchecked financial fraud, and now they're going to get burned. And sadly the time to stop this was four years ago, it's too late now. But on the backside of several years of this orgy of greed and corruption, there might be an opportunity for a new generation of Democrats to step up. I don't know what that party will look like, or if the republic will even survive, but hopefully they will take the crypto threat seriously and not make the same mistakes again.

MLIR Part 8 - GPU Compilation with MLIR

Sat, 19 Apr 2025 01:00:00 +0000

GPU Compilation with MLIR

Continuing on from last time, now that we have our transformer primitives that we need to optimize, let's look at how we can translate high-level tensor operations (like softmax, attention, etc) expressed in MLIR down to low-level code that can run in parallel on Nvidia GPUs to improve our performance. To do that we're going to start to put together the making of a small compiler.

Now we're going to need to switch to a machine with an Nvidia GPU (sorry no MacOS). So either fire up your Linux machine with a Nvidia GPU or go rent one from the various providers.

Installing CUDA Toolkit notoriously painful, so if you rent a GPU from a cloud provider this is already done for you. If you need to setup a a bespoke instance you should use one of the official docker images from Nvidia like:

docker pull nvidia/cuda:12.1.0-devel-ubuntu22.04
docker run -it --gpus all nvidia/cuda:12.1.0-devel-ubuntu22.04 bash

But if you want/need to install it on your own machine here's some instructions, although you should refer to the many guides online for the most up to date instructions. If you have a machine which does not have CUDA Toolkit installed, you can install it using the following steps.

wget https://developer.download.nvidia.com/compute/cuda/repos/ubuntu2204/x86_64/cuda-keyring_1.0-1_all.deb
sudo dpkg -i cuda-keyring_1.0-1_all.deb
sudo apt-get update
sudo apt-get install build-essential

sudo apt-get -y install cuda-toolkit-12-x

Make sure you have the nvcc compiler installed, again if you are renting a GPU this is probably already done for you.

$ nvcc --version
nvcc: NVIDIA (R) Cuda compiler driver
Copyright (c) 2005-2021 NVIDIA Corporation
Built on Thu_Nov_18_09:45:30_PST_2021
Cuda compilation tools, release 11.5, V11.5.119
Build cuda_11.5.r11.5/compiler.30672275_0

Verify that you have a Nvidia GPU installed:

lspci | grep -i nvidia

And then test the CUDA version and your driver version:

$ nvidia-smi
+---------------------------------------------------------------------------------------+
| NVIDIA-SMI 535.183.01             Driver Version: 535.183.01   CUDA Version: 12.2     |
|-----------------------------------------+----------------------+----------------------+

Note the specific CUDA version (In this case 12.2) this is important because you'll need to instal libraries specific to this version.

Now normally we would have to recompile MLIR with the CUDA runner enabled, which sucks. So I've made a docker image that has MLIR with the CUDA runner enabled. So if you're renting a GPU from RunPod or LambdaLabs you can just use this base image. Or if you have a local machine you can pass the GPU through to the container using NVIDIA Container Toolkit.

docker pull ghcr.io/sdiehl/docker-mlir-cuda:main
docker run -it ghcr.io/sdiehl/docker-mlir-cuda:main bash

Otherwise you have compile MLIR from source again. Here are the steps:

git clone https://github.com/llvm/llvm-project
mkdir llvm-project/build
cd llvm-project/build
RUN cmake -G Ninja ../llvm \
   -DCUDACXX=/usr/local/cuda/bin/nvcc \
   -DCUDA_PATH=/usr/local/cuda \
   -DCMAKE_CUDA_ARCHITECTURES="75;80;86;90" \ # Add your GPU architecture here
   -DCMAKE_C_COMPILER=clang \
   -DCMAKE_CXX_COMPILER=clang++ \
   -DCMAKE_CUDA_COMPILER=/usr/local/cuda/bin/nvcc \
   -DLLVM_ENABLE_PROJECTS=mlir \
   -DLLVM_BUILD_EXAMPLES=ON \
   -DLLVM_TARGETS_TO_BUILD="Native;NVPTX;AMDGPU" \
   -DCMAKE_BUILD_TYPE=Release \
   -DLLVM_ENABLE_ASSERTIONS=ON \
   -DLLVM_CCACHE_BUILD=ON \
   -DMLIR_ENABLE_CUDA_RUNNER=ON \
   -DMLIR_ENABLE_CUDA_CONVERSIONS=ON \
   -DMLIR_ENABLE_NVPTXCOMPILER=ON

RUN cmake --build . -t mlir-opt mlir-translate mlir-transform-opt mlir-runner
RUN cmake --build . -t install

Heads up that this is going to be a somewhat weird crash course in CUDA programming. After all our goal is to build a compiler that targets the GPU from MLIR, so we're going to very quickly cover GPU basics and then delve straight into low-level assembly programming of the GPU very quickly. Most people don't write PTX directly in day to day work, unless they're working on compilers. If this is your first time writing CUDA code, it might be useful to read one of the many guides on CUDA programming online that cover GPU programming in more detail first.

CUDA Ecosystem

The CUDA compilation process involves several key components and intermediate representations that are important to understand for GPU programming. Let's first explore how CUDA programs are compiled and executed.

First CUDA is an extension of C++ that allows you to program the GPU. It's a language built on top of C++ that adds features specifically for GPU programming. It usese its own compiler nvcc to compile to PTX (Parallel Thread Execution), which is an intermediate assembly language for NVIDIA GPUs. PTX provides a stable programming model and instruction set for parallel computing. It's architecture-neutral, meaning it can target multiple generations of NVIDIA hardware.

The compilation process then moves from PTX to device-specific binary code called CUBIN (CUDA Binary). A CUBIN file contains the actual machine code that runs on specific GPU architectures. These files are ELF-formatted and contain not just executable code, but also symbols, relocators, and debug information. While CUBIN files are typically embedded in the host executable by default, they can be generated separately using nvcc's -cubin option.

nvcc manages this complex compilation process. It coordinates multiple compilation stages and can produce various output formats depending on your needs:

It can generate PTX code for future JIT (Just-In-Time) compilation
It can create architecture-specific CUBIN files
It can combine multiple PTX and CUBIN files into a single FATBIN file
It can embed these GPU binaries into host executables

When you invoke a compiled program on the host it will then do the following:

Determines the available GPU architecture
Selects the appropriate CUBIN from the FATBIN if available
Falls back to JIT-compiling the PTX code if necessary for newer architectures
Loads and executes the code on the GPU

All of this is handled for the end user by the compiler if you use the nvcc compiler.

The FATBIN format is particularly important as it allows a single executable to support multiple GPU architectures. It can contain both PTX code (for future compatibility through JIT compilation) and pre-compiled CUBIN files (for optimal performance on known architectures). Now let's look at some simple C++ code that uses CUDA.

#include <stdio.h>

// CUDA kernel function
__global__ void helloKernel() {
  printf("Hello, CUDA!\n");
}

int main() {
  // Call the CUDA kernel
  helloKernel<<<1, 1>>>();

  // Wait for the kernel to finish
  cudaDeviceReset(0);

  return 0;
}

In CUDA's extension of C++ there is special syntax for launching the kernel. The helloKernel function is the kernel we want to execute on the GPU. The <<<1, 1>>> is the CUDA syntax for launching the kernel. The first argument is the number of blocks to launch, and the second argument is the number of threads per block.

kernel<<<blocks, threads>>>(...)

More on threads and blocks later. Now inside of the kernel we have access to special variables blockDim, blockIdx, and threadIdx. As a simple example let's look at a kernel that squares each element of an array. Here we have a square kernel which we'll describe the internals of later, for now it simply squares each element of the array.

__global__ void square(int* array, int n) {
    int tid = blockDim.x * blockIdx.x + threadIdx.x;
    if (tid < n)
        array[tid] = array[tid] * array[tid];
}

To get a CUBIN code we can use the following command:

nvcc -o square square.cu

We can run th executable code which contains the compiled CUBIN code in a binary that runs the host logic on the CPU and the CUBIN code on the GPU.

./square

To get a PTX code out of nvcc we can use the following option:

nvcc -ptx square.cu -o square.ptx

The PTX code will look like this:

.visible .entry square(int*, int)(
        .param .u64 square(int*, int)_param_0,
        .param .u32 square(int*, int)_param_1
)
{

        ld.param.u64    %rd1, [square(int*, int)_param_0];
        ld.param.u32    %r2, [square(int*, int)_param_1];
        mov.u32         %r3, %ntid.x;
        mov.u32         %r4, %ctaid.x;
        mov.u32         %r5, %tid.x;
        mad.lo.s32      %r1, %r3, %r4, %r5;
        setp.ge.s32     %p1, %r1, %r2;
        @%p1 bra        $L__BB0_2;

        cvta.to.global.u64      %rd2, %rd1;
        mul.wide.s32    %rd3, %r1, 4;
        add.s64         %rd4, %rd2, %rd3;
        ld.global.u32   %r6, [%rd4];
        mul.lo.s32      %r7, %r6, %r6;
        st.global.u32   [%rd4], %r7;

$L__BB0_2:
        ret;

}

To get an understands of what's going on here, let's break down the PTX instruction by instruction. There are two parameters to the kernel, the first is a pointer to the input integer array param_0 which is the device address of the input integer array, and the second is param_1 which is the size of the input integer array.

Instruction	Description
`ld.param.u64 %rd1, [square(int*, int)_param_0];`	Loads the device address of the input integer array from the kernel parameter.
`ld.param.u32 %r2, [square(int*, int)_param_1];`	Loads the size of the input integer array from the kernel parameter.
`mov.u32 %r3, %ntid.x;`	Gets the number of threads per block in the x-dimension.
`mov.u32 %r4, %ctaid.x;`	Gets the ID of the current thread block in the x-dimension.
`mov.u32 %r5, %tid.x;`	Gets the ID of the current thread within its block in the x-dimension.
`mad.lo.s32 %r1, %r3, %r4, %r5;`	Calculates a linear, global-like index for the current thread based on its block and thread ID.
`setp.ge.s32 %p1, %r1, %r2;`	Sets the predicate flag `%p1` to true if the calculated index is greater than or equal to the array size (bounds check).
`@%p1 bra $L__BB0_2;`	If the calculated index is out of bounds ( `%p1` is true), the thread branches to the return statement, effectively doing nothing.
`cvta.to.global.u64 %rd2, %rd1;`	Converts the generic device address of the array to a global address.
`mul.wide.s32 %rd3, %r1, 4;`	Calculates the byte offset into the array for the current thread's element (assuming `int` size is 4 bytes).
`add.s64 %rd4, %rd2, %rd3;`	Calculates the absolute global memory address of the array element corresponding to the current thread's index.
`ld.global.u32 %r6, [%rd4];`	Loads the 32-bit integer value from the calculated global memory address into register `%r6`.
`mul.lo.s32 %r7, %r6, %r6;`	Squares the integer value in `%r6` and stores the lower 32 bits of the result in `%r7`.
`st.global.u32 [%rd4], %r7;`	Stores the squared integer value from `%r7` back into the same global memory location, overwriting the original value.
`$L__BB0_2:`	Label marking the point to branch to for out-of-bounds threads.
`ret;`	Returns from the kernel execution for the current thread.

You can also use the cuobjdump -sass command to disassemble the CUBIN code into SASS (SASS stands for "Shader ASSembly"):
On -arch=sm_90 our kernel looks like this:

square(int*, int):
 LDC R1, c[0x0][0x28]
 S2R R5, SR_CTAID.X
 ULDC UR4, c[0x0][0x0]
 S2R R0, SR_TID.X
 IMAD R5, R5, UR4, R0
 ULDC UR4, c[0x0][0x218]
 ISETP.GE.AND P0, PT, R5, UR4, PT
 @P0 EXIT
 LDC.64 R2, c[0x0][0x210]
 ULDC.64 UR4, c[0x0][0x208]
 IMAD.WIDE R2, R5, 0x4, R2
 LDG.E R0, desc[UR4][R2.64]
 IMAD R5, R0, R0, RZ
 STG.E desc[UR4][R2.64], R5
 EXIT
.L_x_0:
 BRA `(.L_x_0)
 NOP
 NOP
 NOP
 NOP
 NOP
 NOP
 NOP
 NOP
.L_x_1:

GPU Architectures

The above CUDA kernel, when launched across multiple threads, calculates a unique index for each thread and, if that index is within the bounds of the input integer array, loads the integer at that index from global memory, squares it, and writes the result back to the same memory location, effectively performing an in-place squaring of the array elements in parallel. Threads whose calculated index falls outside the array bounds do not perform any memory operations.

The GPU code such as sm_53, consistently begins with the prefix sm_. A single virtual GPU architecture may encompass multiple corresponding real architectures. The CUBIN can be executed on all GPUs within the same generation, but it is incompatible with GPUs from older or newer generations. For example, a CUBIN compiled for sm_52 is compatible with sm_50, sm_52, and sm_53 GPUs, but not with sm_60 GPUs. Furthermore, the performance of a CUBIN compiled for sm_52 when executed on sm_53 GPUs may be inferior to that of a CUBIN specifically compiled for sm_53 running on the same architecture.

# Compile for sm_52
nvcc square.cu -o square --gpu-architecture=compute_52 --gpu-code=sm_52

# Compile for sm_52, sm_53, sm_60
nvcc square.cu -o square --gpu-architecture=compute_52 --gpu-code=sm_52,sm_53,sm_60

The most common architectures are:

Architecture	SM Version	GPUs	Features
Maxwell	sm_50, sm_52, sm_53	GTX 750 Ti, GTX 960, GTX 970, GTX 980	Dynamic Parallelism, CUDA Dynamic Parallelism
Pascal	sm_60, sm_61, sm_62	P100, GTX 1080, GTX 1080 Ti	HBM2 Memory, NVLink, Unified Memory
Volta	sm_70, sm_72	V100, Titan V	First-gen Tensor Cores, Independent Thread Scheduling
Turing	sm_75	T4, RTX 2080, RTX 2080 Ti	First-gen RT Cores, Second-gen Tensor Cores
Ampere	sm_80, sm_86, sm_87	A100, A40, RTX 3090	Third-gen Tensor Cores, TF32 precision, Structural Sparsity
Ada Lovelace	sm_89	RTX 4090, L40, L40S	Third-gen RT Cores, Fourth-gen Tensor Cores, AV1 encode/decode
Hopper	sm_90, sm_90a	H100, H200	Fourth-gen Tensor Cores, Transformer Engine, 900 GB/s NVLink
Blackwell	sm_100, sm_100a, sm_101, sm_101a, sm_120, sm_120a	B100, B200	Fifth-gen Tensor Cores, Improved occupancy, Enhanced shared memory

Cuda Python Ecosystem

To use NVIDIA CUDA libraries in a Python Poetry project, first add the NVIDIA package index. If you're using Poetry, you can do this by adding the the nvidia-pyindex package and following to extra index url.

poetry add nvidia-pyindex --source https://pypi.ngc.nvidia.com

[extra]
index-url = "https://pypi.ngc.nvidia.com"

The following libraries are now available. The cu12 suffix indicates the CUDA 12.x version, you may need to adjust this depending on your CUDA version. The one core library you'll need to install is cuda-python which is available on PyPI.

cuda-python - Pythonic access to CUDA Runtime and other core functionalities

Then the core libraries are:

nvidia-cuda-runtime-cu12 - Core runtime library providing essential runtime functionality
nvidia-cublas-cu12 - cuBLAS library for GPU-accelerated Basic Linear Algebra Subroutines
nvidia-cudnn-cu12 - cuDNN library of deep learning primitives (scaled dot-product attention, convolution, matrix multiplication, softmax, and pooling)
nvidia-cudnn-frontend - Python bindings for cuDNN frontend API

There are also instrumentation and compiler utilities:

nvidia-cuda-nvrtc-cu12 - Runtime Compilation library (NVRTC) for program compilation
nvidia-nvml-dev-cu12 - Management Library (NVML) for monitoring and managing GPUs
nvidia-nvtx-cu12 - Tools Extension (NVTX) for custom profiling and tracing instrumentation
nvidia-cuda-nvcc-cu12 - Compiler (NVCC) for compiling C/C++ code
nvidia-nvjitlink-cu12 - JIT Linker for runtime linking of device code
nvidia-cuda-sanitizer-api-cu12 - Memory Checker for detecting memory errors in applications
nvidia-cuda-cupti-cu12 - Profiling Tools Interface (CUPTI) for performance analysis and profiling

The other librares are more specialized to specific tasks in scientific computing, signal processing, etc. Not going to cover these in detail here but they exist.

nvidia-cufft-cu12 - cuFFT library for computing Fast Fourier Transforms
nvidia-curand-cu12 - cuRAND library for generating random numbers
nvidia-cusolver-cu12 - cuSOLVER library for dense and sparse direct solvers
nvidia-cusparse-cu12 - cuSPARSE library for sparse matrix operations
nvidia-npp-cu12 - Performance Primitives (NPP) for image, video, and signal processing
nvidia-nvjpeg-cu12 - nvJPEG library for hardware-accelerated JPEG encoding/decoding
nvidia-opencl-cu12 - Implementation of OpenCL for GPU computing

Threads, Blocks, and Warps

When we write CUDA, a kernel refers to a function that you define to execute on the GPU. When you initiate a kernel launch, you are not merely invoking a single function; instead, you are creating hundreds or even thousands of parallel threads that concurrently execute that function across various data elements.

This execution model is commonly known as the Single-Instruction Multiple-Thread (SIMT) paradigm, which emphasizes executing one program across many pieces of data. Say for example we have a kernel that computes the square of each element in an array. Don't worry about the magical blockDim.x and blockIdx.x, more on that later.

__global__ void square(float* array, int n) {
    int tid = blockDim.x * blockIdx.x + threadIdx.x;
    if (tid < n)
        array[tid] = array[tid] * array[tid];
}

CUDA kernels possess two key properties: they cannot explicitly return a value, necessitating that all result data be written to an array passed to the function (for scalar computations, this typically involves passing a one-element array); additionally, kernels must explicitly declare their thread hierarchy upon invocation, specifying the number of thread blocks and the number of threads per block. It is important to note that while a kernel is compiled once, it can be executed multiple times with varying block sizes or grid sizes.

Ok breaking this down, this bit of code is just giving each thread its own unique index, tid, to work with in the arrays. The kernel uses that index to let each thread add one element from A and B together. The __global__ keyword tells us that this function is a CUDA kernel running on the GPU, and we can kick it off from the CPU side. That if (tid < n) check is there because we might end up launching a few more threads than we actually need for the array (we usually round up to a nice number), so any extra threads just sit idle if their index goes out of bounds.

To execute a kernel from our main CPU program, known as the "host code," we must define the number of threads to be used. While the kernel operates on the GPU, it is essential to have CPU code that sets up and launches the kernel. For instance our runner code might look like this:

int N = 10000;
int threadsPerBlock = 256;
int numberOfBlocks = (N + threadsPerBlock - 1) / threadsPerBlock;

square<<<numberOfBlocks, threadsPerBlock>>>(d_array, N);

To unpack the ideas here, CUDA organizes threads into warps, which consist of 32 threads executing in unison, and these warps are further organized into blocks. Each block operates on a Streaming Multiprocessor (SM), which has finite resources such as registers and shared memory. The size of the block influences the allocation of these resources and determines the number of warps that can run simultaneously, which is known as occupancy.

Efficient resource management is crucial for maximizing GPU performance. The GPU scheduler is responsible for distributing blocks across the available SMs. When the number of blocks exceeds the number of SMs, the excess blocks are queued and scheduled for execution as resources become available. This scheduling process is influenced by various factors, including the amount of shared memory and the size of the register file per SM, which ultimately determine the number of blocks that can be executed concurrently.

The other major issue is so-called warp divergence. This refers to the situation where threads within a warp diverge in their execution paths due to conditional statements, such as if-statements. Ideally, all threads in a warp should execute the same instruction simultaneously. However, when some threads take one route while others take another, the execution becomes serialized, leading to inefficiencies. The GPU hardware utilizes mask bits to manage which threads should follow each path, ensuring that all threads complete their tasks correctly. While this mechanism preserves correctness, it can adversely affect performance, as idle threads waste computational resources during divergent execution paths. Consequently, the overall throughput of the GPU may decline, particularly in cases with significant divergence. To enhance performance, developers should aim to minimize conditional branching within warps, thereby optimizing GPU execution efficiency.

Memory Hierarchy

There are three types of memory in a GPU:

Register Memory: The fastest type of GPU memory, located directly on the GPU chip. It's accessible only to individual threads and has the shortest lifetime, lasting only for the duration of the thread.
Shared Memory: This memory is shared by all threads within a GPU block. It's faster than global memory but slower than register memory. Shared memory allows for inter-thread communication and data sharing, lasting for the duration of the block.
Global Memory: The largest memory pool in a GPU, accessible by all threads across all blocks. It's slower than register and shared memory but has the largest capacity. Global memory is used for storing data that needs to be shared across multiple blocks or threads.

The most important performance consideration is memory transfer overhead between CPU (host) and GPU (device). Since data transfer between host and device memory is relatively slow (relative to on-chip memory access), it's beneficial to minimize these transfers by keeping data on the GPU as long as possible. This often means performing multiple computations on the same data before transferring results back to the host, rather than transferring data back and forth for each operation. You want to live on the GPU as much as possible only returning to the CPU when necessary.

It's also crucial to understand memory coalescing - the ability to combine multiple memory accesses into a single transaction. Memory coalescing occurs when threads in a warp access contiguous memory locations. For optimal performance, developers should ensure that memory access patterns are coalesced whenever possible, as uncoalesced memory access can significantly impact performance by requiring multiple memory transactions.

Memory bank conflicts can also impact performance, particularly when using shared memory. Bank conflicts occur when multiple threads attempt to access different addresses in the same memory bank simultaneously. To avoid bank conflicts, you should carefully consider their shared memory access patterns and potentially pad their data structures to ensure optimal memory access distribution across banks. Using appropriate padding and memory access patterns can help maximize memory bandwidth utilization.

Kernel Invocation & Memory Movement

To manage the CUDA runtime there are several core functions in the Python API (which are just wrappers around the C API). The following are the core functions from the cuda.cuda module in the Python bindings.

cuInit - Initializes the CUDA driver API.
cuDeviceGet - Retrieves a handle to the first compute device.
cudaSetDevice - Sets the current device.
cuCtxCreate - Creates a compute context on the specified device.
cuModuleLoadData - JIT compiles a PTX string to a device binary.
cuModuleGetFunction - Retrieves a handle to a kernel function from a module.
cuLaunchKernel - Launches a kernel on the specified device.
cuMemcpyHtoD - Copies data from host to device memory.
cuMemcpyDtoH - Copies data from device to host memory.
cuMemFree - Frees memory on the device.
cuMemAlloc - Allocates memory on the device.
cuCtxDestroy - Destroys a compute context.
cuModuleUnload - Unloads a module from the device.

The error handling is a bit annoying in the CUDA Python API because it's a wrapper around C API which uses integer return codes. So for all of these functions you need to check the return value and raise an exception if it's not a success value. To make this easier there is a helper function checkCudaErrors that will raise an exception if the return value is not a success value.

To setup a CUDA context we can use the following boilerplate functions:

# gpu_setup.py
# Setup CUDA and create a context.

import cuda.cuda as cu  # type: ignore
import cuda.cudart as cudart  # type: ignore
import cuda.nvrtc as nvrtc  # type: ignore


def _cudaGetErrorEnum(error):
    if isinstance(error, cu.CUresult):
        err, name = cu.cuGetErrorName(error)
        return name if err == cu.CUresult.CUDA_SUCCESS else "<unknown>"
    elif isinstance(error, cudart.cudaError_t):
        return cudart.cudaGetErrorName(error)[1]
    elif isinstance(error, nvrtc.nvrtcResult):
        return nvrtc.nvrtcGetErrorString(error)[1]
    else:
        raise RuntimeError(f"Unknown error type: {error}")


def checkCudaErrors(result):
    if result[0].value:
        raise RuntimeError(
            f"CUDA error code={result[0].value}({_cudaGetErrorEnum(result[0])})"
        )
    if len(result) == 1:
        return None
    elif len(result) == 2:
        return result[1]
    else:
        return result[1:]


def findCudaDevice():
    devID = 0
    checkCudaErrors(cudart.cudaSetDevice(devID))
    return devID


def findCudaDeviceDRV():
    devID = 0
    checkCudaErrors(cu.cuInit(0))
    cuDevice = checkCudaErrors(cu.cuDeviceGet(devID))
    return cuDevice


def setup_cuda(device_id=None):
    print("Initializing CUDA...")
    # Initialize CUDA
    checkCudaErrors(cu.cuInit(0))

    # Get device
    if device_id is None:
        device = findCudaDeviceDRV()
        device_id = 0  # For printing purposes
    else:
        device = checkCudaErrors(cu.cuDeviceGet(device_id))

    # Create context
    context = checkCudaErrors(cu.cuCtxCreate(0, device))

    print(f"CUDA context created on device {device_id}.")
    return context


def cleanup_cuda(context):
    if context:
        print("Destroying CUDA context...")
        checkCudaErrors(cu.cuCtxDestroy(context))
        print("CUDA context destroyed.")

Now let's look at how to manage memory between the host (CPU) and device (GPU) using the CUDA Python API. The following example demonstrates the essential memory operations you'll need for GPU programming:

First, we allocate memory on the GPU using cuMemAlloc. This reserves space on the device for our data.
Next, we transfer data from the host to the device with cuMemcpyHtoD (Host to Device).
After computations (which we'll cover later), we retrieve results using cuMemcpyDtoH (Device to Host).

In our example below, we create a simple float array, send it to the GPU, and then copy it back to verify everything worked correctly. This pattern forms the foundation of GPU computing:

# gpu_memory.py
# Minimal example demonstrating CUDA context setup and basic memory movement

from gpu_setup import setup_cuda, checkCudaErrors, cleanup_cuda
import numpy as np
import ctypes
import cuda.cuda as cu  # type: ignore

# Setup CUDA context
context = setup_cuda()

try:
    # Allocate memory on GPU
    buffer_size = 5 * ctypes.sizeof(ctypes.c_float)
    device_ptr = checkCudaErrors(cu.cuMemAlloc(buffer_size))

    # Create and initialize host array
    host_array = np.array([1.0, 2.0, 3.0, 4.0, 5.0], dtype=np.float32)
    print(f"Host array: {host_array}")

    # Copy data from host to device
    checkCudaErrors(cu.cuMemcpyHtoD(device_ptr, host_array.ctypes.data, buffer_size))

    # Create array for results
    result_array = np.zeros(5, dtype=np.float32)

    # Copy data back from device to host
    checkCudaErrors(cu.cuMemcpyDtoH(result_array.ctypes.data, device_ptr, buffer_size))
    print(f"Result array: {result_array}")

    # Free GPU memory
    checkCudaErrors(cu.cuMemFree(device_ptr))

finally:
    # Always clean up the context
    cleanup_cuda(context)

Now let's launch a simple custom kernel that performs a basic operation. This example shows the complete workflow for executing GPU code directly from PTX assembly without needing to compile CUDA C++ code. The kernel simply sets the first element of an array to the value 42, but it illustrates the essential components of GPU kernel execution: initializing a CUDA context, allocating GPU memory, defining a kernel in PTX assembly language, loading the PTX code into a CUDA module, setting up execution dimensions (a single thread in a single block), launching the kernel with appropriate arguments, synchronizing to ensure completion, and finally transferring the result back to the host for verification. The PTX assembly code includes thread and block ID checks to ensure only the first thread performs the assignment.

# gpu_memory.py
# Minimal example demonstraitng lauching a kernel

from gpu_setup import setup_cuda, checkCudaErrors, cleanup_cuda
import numpy as np
import cuda.cuda as cu  # type: ignore

# This is the trivial kernel that sets the first element 
# of the array to 42 using a single thread

# __global__ void set_value_kernel(int *data) {
#     if (threadIdx.x == 0 && blockIdx.x == 0) {
#         *data = 42;
#     }
# }

ptx_kernel = """"
.visible .entry kernel(int*)( .param .u64 kernel(int*)_param_0) {
    ld.param.u64    %rd1, [kernel(int*)_param_0];
    mov.u32         %r1, %tid.x;
    mov.u32         %r2, %ctaid.x;
    or.b32          %r3, %r1, %r2;
    setp.ne.s32     %p1, %r3, 0;
    @%p1 bra        $L__BB0_2;
    cvta.to.global.u64      %rd2, %rd1;
    mov.u32         %r4, 42;
    st.global.u32   [%rd2], %r4;
$L__BB0_2:
    ret;
}
"""

# Setup CUDA context
context = setup_cuda()

try:
    # Allocate a single integer on the device
    data_size = np.dtype(np.int32).itemsize
    d_data = checkCudaErrors(cu.cuMemAlloc(data_size))

    # Set up grid and block dimensions - just one thread
    grid_dims = (1, 1, 1)
    block_dims = (1, 1, 1)

    # Prepare arguments for the kernel
    args = [d_data]
    arg_types = [None]  # None for pointer types

    # Load the module
    module = checkCudaErrors(cu.cuModuleLoadData(ptx_kernel.encode("utf-8")))

    # Get kernel function
    kernel_func = checkCudaErrors(
        cu.cuModuleGetFunction(module, "kernel".encode("utf-8"))
    )

    # Prepare kernel arguments
    kernel_args = (tuple(args), tuple(arg_types))

    # Launch kernel
    checkCudaErrors(
        cu.cuLaunchKernel(
            kernel_func,
            grid_dims[0],
            grid_dims[1],
            grid_dims[2],
            block_dims[0],
            block_dims[1],
            block_dims[2],
            0,  # shared memory bytes
            0,  # stream
            kernel_args,  # kernel args
            0,  # extra
        )
    )

    # Synchronize
    checkCudaErrors(cu.cuCtxSynchronize())

    # Copy result back to host
    host_data = np.zeros(1, dtype=np.int32)
    checkCudaErrors(cu.cuMemcpyDtoH(host_data.ctypes.data, d_data, host_data.nbytes))

    # Verify result
    print(f"Result: {host_data[0]}")
    assert host_data[0] == 42, f"Expected 42 but got {host_data[0]}"
    print("Success! Kernel executed correctly.")

    # Free device memory
    checkCudaErrors(cu.cuMemFree(d_data))

    # Unload module
    checkCudaErrors(cu.cuModuleUnload(module))

finally:
    cleanup_cuda(context)

Thread Blocks and Grids

Previously, we discussed how threads are organized into warps, typically comprising 32 threads each, which are then grouped into blocks. These blocks are assigned to SMs for execution. Now, let’s broaden our perspective. A thread block can be understood as a set of threads that work together using shared memory and synchronization mechanisms, all executing on the same SM.

To inspect the GPU we can use the cuda-python library to interrogate the GPU driver API to get information about the available parallelism properties.

from cuda.cuda import CUdevice_attribute, cuDeviceGetAttribute, cuDeviceGetName, cuInit

(err,) = cuInit(0)

err, DEVICE_NAME = cuDeviceGetName(128, 0)
DEVICE_NAME = DEVICE_NAME.decode("ascii").replace("\x00", "")

err, MAX_THREADS_PER_BLOCK = cuDeviceGetAttribute(
    CUdevice_attribute.CU_DEVICE_ATTRIBUTE_MAX_THREADS_PER_BLOCK, 0
)
err, MAX_BLOCK_DIM_X = cuDeviceGetAttribute(
    CUdevice_attribute.CU_DEVICE_ATTRIBUTE_MAX_BLOCK_DIM_X, 0
)
err, MAX_GRID_DIM_X = cuDeviceGetAttribute(
    CUdevice_attribute.CU_DEVICE_ATTRIBUTE_MAX_GRID_DIM_X, 0
)
err, SMs = cuDeviceGetAttribute(
    CUdevice_attribute.CU_DEVICE_ATTRIBUTE_MULTIPROCESSOR_COUNT, 0
)

print(f"GPU Device: {DEVICE_NAME}")
print(f"Number of multiprocessors: {SMs}")
print(f"Maximum number of threads per block: {MAX_THREADS_PER_BLOCK:10}")
print(f"Maximum number of blocks per grid: {MAX_BLOCK_DIM_X:10}")
print(f"Maximum number of threads per grid: {MAX_GRID_DIM_X:10}")

For example on an A100 GPU we get the following:

Device Name: A100
Maximum number of multiprocessors: 108
Maximum number of threads per multiprocessor: 1024
Maximum number of threads per block: 1024
Maximum number of blocks per grid: 2147483647

The use of blocks is driven by practical considerations: there is a hardware limit on the number of threads that can be launched in a single block, typically capped at 1024 threads on modern GPUs. If your computation requires more threads than this limit, you must divide them into multiple blocks. Think of a block as a team of threads collaboratively addressing a specific segment of data. The complete grid represents all the blocks initiated by a kernel, symbolizing the various teams working together to accomplish the overall task.

For example if we wanted to add two arrays of 2048 elements, we could utilize two blocks of 1024 threads each—where block 0 processes indices 0-1023 and block 1 processes indices 1024-2047. In general, if you have N elements and your block can accommodate a maximum of B threads, you would launch ceil(N/B) blocks to ensure all elements are processed.

Blocks are also super handy for scaling and scheduling. Think of it this way: your GPU has a bunch of SMs (let's say 20), and each SM can juggle a few blocks at once depending on what resources are available. So if you throw 100 blocks at it, but only 20 can run at the same time (one on each SM). The GPU kicks off those 20 blocks in parallel, and whenever one wraps up, it immediately grabs another waiting block and puts it to work on that freed-up SM.

From your perspective as a programmer, all 100 blocks are working together to get your answer - it's like having 100 * blockSize threads all running. But behind the scenes, the GPU is cleverly distributing those blocks across its hardware. The beauty is you don't need to stress about launching more threads than your GPU can physically handle at once. The runtime just time-slices those blocks as needed. Plus, blocks give you a natural way to spread work across multiple GPUs or dial back how much parallel work happens at once (which can be a essentiall when you're bumping up against resource limits like shared memory or registers).

Threads within the same block have powerful collaboration capabilities that set them apart. They share access to fast on-chip memory and can synchronize using barrier operations, enabling efficient coordination for tasks requiring inter-thread communication. However, this collaboration is strictly limited to threads in the same block.-Threads across different blocks must resort to slower global memory for communication and cannot directly synchronize with each other. This decision serves an important purpose: it allows for flexible scheduling of blocks across SMs and enables CUDA programs to scale seamlessly across various GPU architectures, regardless of how many SMs they contain.

We typically choose thread block sizes that are powers of 2 (such as 128, 256, or 512) to align with the GPU's warp size of 32 threads and optimize for hardware characteristics. This sizing impacts several performance factors: it maximizes resource utilization, optimizes memory access patterns, and enhances the GPU's ability to effectively hide memory latency through efficient thread scheduling.

# N is size of the array to process
N = 10000

# We calculate the number of blocks needed based on the total elements and threads per block
 # Typically a power of 2 like 128, 256, or 512
threads_per_block = 256

# Ceiling division to ensure all elements are processed
num_blocks = (N + threads_per_block - 1) // threads_per_block

Shared Memory & Synchronization

Shared memory in CUDA represents one of the most powerful optimization tools available to improving performance, it functions as a programmable cache that dramatically reduces memory access latency. Located on-chip within each SM, shared memory offers bandwidth that can be 100x higher than global memory while providing latency that's roughly 100x lower. This performance advantage stems from its physical proximity to the compute cores—unlike global memory which resides off-chip and requires data to travel across the much slower PCIe bus or memory controllers. When threads in a block cooperate on calculations involving the same data, shared memory eliminates redundant global memory loads, effectively amortizing the cost of accessing global memory across all threads in the block.

The mechanics behind shared memory reflect CUDA's thread hierarchy design. When a kernel launches, each thread block gets allocated its own dedicated portion of shared memory that persists for the block's lifetime and is visible only to threads within that specific block. This memory is organized into banks (typically 32 banks on modern GPUs) that can be accessed simultaneously by different threads, enabling high-bandwidth parallel access. However, when multiple threads attempt to access different addresses within the same bank (i.e. bank conflicts) these accesses get serialized, degrading performance.

The __syncthreads() function is core to working with shared memory. It forces all threads in a block to wait until everyone reaches that point in the code before continuing execution. This prevents nasty race conditions where some threads might try to read data that other threads haven't finished writing yet, which is a common source of subtle and hard-to-debug errors.

In this example we declare a __shared__ array that is visible to all threads in the block. We then load data from global memory to shared memory, synchronize to make sure all threads have loaded their data, process the data in shared memory, and then write the results back to global memory.

#include <stdio.h>

__global__ void sharedMemoryExample(float* input, float* output, int n) {
    // Declare shared memory array - visible to all threads in the block
    __shared__ float sharedData[256];
    
    // Calculate global thread ID
    int tid = blockIdx.x * blockDim.x + threadIdx.x;
    
    // Load data from global memory to shared memory
    if (tid < n) {
        sharedData[threadIdx.x] = input[tid];
    }
    
    // Synchronize to make sure all threads have loaded their data
    __syncthreads();
    
    // Process data in shared memory (simple example: add 1 to each element)
    if (tid < n) {
        sharedData[threadIdx.x] += 1.0f;
    }
    
    // Synchronize again before writing results back
    __syncthreads();
    
    // Write the processed data back to global memory
    if (tid < n) {
        output[tid] = sharedData[threadIdx.x];
    }
}

Using shared memory enables algorithmic techniques that would otherwise be impractical. In tiled algorithms, data is processed in small chunks (called tiles) that fit within shared memory, allowing operations like matrix multiplication to achieve near-theoretical peak performance by dramatically reducing global memory traffic. For stencil computations, shared memory allows threads to collaborate on overlapping regions, eliminating duplicate global memory loads. In reduction operations like sum or max calculations, shared memory facilitates efficient parallel reduction patterns where threads progressively combine results within a block. The key design pattern is to load data from global to shared memory, perform computation exclusively on shared memory, then write results back to global memory. This transforms what would otherwise be memory-bound computations into compute-bound ones, effectively leveraging the GPU's massive computational throughput while minimizing its primary bottleneck: memory access latency.

Connecting to MLIR

Ok, so our goal now is to be able to dynamically (i.e. at runtime) specify high-level tensor operations and have them be lowered to the appropriate GPU code using MLIR. We'll leverage MLIR's progressive lowering capabilities to transform high-level tensor operations into optimized GPU code through a series of well-defined stages:

High-Level Representation: We start with abstract tensor computations expressed in the linalg dialect (matrix multiplication, convolutions, element-wise operations). These operations represent pure mathematical intent without implementation details, keeping our code close to the domain.
Affine Transformation: Using passes like -convert-linalg-to-loops or -convert-linalg-to-affine-loops, we transform these high-level operations into the affine dialect, which represents loops and memory accesses with precise mathematical relationships. This exposes opportunities for crucial optimizations like tiling, fusion, and loop interchange that improve memory locality and computational efficiency.
GPU Mapping: We then map these loop structures to the GPU's execution model through passes like -convert-affine-for-to-gpu and -convert-parallel-loops-to-gpu. This transforms our code into the gpu dialect, which explicitly represents concepts like thread blocks and threads while remaining hardware-agnostic.
Hardware-Specific Lowering: Finally, we transition to NVIDIA-specific functionality through the nvvm dialect, and ultimately to LLVM IR with GPU intrinsics. The final stages convert this to NVPTX assembly and then to CUBIN machine code that runs directly on the GPU.

Throughout this pipeline, each lowering step preserves program semantics while moving closer to the target hardware. We systematically transform from mathematical expressions to explicit loop nests, then to GPU execution constructs, and finally to hardware-specific code. This approach allows us to express computations at a high level while still generating highly optimized GPU code that leverages the full capabilities of the hardware.

The `gpu` Dialect

The GPU dialect in MLIR provides middle-level abstractions for launching GPU kernels that follow programming models similar to CUDA or OpenCL. This dialect abstracts away device-specific and driver-specific operations needed to launch GPU kernels, providing a streamlined path toward GPU execution from MLIR.

The dialect uses gpu as its canonical prefix and exposes operations that wrap common GPU primitives. In some idealized future world this might be used to target multiple GPU backends, but for now we'll just focus on the Nvidia specific operations with the goal of lowering to PTX.

Device Operations

gpu.launch - Launches a GPU kernel with the specified grid and block dimensions. Takes block and thread configurations and contains the kernel body.
gpu.launch_func - Launches a GPU function with the specified grid and block dimensions. Takes a function reference and block and thread configurations.
gpu.barrier - Synchronizes all threads within a thread block, ensuring all threads reach this point before continuing execution.
gpu.binary - Represents a binary blob containing compiled GPU code (e.g. PTX or CUBIN format) that can be loaded and executed.
gpu.printf - Prints formatted output from within GPU kernels, similar to C's printf function. Useful for debugging GPU code.
gpu.return - Returns values from a GPU function/kernel back to the host.
gpu.terminator - Marks the end of a GPU launch region, required as the last operation in a gpu.launch body.
gpu.wait - Waits for asynchronous GPU operations to complete before continuing host execution.
gpu.yield - Yields values from a structured control flow region in GPU code, similar to scf.yield.

Thread and Block Operations

gpu.block_id - Returns the ID of the current block within the grid along a specified dimension (x, y, or z)
gpu.block_dim - Returns the dimensions of blocks in the grid along a specified dimension (x, y, or z)
gpu.block_size - Returns the total number of threads in a block along a specified dimension (x, y, or z)
gpu.grid_id - Returns the ID of the current grid being executed along a specified dimension (x, y, or z)
gpu.grid_dim - Returns the dimensions of the grid along a specified dimension (x, y, or z)
gpu.grid_size - Returns the total number of blocks in the grid along a specified dimension (x, y, or z)
gpu.thread_id - Returns the ID of the current thread within its block along a specified dimension (x, y, or z)

Memory Operations

gpu.alloc - Allocates memory on the GPU device. Takes a shape and element type and returns a memref pointing to the allocated memory.
gpu.memcpy - Copies memory between host and device or between different locations on the device. Can handle host-to-device, device-to-host, and device-to-device transfers.
gpu.dealloc - Deallocates memory previously allocated on the GPU device using gpu.alloc.
gpu.host_register - Registers a memref as host-local memory, allowing it to be accessed directly by the host.
gpu.host_unregister - Unregisters a memref for access from device.

The dialect is designed to be a target-agnostic representation that can be lowered to specific GPU backends. It provides abstractions for kernel invocations and may eventually include device management capabilities that aren't present at lower levels like LLVM IR intrinsics for GPUs.

The dialect expects GPU code to be organized within gpu.module operations and kernels to be represented as gpu.func operations. This structure provides a clear separation between host and device code, making it easier to handle the compilation and execution pipeline. Non-kernel functions, such as device library calls, can be defined using func.func or other non-GPU dialect operations, providing some flexibility in how GPU programs are structured.

module {

  // GPU module
  gpu.module @gpu_module {
    // GPU function
    gpu.func @kernel() {
        %0 = arith.addi %arg0, %arg0 : i32
        %1 = arith.addi %arg0, %arg0 : i32
        %2 = arith.addi %0, %1 : i32
        gpu.return
    }
  }

  // Host function
  func.func @main() {
      gpu.launch_func @gpu_module::@kernel 
        blocks(%0, %1, %2) in (%3 = %c1, %4 = %c1, %5 = %c1) 
        threads(%6, %7, %8) in (%9 = %c2, %10 = %c1, %11 = %c1) 
        args() 
  }
}

The alternative form is to use the gpu.launch operation which embeds the kernel function in a region passed as an argument to the launch operation. The gpu.terminator operation is used to mark the end of the region.

func.func @main() {
    %c2 = arith.constant 2 : index
    %c1 = arith.constant 1 : index
    gpu.launch
        blocks(%0, %1, %2) in (%3 = %c1, %4 = %c1, %5 = %c1)
        threads(%6, %7, %8) in (%9 = %c2, %10 = %c1, %11 = %c1) {
          gpu.printf "Hello from %d\n" %6 : index
          gpu.terminator
        }
    return
}

`nvgpu` Dialect

The nvgpu dialect functions as an intermediary in the MLIR ecosystem, connecting higher-level target-agnostic dialects like gpu and vector with the lower-level NVVM dialect specifically designed for NVIDIA GPUs. By representing PTX-specific operations while continuing to use MLIR's high-level abstractions such as memref and tensor dialects, it creates a bridge that preserves the benefits of both worlds.

Using this dialect we can access NVIDIA-specific hardware features through the NVGPU dialect without needing to directly manipulate complex NVVM intrinsics. This intermediate layer significantly simplifies the generation of efficient GPU code while maintaining the clarity and expressiveness of higher-level MLIR representations.

The dialect primarily focuses on exposing advanced NVIDIA GPU capabilities such as the Tensor Memory Accelerator (TMA) for efficient tensor transfers between global and shared memory. It also provides mechanisms for asynchronous memory operations that enable computation and memory transfers to overlap, effectively hiding latency. Memory access patterns are optimized through swizzling techniques that reduce bank conflicts, while memory barriers (mbarriers) offer sophisticated synchronization tools for coordinating operations across threads.

Warp-level programming receives special attention in the NVGPU dialect, with fine-grained controls that expose hardware-specific features like warp matrix multiply-accumulate operations and synchronization primitives. These capabilities are essential for implementing high-performance matrix operations and other compute-intensive workloads by leveraging specialized hardware units on newer NVIDIA GPUs like Hopper and Blackwell chips.

The dialect's position in the compilation pipeline is strategically important, sitting between the more general GPU dialect and the hardware-specific NVVM dialect. This placement allows it to translate higher-level concepts into optimized hardware-specific operations while shielding developers from unnecessary complexity. When it's time to generate final code, the NVGPU dialect can be lowered to NVVM using the -convert-nvgpu-to-nvvm pass, which transforms the NVGPU operations into corresponding NVVM dialect intrinsics.

For now we're going punt on these features, but later on we'll explore these capabilities (particularly TMA and async memory operations) in greater detail.

`nvvm` Dialect

The NVVM dialect is a target-specific dialect that represents the LLVM IR for NVIDIA GPUs. It includes operations for GPU-specific constructs, such as thread and block indexing, synchronization, and memory operations.

NVVM IR is a compiler IR (intermediate representation) based on the LLVM IR. The NVVM IR is designed to represent GPU compute kernels (for example, CUDA kernels). High-level language front-ends, like the CUDA C compiler front-end, can generate NVVM IR. The NVVM compiler (which is based on LLVM) generates PTX code from NVVM IR.

CUDA Builtin	NVVM Intrinsic	MLIR Operation
`threadId.{x,y,z}`	`@llvm.nvvm.read.ptx.sreg.tid.{x,y,z}`	`gpu.thread_id {x,y,z}`
`blockIdx.{x,y,z}`	`@llvm.nvvm.read.ptx.sreg.ctaid.{x,y,z}`	`gpu.block_id {x,y,z}`
`blockDim.{x,y,z}`	`@llvm.nvvm.read.ptx.sreg.ntid.{x,y,z}`	`gpu.block_dim {x,y,z}`
`gridDim.{x,y,z}`	`@llvm.nvvm.read.ptx.sreg.nctaid.{x,y,z}`	`gpu.grid_dim {x,y,z}`
`__syncthreads()`	`@llvm.nvvm.barrier0()`	`gpu.barrier`

MLIR Python Bindings

The MLIR Python bindings provide a interface to the MLIR C++ internals, allowing developers to programmatically manipulate MLIR's intermediate representations without relying on command-line tools. These bindings expose the core MLIR functionality through Python, enabling users to parse MLIR text, construct and modify the MLIR AST, apply transformation passes, and even JIT-compile and execute MLIR code directly from Python.

Working with the Python bindings eliminates many of the friction points associated with the traditional command-line approach to MLIR. Rather than chaining together multiple command-line invocations, developers can create end-to-end compilation pipelines entirely within Python, making the development process more interactive and debuggable. However, building these bindings from source can be challenging due to their complex dependencies on LLVM and MLIR. To simplify adoption, pre-built wheels are available that package the bindings with all necessary dependencies, making installation as straightforward as a pip command.

To install the bindings, you can use pip:

pip install mlir_python_bindings -f https://github.com/makslevental/mlir-wheels/releases/expanded_assets/latest

Or if you're using Poetry add the following to your pyproject.toml:

[tool.poetry.dependencies]
python = "^3.10"
mlir-python-bindings = { version = "*", source = "mlir-wheels"}

[[tool.poetry.source]]
name = "mlir-wheels"
url = "https://github.com/makslevental/mlir-wheels/releases/expanded_assets/latest"
priority = "supplemental"

Ok now let's use the Python bindings to lower a simple vector addition kernel to PTX.

module {
  func.func @square(%input: tensor<10x10xf32>, %output: tensor<10x10xf32>) -> tensor<10x10xf32> {
    %x0 = linalg.square ins(%input : tensor<10x10xf32>) outs(%output : tensor<10x10xf32>) -> tensor<10x10xf32>
    return %x0 : tensor<10x10xf32>
  }
}

Here we'll apply the passes

from mlir.ir import Context, Module
from mlir.passmanager import PassManager

mlir_module_str = open("vecadd.mlir").read()

with Context():
    # Parse the input module
    module = Module.parse(mlir_module_str)

pm = PassManager()
pm.enable_ir_printing(print_after_change=True)
pm.add("canonicalize")
pm.add(
    "one-shot-bufferize{ bufferize-function-boundaries function-boundary-type-conversion=identity-layout-map }"
)
pm.add("canonicalize")
pm.add("convert-linalg-to-affine-loops")
pm.add("func.func(affine-loop-invariant-code-motion)")
pm.add("func.func(convert-affine-for-to-gpu)")
pm.add("gpu-kernel-outlining")
pm.add("lower-affine")
pm.add("gpu-decompose-memrefs")
pm.add("expand-strided-metadata")
pm.add("normalize-memrefs")
pm.add(
    "gpu.module(convert-gpu-to-nvvm{index-bitwidth=0 use-bare-ptr-memref-call-conv })"
)
pm.add(f"nvvm-attach-target{ {chip={chip_type} features=+ptx80 O=3} }")
pm.add("convert-nvvm-to-llvm")
pm.add("reconcile-unrealized-casts")
pm.add("gpu-to-llvm { use-bare-pointers-for-host use-bare-pointers-for-kernels }")
pm.run(module.operation)

print(module)

Ok so there's a lot going on here, let's break down each flag in the command:

one-shot-bufferize{ bufferize-function-boundaries function-boundary-type-conversion=identity-layout-map }: Converts tensor operations to buffer operations in a single pass, handling function boundaries with identity layout mapping.
convert-linalg-to-affine-loops: Transforms high-level linalg operations into affine loop nests that explicitly iterate over tensor elements.
func.func(affine-loop-invariant-code-motion): Performs loop-invariant code motion on affine loops, moving computations outside loops when possible to reduce redundant calculations.
func.func(convert-affine-for-to-gpu): Maps affine loops to GPU execution model, distributing iterations across GPU threads and blocks.
gpu-kernel-outlining: Extracts GPU kernel regions into separate GPU functions that can be launched from host code.
lower-affine: Converts affine dialect operations to standard control flow and arithmetic operations.
gpu-decompose-memrefs: Decomposes complex memref types into simpler ones that can be handled by the GPU backends.
expand-strided-metadata: Expands metadata for strided memory accesses to explicit calculations.
normalize-memrefs: Normalizes memory references to a form expected by the GPU backends.
gpu.module(convert-gpu-to-nvvm{index-bitwidth=0 use-bare-ptr-memref-call-conv }): Converts GPU dialect operations to NVVM dialect (NVIDIA's LLVM-based IR), using bare pointer calling conventions for memrefs.
nvvm-attach-target{chip={chip_type} features=+ptx80 O=3}: Attaches target-specific information to the NVVM module, specifying the GPU architecture, PTX version 8.0 features, and optimization level 3.
convert-nvvm-to-llvm: Translates NVVM dialect to standard LLVM dialect for further processing.
reconcile-unrealized-casts: Resolves any remaining type conversion issues by reconciling unrealized cast operations.
gpu-to-llvm { use-bare-pointers-for-host use-bare-pointers-for-kernels }: Converts remaining GPU dialect operations to LLVM dialect, using bare pointers for both host and device code.

After lowering our linalg operations to affine loops with convert-linalg-to-affine-loops we get the following MLIR module:

module {
  func.func @square(%arg0: memref<10x10xf32>, %arg1: memref<10x10xf32>) -> memref<10x10xf32> {
    affine.for %arg2 = 0 to 10 {
      affine.for %arg3 = 0 to 10 {
        %0 = affine.load %arg0[%arg2, %arg3] : memref<10x10xf32>
        %1 = arith.mulf %0, %0 : f32
        affine.store %1, %arg1[%arg2, %arg3] : memref<10x10xf32>
      }
    }
    return %arg1 : memref<10x10xf32>
  }
}

After the convert-affine-for-to-gpu pass. This pass transforms affine loops into GPU kernel launch region.

func.func @square(%arg0: memref<10x10xf32>, %arg1: memref<10x10xf32>) -> memref<10x10xf32> {
  %c0 = arith.constant 0 : index
  %c10 = arith.constant 10 : index
  %0 = arith.subi %c10, %c0 : index
  %c1 = arith.constant 1 : index
  %c0_0 = arith.constant 0 : index
  %c10_1 = arith.constant 10 : index
  %1 = arith.subi %c10_1, %c0_0 : index
  %c1_2 = arith.constant 1 : index
  %c1_3 = arith.constant 1 : index
  gpu.launch
    blocks(%arg2, %arg3, %arg4) in (%arg8 = %0, %arg9 = %c1_3, %arg10 = %c1_3)
    threads(%arg5, %arg6, %arg7) in (%arg11 = %1, %arg12 = %c1_3, %arg13 = %c1_3) {
    %2 = arith.addi %c0, %arg2 : index
    %3 = arith.addi %c0_0, %arg5 : index
    %4 = affine.load %arg0[%2, %3] : memref<10x10xf32>
    %5 = arith.mulf %4, %4 : f32
    affine.store %5, %arg1[%2, %3] : memref<10x10xf32>
    gpu.terminator
  }
  return %arg1 : memref<10x10xf32>
}

Applying the gpu-kernel-outlining pass. This pass extracts the GPU kernel launch region into a separate GPU function which has the GPU intrinsics to reference the block and thread indices.

module attributes {gpu.container_module} {
  func.func @square(%arg0: memref<10x10xf32>, %arg1: memref<10x10xf32>) -> memref<10x10xf32> {
    %c0 = arith.constant 0 : index
    %c10 = arith.constant 10 : index
    %0 = arith.subi %c10, %c0 : index
    %c1 = arith.constant 1 : index
    %c0_0 = arith.constant 0 : index
    %c10_1 = arith.constant 10 : index
    %1 = arith.subi %c10_1, %c0_0 : index
    %c1_2 = arith.constant 1 : index
    %c1_3 = arith.constant 1 : index
    gpu.launch_func  @square_kernel::@square_kernel
        blocks in (%0, %c1_3, %c1_3)
        threads in (%1, %c1_3, %c1_3)
        args(%c0 : index, %c0_0 : index, %arg0 : memref<10x10xf32>, %arg1 : memref<10x10xf32>)
    return %arg1 : memref<10x10xf32>
  }
  gpu.module @square_kernel {
    gpu.func @square_kernel(%arg0: index, %arg1: index, %arg2: memref<10x10xf32>, %arg3: memref<10x10xf32>) kernel {
      %block_id_x = gpu.block_id  x
      %block_id_y = gpu.block_id  y
      %block_id_z = gpu.block_id  z
      %thread_id_x = gpu.thread_id  x
      %thread_id_y = gpu.thread_id  y
      %thread_id_z = gpu.thread_id  z
      %grid_dim_x = gpu.grid_dim  x
      %grid_dim_y = gpu.grid_dim  y
      %grid_dim_z = gpu.grid_dim  z
      %block_dim_x = gpu.block_dim  x
      %block_dim_y = gpu.block_dim  y
      %block_dim_z = gpu.block_dim  z
      %0 = arith.addi %arg0, %block_id_x : index
      %1 = arith.addi %arg1, %thread_id_x : index
      %2 = affine.load %arg2[%0, %1] : memref<10x10xf32>
      %3 = arith.mulf %2, %2 : f32
      affine.store %3, %arg3[%0, %1] : memref<10x10xf32>
      gpu.return
    }
  }
}

The rest of the passes are fairly mechanical lowering passes that convert the GPU dialect to NVVM dialect. We then get a module with a gpu.module that contains the GPU kernel.

module attributes {gpu.container_module} {
  llvm.func @square(%arg0: !llvm.ptr, %arg1: !llvm.ptr) -> !llvm.ptr {
    %0 = llvm.mlir.poison : !llvm.struct<(ptr, ptr, i64, array<2 x i64>, array<2 x i64>)>
    %1 = llvm.insertvalue %arg1, %0[0] : !llvm.struct<(ptr, ptr, i64, array<2 x i64>, array<2 x i64>)> 
    %2 = llvm.insertvalue %arg1, %1[1] : !llvm.struct<(ptr, ptr, i64, array<2 x i64>, array<2 x i64>)> 
    %3 = llvm.mlir.constant(0 : index) : i64
    %4 = llvm.insertvalue %3, %2[2] : !llvm.struct<(ptr, ptr, i64, array<2 x i64>, array<2 x i64>)> 
    %5 = llvm.mlir.constant(10 : index) : i64
    %6 = llvm.insertvalue %5, %4[3, 0] : !llvm.struct<(ptr, ptr, i64, array<2 x i64>, array<2 x i64>)> 
    %7 = llvm.mlir.constant(10 : index) : i64
    %8 = llvm.insertvalue %7, %6[4, 0] : !llvm.struct<(ptr, ptr, i64, array<2 x i64>, array<2 x i64>)> 
    %9 = llvm.mlir.constant(10 : index) : i64
    %10 = llvm.insertvalue %9, %8[3, 1] : !llvm.struct<(ptr, ptr, i64, array<2 x i64>, array<2 x i64>)> 
    %11 = llvm.mlir.constant(1 : index) : i64
    %12 = llvm.insertvalue %11, %10[4, 1] : !llvm.struct<(ptr, ptr, i64, array<2 x i64>, array<2 x i64>)> 
    %13 = llvm.mlir.poison : !llvm.struct<(ptr, ptr, i64, array<2 x i64>, array<2 x i64>)>
    %14 = llvm.insertvalue %arg0, %13[0] : !llvm.struct<(ptr, ptr, i64, array<2 x i64>, array<2 x i64>)> 
    %15 = llvm.insertvalue %arg0, %14[1] : !llvm.struct<(ptr, ptr, i64, array<2 x i64>, array<2 x i64>)> 
    %16 = llvm.mlir.constant(0 : index) : i64
    %17 = llvm.insertvalue %16, %15[2] : !llvm.struct<(ptr, ptr, i64, array<2 x i64>, array<2 x i64>)> 
    %18 = llvm.mlir.constant(10 : index) : i64
    %19 = llvm.insertvalue %18, %17[3, 0] : !llvm.struct<(ptr, ptr, i64, array<2 x i64>, array<2 x i64>)> 
    %20 = llvm.mlir.constant(10 : index) : i64
    %21 = llvm.insertvalue %20, %19[4, 0] : !llvm.struct<(ptr, ptr, i64, array<2 x i64>, array<2 x i64>)> 
    %22 = llvm.mlir.constant(10 : index) : i64
    %23 = llvm.insertvalue %22, %21[3, 1] : !llvm.struct<(ptr, ptr, i64, array<2 x i64>, array<2 x i64>)> 
    %24 = llvm.mlir.constant(1 : index) : i64
    %25 = llvm.insertvalue %24, %23[4, 1] : !llvm.struct<(ptr, ptr, i64, array<2 x i64>, array<2 x i64>)> 
    %26 = llvm.mlir.constant(1 : index) : i64
    %27 = llvm.mlir.constant(0 : index) : i64
    %28 = llvm.mlir.constant(10 : index) : i64
    %29 = llvm.extractvalue %25[1] : !llvm.struct<(ptr, ptr, i64, array<2 x i64>, array<2 x i64>)> 
    %30 = llvm.extractvalue %12[1] : !llvm.struct<(ptr, ptr, i64, array<2 x i64>, array<2 x i64>)> 
    gpu.launch_func  @square_kernel::@square_kernel blocks in (%28, %26, %26) threads in (%28, %26, %26) : i64 args(%27 : i64, %27 : i64, %29 : !llvm.ptr, %30 : !llvm.ptr)
    %31 = llvm.extractvalue %12[0] : !llvm.struct<(ptr, ptr, i64, array<2 x i64>, array<2 x i64>)> 
    llvm.return %31 : !llvm.ptr
  }
  gpu.module @square_kernel [#nvvm.target<O = 3, chip = "sm_90", features = "+ptx80">] {
    llvm.func @square_kernel(%arg0: i64, %arg1: i64, %arg2: !llvm.ptr, %arg3: !llvm.ptr) attributes {gpu.kernel, nvvm.kernel} {
      %0 = llvm.mlir.constant(10 : index) : i64
      %1 = nvvm.read.ptx.sreg.ctaid.x : i32
      %2 = llvm.sext %1 : i32 to i64
      %3 = nvvm.read.ptx.sreg.tid.x : i32
      %4 = llvm.sext %3 : i32 to i64
      %5 = llvm.add %arg0, %2 : i64
      %6 = llvm.add %arg1, %4 : i64
      %7 = llvm.mul %5, %0 : i64
      %8 = llvm.add %7, %6 : i64
      %9 = llvm.getelementptr %arg2[%8] : (!llvm.ptr, i64) -> !llvm.ptr, f32
      %10 = llvm.load %9 : !llvm.ptr -> f32
      %11 = llvm.fmul %10, %10 : f32
      %12 = llvm.mul %5, %0 : i64
      %13 = llvm.add %12, %6 : i64
      %14 = llvm.getelementptr %arg3[%13] : (!llvm.ptr, i64) -> !llvm.ptr, f32
      llvm.store %11, %14 : f32, !llvm.ptr
      llvm.return
    }
  }
}

We can extract the GPU function from the module.

module {
      llvm.func @square_kernel(%arg0: i64, %arg1: i64, %arg2: !llvm.ptr, %arg3: !llvm.ptr) attributes {gpu.kernel, nvvm.kernel} {
        %0 = llvm.mlir.constant(10 : index) : i64
        %1 = nvvm.read.ptx.sreg.ctaid.x : i32
        %2 = llvm.sext %1 : i32 to i64
        %3 = nvvm.read.ptx.sreg.tid.x : i32
        %4 = llvm.sext %3 : i32 to i64
        %5 = llvm.add %arg0, %2 : i64
        %6 = llvm.add %arg1, %4 : i64
        %7 = llvm.mul %5, %0 : i64
        %8 = llvm.add %7, %6 : i64
        %9 = llvm.getelementptr %arg2[%8] : (!llvm.ptr, i64) -> !llvm.ptr, f32
        %10 = llvm.load %9 : !llvm.ptr -> f32
        %11 = llvm.fmul %10, %10 : f32
        %12 = llvm.mul %5, %0 : i64
        %13 = llvm.add %12, %6 : i64
        %14 = llvm.getelementptr %arg3[%13] : (!llvm.ptr, i64) -> !llvm.ptr, f32
        llvm.store %11, %14 : f32, !llvm.ptr
        llvm.return
      }
}

Then translate the MLIR module to LLVM IR.

; ModuleID = 'LLVMDialectModule'
source_filename = "LLVMDialectModule"

define ptx_kernel void @square_kernel(i64 %0, i64 %1, ptr %2, ptr %3) {
  %5 = call i32 @llvm.nvvm.read.ptx.sreg.ctaid.x()
  %6 = sext i32 %5 to i64
  %7 = call i32 @llvm.nvvm.read.ptx.sreg.tid.x()
  %8 = sext i32 %7 to i64
  %9 = add i64 %0, %6
  %10 = add i64 %1, %8
  %11 = mul i64 %9, 10
  %12 = add i64 %11, %10
  %13 = getelementptr float, ptr %2, i64 %12
  %14 = load float, ptr %13, align 4
  %15 = fmul float %14, %14
  %16 = mul i64 %9, 10
  %17 = add i64 %16, %10
  %18 = getelementptr float, ptr %3, i64 %17
  store float %15, ptr %18, align 4
  ret void
}

; Function Attrs: nocallback nofree nosync nounwind speculatable willreturn memory(none)
declare noundef i32 @llvm.nvvm.read.ptx.sreg.ctaid.x() #0

; Function Attrs: nocallback nofree nosync nounwind speculatable willreturn memory(none)
declare noundef i32 @llvm.nvvm.read.ptx.sreg.tid.x() #0

attributes #0 = { nocallback nofree nosync nounwind speculatable willreturn memory(none) }

!llvm.module.flags = !{!0}

!0 = !{i32 2, !"Debug Info Version", i32 3}

Then compile to PTX using the nvptx backend to LLVM, which we invokve via llc.

//
// Generated by LLVM NVPTX Back-End
//

.version 7.8
.target sm_90
.address_size 64

	// .globl	square_kernel           // -- Begin function square_kernel
                                        // @square_kernel
.visible .entry square_kernel(
	.param .u64 square_kernel_param_0,
	.param .u64 square_kernel_param_1,
	.param .u64 .ptr .align 1 square_kernel_param_2,
	.param .u64 .ptr .align 1 square_kernel_param_3
)
{
	.reg .b32 	%r<3>;
	.reg .f32 	%f<3>;
	.reg .b64 	%rd<15>;

// %bb.0:
	ld.param.u64 	%rd1, [square_kernel_param_0];
	ld.param.u64 	%rd2, [square_kernel_param_3];
	cvta.to.global.u64 	%rd3, %rd2;
	ld.param.u64 	%rd4, [square_kernel_param_1];
	ld.param.u64 	%rd5, [square_kernel_param_2];
	cvta.to.global.u64 	%rd6, %rd5;
	mov.u32 	%r1, %ctaid.x;
	cvt.s64.s32 	%rd7, %r1;
	mov.u32 	%r2, %tid.x;
	cvt.s64.s32 	%rd8, %r2;
	add.s64 	%rd9, %rd1, %rd7;
	add.s64 	%rd10, %rd4, %rd8;
	mad.lo.s64 	%rd11, %rd9, 10, %rd10;
	shl.b64 	%rd12, %rd11, 2;
	add.s64 	%rd13, %rd6, %rd12;
	ld.global.f32 	%f1, [%rd13];
	mul.rn.f32 	%f2, %f1, %f1;
	add.s64 	%rd14, %rd3, %rd12;
	st.global.f32 	[%rd14], %f2;
	ret;
                                        // -- End function
}

MLIR Pipeline

Now we can construct two modules compile.py and run.py module implements our GPU code generation pipeline, transforming high-level MLIR into optimized PTX assembly.

The full source code is available on Github and also as a notebook.

In our example we define a primary function compile_mlir_to_ptx that orchestrates the entire compilation process. Inside, it first parses the MLIR string into a module representation, then applies our GPU compilation pipeline through a carefully ordered sequence of transformation passes. These passes progressively lower the code from high-level tensor operations to GPU-specific constructs, including bufferization to handle memory accesses, converting linalg operations to affine loops, mapping those loops to GPU blocks and threads, and finally generating NVIDIA-specific code via the NVVM dialect. After transformations, the function extracts the GPU module and converts it to PTX assembly using LLVM tools, resulting in code that can be directly executed on NVIDIA GPUs without further compilation.

import subprocess

from mlir.ir import Context, Module
from mlir.passmanager import PassManager


def compile_mlir_to_ptx(mlir_module_str: str, chip_type="sm_75"):
    """Compiles MLIR module string to PTX code."""
    with Context():
        # Parse the input module
        module = Module.parse(mlir_module_str)

        # Apply GPU compilation pipeline
        module, gpu_module = apply_gpu_pipeline(module, chip_type)

        # Generate PTX from the GPU module
        ptx = generate_ptx(str(gpu_module), chip_type)

    return ptx


def apply_gpu_pipeline(module, chip_type="sm_75"):
    """Applies the GPU compilation pipeline to the MLIR module."""
    pm = PassManager()
    pm.enable_ir_printing(print_after_change=True)
    pm.add("canonicalize")
    pm.add(
        "one-shot-bufferize{ bufferize-function-boundaries function-boundary-type-conversion=identity-layout-map }"
    )
    pm.add("canonicalize")
    pm.add("convert-linalg-to-affine-loops")
    pm.add("func.func(affine-loop-invariant-code-motion)")
    pm.add("func.func(convert-affine-for-to-gpu)")
    pm.add("gpu-kernel-outlining")
    pm.add("lower-affine")
    pm.add("gpu-decompose-memrefs")
    pm.add("expand-strided-metadata")
    pm.add("normalize-memrefs")
    pm.add(
        "gpu.module(convert-gpu-to-nvvm{index-bitwidth=0 use-bare-ptr-memref-call-conv })"
    )
    pm.add(f"nvvm-attach-target{ {chip={chip_type} features=+ptx80 O=3} }")
    pm.add("convert-nvvm-to-llvm")
    pm.add("reconcile-unrealized-casts")
    pm.add("gpu-to-llvm { use-bare-pointers-for-host use-bare-pointers-for-kernels }")
    pm.run(module.operation)

    # Extract the GPU module
    gpu_module = extract_gpu_module(module)

    return module, gpu_module


def extract_gpu_module(module: Module) -> Module:
    """Extracts the GPU module from a transformed MLIR module."""
    # Navigate the operation tree to find the GPU module
    # Structure: module -> region[0] -> block[0] -> operations[1] (GPU host-device code)
    # -> region[0] -> block[0] -> operations[0] (GPU module)
    try:
        main_func_op = module.operation.regions[0].blocks[0].operations[1]
        gpu_module_op = main_func_op.regions[0].blocks[0].operations[0]

        # Create a new module from the GPU module operation
        gpu_module = Module.parse(str(gpu_module_op))
        return gpu_module
    except (IndexError, AttributeError) as e:
        raise RuntimeError(f"Failed to extract GPU module: {e}") from e


def generate_ptx(gpu_module_str, chip_type="sm_75"):
    """Generates PTX from an MLIR GPU module string."""
    # First convert MLIR to LLVM IR
    llvm_ir_result = subprocess.run(
        ["mlir-translate", "--mlir-to-llvmir", "-"],
        input=gpu_module_str,
        capture_output=True,
        text=True,
    )

    if llvm_ir_result.returncode != 0:
        print("Error generating LLVM IR:")
        print(llvm_ir_result.stderr)
        return None

    llvm_ir = llvm_ir_result.stdout

    # Then convert LLVM IR to PTX
    ptx_result = subprocess.run(
        ["llc", "-march=nvptx64", f"-mcpu={chip_type}", "-"],
        input=llvm_ir,
        capture_output=True,
        text=True,
    )

    if ptx_result.returncode != 0:
        print("Error generating PTX:")
        print(ptx_result.stderr)
        return None

    return ptx_result.stdout

Now we can define the run_kernel function which serves as the interface between our Python code and the GPU hardware, managing the execution of our compiled PTX kernels. It takes a PTX code string, kernel name, arguments with their types, and the grid and block dimensions that define our parallelization strategy. The function first loads the PTX code into a CUDA module using the CUDA driver API, then retrieves a handle to the named kernel function. After preparing the kernel arguments in the format expected by the CUDA runtime, it launches the kernel with the specified execution configuration, determining how many thread blocks and threads per block will process our data.

def run_kernel(
    ptx_code,
    kernel_name,
    args,
    arg_types,
    grid_dims,
    block_dims,
):
    """Run a PTX kernel."""
    module = checkCudaErrors(cu.cuModuleLoadData(ptx_code.encode("utf-8")))

    kernel_func = checkCudaErrors(
        cu.cuModuleGetFunction(module, kernel_name.encode("utf-8"))
    )

    kernel_args = (tuple(args), tuple(arg_types))

    checkCudaErrors(
        cu.cuLaunchKernel(
            kernel_func,
            grid_dims[0],
            grid_dims[1],
            grid_dims[2],
            block_dims[0],
            block_dims[1],
            block_dims[2],
            0,  # shared memory bytes
            0,  # stream
            kernel_args,  # kernel args
            0,  # extra
        )
    )

    checkCudaErrors(cu.cuCtxSynchronize())

    checkCudaErrors(cu.cuModuleUnload(module))

The following code is a complete end-to-end example of GPU kernel execution using our compilation pipeline. It first compiles MLIR code from a file into PTX assembly, then sets up a CUDA context and allocates memory on both host and device. The example prepares a square matrix operation where each thread processes one element, organizing computation with a grid dimension matching the matrix rows and block dimension matching the columns. After copying input data to the GPU, it executes the kernel with the appropriate arguments and dimensions, then retrieves the results back to the host into a NumPy array.

import ctypes
import numpy as np
import cuda.cuda as cu
import cuda.cudart as cudart
import cuda.nvrtc as nvrtc
import subprocess
from compile import compile_mlir_to_ptx
from run import run_kernel

ptx_code = compile_mlir_to_ptx(open('square.mlir').read())

cuda_context = setup_cuda()

try:
    # Allocate device memory
    d_input = allocate_device_memory(input_data.nbytes)
    output_data = np.zeros((size, size), dtype=np.float32)
    d_output = allocate_device_memory(output_data.nbytes)

    # Copy input data to device
    copy_host_to_device(input_data, d_input)

    # Run kernel
    grid_dims = (size, 1, 1)  # One thread block per row
    block_dims = (size, 1, 1)  # One thread per column

    # Prepare arguments according to the PTX code
    # square_kernel(
    #     .param .u64 square_kernel_param_0,                // Grid dimension offset
    #     .param .u64 square_kernel_param_1,                // Block dimension offset
    #     .param .u64 .ptr .align 1 square_kernel_param_2,  // Input pointer
    #     .param .u64 .ptr .align 1 square_kernel_param_3   // Output pointer
    # )
    args = [
        0,  # Grid dimension offset
        0,  # Block dimension offset
        d_input,  # Input pointer
        d_output,  # Output pointer
    ]
    arg_types = [ctypes.c_int, ctypes.c_int, None, None]  # Using None for pointer types

    print("Running kernel on GPU...")
    run_kernel(
        ptx_code,
        "square_kernel",
        args,
        arg_types,
        grid_dims,
        block_dims,
    )

    # Copy results back to host
    copy_device_to_host(d_output, output_data)

    # Verify results
    print("Verifying results...")
    np.testing.assert_allclose(output_data, expected_output, rtol=1e-5)
    print("Success! Results verified.")

finally:
    # Clean up resources
    free_device_memory(d_input)
    free_device_memory(d_output)
    cleanup_cuda(cuda_context)

And that's it, it's the skeleton of a very tiny compiler pipeline which takes dynamic tensor expressions in MLIR and then compiles them to PTX and executes them on the GPU. Now our goal moving forward is to target that same MLIR from something more natural to program in like a eDSL in Python to express kernel operations and then have our pipeline take that and compile it to MLIR and them for the GPU. More on this in the next section.

Embedding Binaries

As an aside, the alternative path to compiling a GPU kernel is to compile it to a binary and then embed that binary in the MLIR module and then have the host code load the binary and launch the kernel.

The gpu.binary operation in MLIR represents a compiled GPU kernel that can be loaded and executed on a GPU device. It encapsulates the binary representation of GPU code, which can be in various formats such as PTX assembly, CUBIN binary, or HSACO for AMD GPUs. This operation is particularly useful when you want to embed pre-compiled GPU kernels directly into your MLIR module, allowing for direct execution without going through the compilation pipeline at runtime.

The gpu-module-to-binary pass is a transformation that converts GPU modules into GPU binaries. This pass scans through the MLIR module to find all nested GPU modules and serializes them according to the target attributes attached to each module. It produces a GPU binary with an object for every target architecture specified. The pass supports various output formats including offloading representation, assembly code, binaries, and fatbinaries.

All this is doing under the hood is running ptxas on the PTX code and embedding the output in the MLIR module with the given arguments the gpu-module-to-binary pass passed to the ptxas command. For exmaple the following MLIR module contains a GPU binary for the sm_70 architecture.

module attributes {gpu.container_module} {
  gpu.binary @vecadd_kernel  [
    #gpu.object<#nvvm.target<chip = "sm_70">,
    offload = "BC\C0\DE5\14 [... truncated ...] kernel20.1.0nvptx64-nvidia-cudaLLVMDialectModule\00\00\00\00">]
}

Then in the host code you can launch the kernel with the following:

gpu.launch_func @vecadd_kernel::@vecadd_kernel
  blocks in (%0, %0, %0)
  threads in (%0, %0, %0) : i64
  args(%1 : i32, %2 : i64)

External Resources

MLIR Part 7 - Transformers

Fri, 11 Apr 2025 01:00:00 +0000

Transformers

The transformer architecture revolutionized the field of natural language processing when introduced in the landmark 2017 paper Attention is All You Need. Breaking away from traditional sequence models, transformers employ self-attention mechanisms (more on this later) as their core building block, enabling them to capture long-range dependencies in data with remarkable efficiency. In essence, the transformer can be viewed as a general-purpose computational substrate—a programmable logical tissue that reconfigures based on training data and can be stacked as layers build large models exhibiting fascinating emergent behaviors.

Each of these layers contains two essential sublayers working in tandem: a multi-head self-attention mechanism and a position-wise feed-forward network. The multi-head attention allows the model to simultaneously focus on different parts of the input sequence, capturing various relationships between tokens from different representational perspectives. The feed-forward network, applied identically to each position, then introduces non-linearity and expands the model's capacity to learn complex patterns.

Since the attention mechanism processes all tokens in parallel, transformers require an innovative approach to handling sequential information. This challenge is addressed through positional encodings—either learned embeddings or fixed sinusoidal functions—that are added to the token embeddings at the input layer. These encodings provide the model with crucial information about token positions that would otherwise be lost in the parallel processing.

The power of transformers stems from their ability to dynamically weight the importance of different tokens during processing. Consider the word "bank" in the sentence "I went to the bank to deposit money." When processing this ambiguous word, the model can attend strongly to contextual clues like "deposit" and "money," helping it correctly interpret "bank" as a financial institution rather than a riverside. This contextual awareness enables transformers to excel at tasks requiring nuanced language understanding.

Layer normalization and residual connections further enhance the transformer architecture. Layer normalization stabilizes the learning process by normalizing activations within each layer, while residual connections create shortcuts for gradient flow during training. These components work together to mitigate the vanishing gradient problem that often plagues deep networks, allowing transformers to be trained effectively despite their depth.

Remarkably, researchers found that as they scaled up transformer models by increasing their layer count, embedding dimensions, and training data, these architectures demonstrated remarkable emergent capabilities. Larger models exhibit abilities not present in their smaller counterparts, including few-shot learning, reasoning, and even rudimentary understanding of concepts they weren't explicitly trained on. This scaling effect has driven much of the recent progress in artificial intelligence.

The decoder-only Transformer architecture which we'll build from scratch here, is composed of multiple identical decoder blocks stacked vertically. Unlike the original Transformer which had both encoder and decoder components, modern language models typically use only the decoder portion for next-token prediction tasks. This architecture has proven highly scalable, with models ranging from hundreds of millions to now billions of parameters in frontier models.

Let's walk through a pure NumPy implementation of the GPT-2 model, component by component. It only comes out to about 100 lines of code in total. The full source code is available on GitHub here.

There are several data structures of the neural network weights that we'll download from the internet later. For now just know that they're a collection of arrays of various dimensions.

LinearParams - A linear layer with weights and bias parameters for the linear transformations.
LayerNormParams - A layer normalization layer with gain and bias parameters for normalization.
AttentionParams - A multi-head attention layer containing query, key, value and output projection parameters.
BlockParams - A transformer block containing attention and feed-forward parameters.
ModelParams - The full model parameters including token embeddings, position embeddings, transformer blocks and final layer norm.
HParams - Hyperparameters for the model including the number of layers, heads, embedding dimension, etc.

In our code we'll use the following abbreviations:

g - Gamma (scale parameter for layer normalization)
b - Beta (bias parameter)
w - Weight matrix/array
wte - Word/Token Embeddings
wpe - Word Position Embeddings
ln - Layer Normalization
mlp - Multi-Layer Perceptron
fc - Fully Connected layer
qkv - Query, Key, Value (attention components)
attn - Attention
proj - Projection (linear transformation)

BPE Tokenization

Byte-Pair Encoding (shortened as BPE) is a tokenization algorithm that addresses the challenge of out-of-vocabulary words by breaking words into smaller units called subwords. Initially developed as a data compression technique, BPE was adapted for natural language processing by treating words as sequences of characters. The core idea of BPE is to iteratively merge the most frequent adjacent symbol pairs in a corpus into new subword units. This process begins by splitting each word in the corpus into individual characters, forming the initial vocabulary consisting of all unique characters.

The BPE algorithm then proceeds with iterative merging. In each iteration, it counts all adjacent symbol pairs across the corpus. The pair with the highest frequency is then selected and merged into a new symbol or subword. This merge operation is applied to all occurrences of the selected pair in the corpus, effectively removing the space between them in the tokenized representations of the words. The newly formed subword is added to the vocabulary. This iterative process continues until the vocabulary reaches a predefined target size or no more frequent pairs can be found. The sequence of merge operations performed during training is crucial for tokenizing new, unseen words.

Once the BPE tokenizer is trained (i.e., the sequence of merges is determined), it can be used to tokenize new text. When tokenizing a word, the tokenizer first checks if the whole word (with the initial word boundary marker) exists in the vocabulary. If not, it splits the word into characters and iteratively applies the learned merge rules in the order they were learned. Any character not present in the initial character set might be replaced by an unknown token (e.g., <UNK>). BPE is widely used in modern language models and is particularly useful for handling rare words and languages without clear word boundaries like Chinese, where initial tokenization might start with individual characters.

We're not going to implement BPE from scratch, but you can find a simple Python implementation here. Instead we'll just load the existing tokenizer from the original GPT-2 repo.

encoder = get_encoder("", "model")

# encode a string into a list of tokens
tokens = encoder.encode("Hello world")

print(tokens) # [15496, 995]

Here we see the tokenizer has encoded the string "Hello world" into a list of tokens [15496, 995] which happens to have two words and two tokens. However the string "Barack Obama" is encoded into [10374, 441, 2486] which has two words and three tokens.

Tokenization and Position Embeddings

From the string input we first tokenize it into a list of tokens and then we look up the token embeddings for each token in the params.wte matrix.

x = params.wte[inputs] + params.wpe[range(len(inputs))]

This line is crucial for preparing the input sequence before it gets processed by the main transformer blocks. It combines two types of information for each token in the input (the position and the token itself). In the model configuration there are two large embedding matrices the token embedding matrix and the position embedding matrix.

Token Embeddings (params.wte[inputs]):

The inputs parameter represents your sequence of input tokens as a list of integers (token IDs). For example, if your input text "Hello world" is tokenized into [15496, 995], then inputs would be [15496, 995].

The params.wte refers to the Word Token Embedding matrix. It's essentially a large table (lookup table) where each row corresponds to a unique token ID in the model's vocabulary, and the row itself is a vector (e.g., of size 768 for the small GPT-2 model). This vector is the learned numerical representation, or "embedding," for that specific token.

The params.wte[inputs] operation performs a lookup. It takes each integer ID in your inputs list and retrieves the corresponding embedding vector from the params.wte matrix. The result is a matrix where each row is the token embedding for the corresponding token in your input sequence. So, for [15496, 995], you'd get a matrix with two rows: the embedding for token 15496 and the embedding for token 995.

Position Embeddings (params.wpe[range(len(inputs))]):

Transformers process tokens in parallel using self-attention, which doesn't inherently know the order of tokens. To provide this sequential information, we use position embeddings. The len(inputs) function calculates the length of your input sequence (e.g., 2 for [15496, 995]). Using range(len(inputs)) generates a sequence of position indices starting from 0: [0, 1] in our example.

The params.wpe refers to the Word Position Embedding matrix. Similar to wte, it's a lookup table, but its rows correspond to positions in a sequence (0, 1, 2, ... up to the maximum sequence length the model can handle). Each row is a learned vector representing that specific position. GPT-2 uses learned positional embeddings, meaning these vectors are parameters learned during training.

Finally, params.wpe[range(len(inputs))] performs a lookup using the position indices. It retrieves the embedding vector for position 0, then position 1, and so on, for the length of your input. The result is a matrix where each row is the position embedding for the corresponding position in the input sequence.

Addition (+):

The token embedding matrix (representing what each token is) and the position embedding matrix (representing where each token is in the sequence) are simply added together element-wise. Both matrices have the same shape (sequence length × embedding dimension).

The resulting matrix x now contains vectors where each vector encodes both the token's identity and its position. This combined representation is the final input that gets fed into the stack of transformer blocks for processing.

In summary, this line x = params.wte[inputs] + params.wpe[range(len(inputs))] creates the initial representation for the input sequence by looking up the learned vector for each token and adding the learned vector for its position. This allows the subsequent transformer layers to process the tokens while being aware of their order.

The size of the matrix is [sequence_length, embedding_dimension]. We denote sequence length as N in the code.

GELU

GELU (Gaussian Error Linear Unit) is an activation function used in the Transformer architecture, particularly within the feed-forward networks (FFN) of each block. Its primary role is to introduce non-linearity into the model, allowing it to learn more complex patterns and relationships in the data. Without non-linear activation functions, stacking multiple layers would be equivalent to a single linear transformation, severely limiting the model's representational power. In math it's defined as:

$$
\text{GELU}(x) = 0.5 \cdot x \cdot \left(1 + \text{erf}\left(\frac{x}{\sqrt{2}}\right)\right)
$$

where erf is the Guass error function. In practice we'll use an approximation where we use the tanh function to approximate the error function so we don't have to compute integrals involved in the error function. In Python this approximation is implemented as:

# gelu:
#   x : (N, 768)
#   out : (N, 768)
def gelu(x: np.ndarray) -> np.ndarray:
    return 0.5 * x * (1 + np.tanh(np.sqrt(2 / np.pi) * (x + 0.044715 * x**3)))

Note that this is a scalar function that is applied element-wise to the input.

Softmax

While GELU handles non-linearity within feed-forward networks, the transformer architecture also needs a way to convert raw scores into meaningful probability distributions. This is where the softmax function comes into play. Softmax is a crucial function used primarily in two places within the Transformer architecture: within the attention mechanism and at the final output layer. Its purpose is to convert a vector of raw scores (logits) into a probability distribution. It takes an input vector and exponentiates each element, making them all positive, and then normalizes these values by dividing by their sum. The result is a vector where all elements are between 0 and 1, and they all sum up to 1.

$$
\text{softmax}(x)_i = \frac{e^{x_i}}{\sum_j e^{x_j}}
$$

In the attention mechanism (attention function), softmax is applied to the scaled dot-product scores between queries and keys. This transforms the raw similarity scores into attention weights, which represent the probability distribution over the value vectors – indicating how much focus each value should receive.

At the final layer of the model (just before generating the next token), softmax is typically applied to the logits produced by the final linear projection. This converts the model's raw output scores for each word in the vocabulary into probabilities, allowing us to interpret the scores and sample the next token based on this distribution.

# softmax:
#   x : (N, 64)
#   out : (N, 64)
def softmax(x: np.ndarray) -> np.ndarray:
    exp_x = np.exp(x - np.max(x, axis=-1, keepdims=True))
    return exp_x / np.sum(exp_x, axis=-1, keepdims=True)

Layer Normalization

Beyond activation functions and probability conversions, neural networks need methods to stabilize training, especially in deep architectures like transformers. Layer Normalization (LayerNorm) serves this critical purpose. Unlike Batch Normalization which normalizes across the batch dimension, Layer Normalization normalizes the inputs across the features (embedding dimension) for each data sample independently.

$$
\text{LayerNorm}(x) = \gamma \cdot \frac{x - \mu}{\sqrt{\sigma^2}} + \beta
$$

Where $\mu$ is the mean and $\sigma^2$ is the variance of the input, and $\gamma$ and $\beta$ are learnable gain and bias parameters.

In a Transformer block, LayerNorm is typically applied before the multi-head attention sub-layer and before the feed-forward network sub-layer (this is known as pre-LN). It works by calculating the mean and variance of all the activations within a single layer for a single training example. It then normalizes the activations using this mean and variance. Crucially, it also introduces learnable gain (g) and bias (b) parameters, allowing the network to scale and shift the normalized output, preserving its representational capacity.

LayerNorm helps mitigate issues like vanishing or exploding gradients, allows for higher learning rates, and makes the model less sensitive to the scale of the parameters and initialization. By normalizing the activations within each layer, it ensures that the inputs to the subsequent layers are consistently scaled, leading to smoother and more stable training dynamics.

# layer_norm:
#   x : (N, 768)
#   g : (768,)
#   b : (768,)
#   out : (N, 768)
def layer_norm(
    x: np.ndarray, g: np.ndarray, b: np.ndarray, eps: float = 1e-5
) -> np.ndarray:
    mean = np.mean(x, axis=-1, keepdims=True)
    variance = np.var(x, axis=-1, keepdims=True)
    return g * (x - mean) / np.sqrt(variance + eps) + b

Linear Projection

With normalization in place to stabilize the network, transformers need a way to transform representations from one space to another. This is where linear layers come in. The linear layer, also known as a fully connected or dense layer, is one of the most fundamental components in neural networks. It performs a linear transformation on the input data.

Mathematically, it computes output = input @ weights + bias, where @ represents matrix multiplication. The input is the data fed into the layer, weights is a matrix of learnable parameters, and bias is a learnable vector that gets added to the result. The weights matrix effectively projects the input vector from its original dimension to a new dimension (defined by the shape of the weights matrix), and the bias allows for shifting the output.

# linear:
#   x : (N, 768)
#   w : (768, 3072)
#   b : (3072,)
#   out : (N, 3072)
def linear(x: np.ndarray, w: np.ndarray, b: np.ndarray) -> np.ndarray:
    return x @ w + b

Feed-Forward Network

Having covered the individual building blocks of normalization, activation, and linear transformation, we can now examine how these components come together in the Feed-Forward Network (FFN). The FFN, sometimes called the position-wise feed-forward network, is the second main sub-layer within each Transformer block (following the multi-head attention sub-layer).

It consists of two linear transformations with a non-linear activation function (the GELU function we explored earlier) applied in between. The first linear layer usually expands the dimensionality of the input (e.g., from 768 to 3072 in GPT-2), the GELU activation introduces non-linearity, and the second linear layer projects the result back down to the original input dimensionality (e.g., 3072 back to 768).

This FFN is applied independently to each position in the sequence. While the attention mechanism allows tokens to interact with each other, the FFN processes the information at each position separately, transforming the representation based on the features learned by the model. It adds significant representational capacity to the model, allowing it to learn more complex functions beyond what the attention mechanism alone can capture.

# ffn:
#   x : (N, 768)
#   c_fc_w : (768, 3072)
#   c_fc_b : (3072,)
#   c_proj_w : (3072, 768)
#   c_proj_b : (768,)
#   out : (N, 768)
def ffn(
    x: np.ndarray,
    c_fc_w: np.ndarray,
    c_fc_b: np.ndarray,
    c_proj_w: np.ndarray,
    c_proj_b: np.ndarray,
) -> np.ndarray:
    return linear(gelu(linear(x, w=c_fc_w, b=c_fc_b)), w=c_proj_w, b=c_proj_b)

Attention

Attention is the core idea of the transformer architecture. It is a mechanism inspired by human visual attention. Just as we focus on certain parts of an image or specific words in a sentence while ignoring others, attention allows a model to dynamically weigh the importance of different parts of the input data when processing a particular element. For sequential data like text, this means that when the model is processing one word, it can "pay attention" to other relevant words in the sequence, regardless of their distance, to better understand the context and meaning. This selective focus helps the model capture long-range dependencies and relationships more effectively than older sequence models.

At the heart of each attention calculation are three key matrices derived from the input sequence:

Query (Q): Represents the current token or position we are processing. Think of it as asking: "What specific information am I looking for right now?"
Key (K): Represents all the tokens in the sequence (including the current one). Think of it as labels or identifiers for the information contained in each token: "What kind of information does each token offer?"
Value (V): Also represents all tokens in the sequence. Think of it as the actual content or representation of each token: "What is the actual information conveyed by each token?"

The process begins with an initial projection where the input sequence x passes through three separate linear layers to generate initial Q, K, and V matrices spanning the entire input dimension. These large matrices are then split into smaller chunks along their embedding dimension, creating separate Q, K, and V sets for each attention "head". Formally self-attention is computed as:

$$
\text{Attention}(Q,K,V)=\text{softmax} \left( \frac{QK^T}{\sqrt{d_k}} \right) \cdot V
$$

where:

Q, K, V are the query, key, and value matrices, and
d_k is the dimension of the key vectors.

The attention function implements the core scaled dot-product attention mechanism, the fundamental building block used within each head of the Multi-Head Attention layer. It calculates how much focus or "attention" each input token (represented by its Value vector) should receive when processing a specific token (represented by its Query vector).

The process starts by computing the dot product between the Q matrix and the transpose of the K matrix (q @ k.T). This step measures the raw similarity or compatibility between each query and all keys. These raw scores are then scaled down by dividing them by the square root of the dimension of the key vectors (np.sqrt(q.shape[-1])).

The causal mask is a mask that is added to these scaled scores. This mask prevents positions from attending to subsequent positions, ensuring predictions are based only on previous tokens. The mask effectively assigns very large negative values to scores corresponding to future tokens.

Next, a softmax function is applied to the masked, scaled scores. This converts the scores into probability distributions (attention weights) where each weight indicates the relative importance of a specific key (and its corresponding value) to the query.

Finally, the function computes the matrix product of these attention weights and the V matrix (attention_weights @ v). This yields the output of the attention mechanism: a weighted sum of the Value vectors, where the weights are the calculated attention probabilities. The resulting vector for each query is thus a blend of information from the input sequence, emphasizing the most relevant parts based on the query-key interactions.

# attention:
#   q : (N, 64)
#   k : (N, 64)
#   v : (N, 64)
#   mask : (N, N)
#   out : (N, 64)
def attention(
    q: np.ndarray, k: np.ndarray, v: np.ndarray, mask: np.ndarray
) -> np.ndarray:
    attention_scores = (q @ k.T) / np.sqrt(q.shape[-1]) + mask
    attention_weights = softmax(attention_scores)
    return attention_weights @ v

We can visualize the attention mechanism by plotting the attention weights for each head. For example for the phrase "The quick brown fox jumps over the lazy dog" we can plot the attention weights in the first block of the transformer stack to see which pairs of words are attended to most by each head. Here we see "jumps" and "fox" are attended to most by the first head.

Multi-Head Attention

While the basic attention mechanism provides a way to capture relationships between tokens, transformers take this a step further with Multi-Head Attention. This enhancement allows the model to capture different types of relationships simultaneously, greatly expanding its representational power. Multi-Head Attention is a core component that allows the model to jointly attend to information from different representation subspaces at different positions. Instead of performing a single attention calculation, MHA runs the attention mechanism multiple times ("heads") in parallel on different learned linear transformations of the input. This allows the model to capture various types of relationships (e.g., syntactic, semantic) simultaneously.

Within each head, scaled dot-product attention is performed. Attention scores are computed by taking the dot product of the Q with all Ks, measuring the relevance between the current token and every other token. These scores are scaled (divided by the square root of the key dimension) and passed through a softmax function to become probabilities (attention weights). These weights indicate how much focus to place on each V.

The size of each attention head's query matrix (64) is derived by dividing the model's embedding dimension (768) by the number of attention heads (12). When the outputs of all heads are concatenated back together, we recover the original embedding dimension:

768/n_head = 768/12 = 64

The attention weights are then used to multiply the corresponding V vectors, producing a weighted sum. This creates an output vector for the head that blends information from the most relevant tokens. Finally, the output vectors from all attention heads are concatenated back together. This combined vector is passed through a final linear layer to produce the overall output of the Multi-Head Attention block. This multi-faceted approach enables the model to capture richer contextual information by looking at the sequence from multiple "perspectives" concurrently.

# mha:
#   x : (N, 768)
#   out : (N, 768)
def mha(
    x: np.ndarray, c_attn: LinearParams, c_proj: LinearParams, n_head: int
) -> np.ndarray:
    # qkv projection
    # [N, 768] -> [N, 3*768]
    x = linear(x, w=c_attn.w, b=c_attn.b)

    # split into qkv
    # [N, 3*768] -> [3, N, 768]
    qkv = np.split(x, 3, axis=-1)

    # split into heads
    # [3, N, 768] -> [3, n_head, N, 64]
    qkv_heads = [np.split(x, n_head, axis=-1) for x in qkv]

    # apply causal mask to hide future inputs
    # [N, N]
    causal_mask = (1 - np.tri(x.shape[0], dtype=x.dtype)) * -1e10

    # perform attention on each head
    # [3, n_head, N, 64] -> [n_head, N, 64]
    out_heads = [attention(q, k, v, causal_mask) for q, k, v in zip(*qkv_heads)]

    # merge heads
    # [n_head, N, 64] -> [N, 768]
    x = np.hstack(out_heads)

    # out projection
    # [N, 768] -> [N, 768]
    return linear(x, w=c_proj.w, b=c_proj.b)

Transformer Block

With both the attention mechanism and feed-forward networks defined, we can now see how these components are integrated into the complete Transformer block. The Transformer block is the fundamental repeating unit of the GPT-2 architecture, combining multi-head attention with feed-forward processing, normalization, and residual connections to create a computational unit that can be stacked multiple times.

Each block takes a sequence of input vectors and processes them through two main sub-layers, incorporating residual connections and layer normalization around each. This structure creates a balanced flow of information that allows both preservation of original inputs (through residual connections) and transformation into new representations.

The first sub-layer is the Multi-Head Attention mechanism we just explored. Before the input enters the MHA, it undergoes layer normalization. The output of the MHA is then added back to the original input (a residual connection), combining the attention-derived context with the original positional representation. This sum then passes to the second sub-layer.

The second sub-layer is the Feed-Forward Network described earlier. Similar to the first sub-layer, the input (which is the output of the first residual connection) first goes through layer normalization. The normalized output is then processed by the FFN. The output of the FFN is then added back to its input via another residual connection. The final output of the transformer block is this sum, which then serves as the input to the next identical transformer block in the stack.

# transformer_block:
#   x : (N, 768)
#   out : (N, 768)
def transformer_block(
    x: np.ndarray,
    mlp: MLPParams,
    attn: AttentionParams,
    ln_1: LayerNormParams,
    ln_2: LayerNormParams,
    n_head: int
) -> np.ndarray:
    # First sub-block: Layer norm -> Attention -> Residual
    a = layer_norm(x, g=ln_1.g, b=ln_1.b)
    a = mha(a, c_attn=attn.c_attn, c_proj=attn.c_proj, n_head=n_head)
    x = x + a

    # Second sub-block: Layer norm -> FFN -> Residual
    m = layer_norm(x, g=ln_2.g, b=ln_2.b)
    m = ffn(
        m,
        c_fc_w=mlp.c_fc.w,
        c_fc_b=mlp.c_fc.b,
        c_proj_w=mlp.c_proj.w,
        c_proj_b=mlp.c_proj.b,
    )
    x = x + m

    return x

Full Model

Now that we've examined the individual components and the Transformer block structure, we can assemble everything into a complete model. These blocks are stacked multiple times (e.g., 12 times in the smallest GPT-2 model) to build a deep network capable of sophisticated language understanding and generation. The combination of attention mechanisms, feed-forward networks, layer normalization, and residual connections creates an architecture that effectively processes sequential information, captures complex dependencies, and trains stably despite its depth.

The gpt2 function represents the complete forward pass of the GPT-2 model for a given sequence of input token IDs. It orchestrates the flow of data through all the previously defined components, transforming raw token IDs into contextual representations and ultimately into predictions for the next token.

The journey begins with embedding the input tokens. This is achieved by summing the token embeddings (looked up in params.wte) and the positional embeddings (looked up in params.wpe) for each token in the input sequence. This initial combined embedding captures both the semantic meaning of each token and its position in the sequence, providing the foundation for all subsequent processing.

This embedded sequence then flows through the stack of Transformer blocks. Each block refines the representation through its attention and feed-forward mechanisms, gradually building more sophisticated contextual understanding. The code explicitly implements this stacking for a 12-layer model, where the output of one block becomes the input to the next. With each successive layer, the model can capture increasingly complex patterns and relationships in the data.

def gpt2(inputs: list[int], params: ModelParams, n_head: int) -> np.ndarray:
    # Get token embeddings and position embeddings
    x = params.wte[inputs] + params.wpe[range(len(inputs))]

    # Apply transformer block stack ( 12 blocks total )
    for i in range(12):
        x = transformer_block(
            x,
            n_head=n_head,
            mlp=params.blocks[i].mlp,
            attn=params.blocks[i].attn,
            ln_1=params.blocks[i].ln_1,
            ln_2=params.blocks[i].ln_2,
        )

    # Apply final layer norm and project to vocabulary
    x = layer_norm(x, g=params.ln_f.g, b=params.ln_f.b)
    logits = x @ params.wte.T  # Project to vocabulary

    return logits

After processing through all the transformer blocks, the resulting sequence undergoes a final layer normalization to stabilize the values. This normalized output with shape (N, 768) (for GPT-2 small) represents the final contextual embeddings for each token in the sequence. To convert these embeddings into predictions over the vocabulary, the model performs a projection using the transposed token embedding matrix (params.wte.T). This clever weight-sharing technique (using the same embedding matrix for both input embedding and output projection) reduces the total parameter count.

The result is a tensor of logits with shape (N, 50257) (for GPT-2), where 50,257 is the vocabulary size. These logits represent the unnormalized prediction scores for each possible next token at each position in the sequence. Every token in the vocabulary receives a score, and these scores can be ranked to determine which tokens are most likely to follow in the sequence. A typical example of these logits for a single position might look like:

array([-114.83902718, -111.23177705, -116.58203861, ..., -118.4023539 ,
       -118.92616557, -113.37047973], shape=(50257,))

For autoregressive generation, we typically only care about predicting the next token after the end of our current sequence. By selecting the logits corresponding to the last position and applying an operation like argmax, we can identify the most likely next token:

next_token = np.argmax(logits[-1, :])

This token ID can then be appended to our sequence, and the process repeated to generate text one token at a time. But for this approach to work, we need properly initialized model parameters loaded from pre-trained weights, which brings us to our next topic.

Safetensors and Model Parameters

To utilize pre-trained models like GPT-2, we need to load and organize their parameters effectively. This section explains how we structure and load these parameters using the safetensors format, a secure and efficient method for storing model weights. For that we load them from HuggingFace in which they are stored in the model.safetensors file.

Safetensors is a fast and safe (i.e. it doesn't use Pickle, which requires execution of arbitrary code) format for storing tensors. The format uses a simple key/value structure where keys are UTF-8 encoded strings representing tensor names (e.g. model.layers.0.attention.weight), values are binary tensor data with a fixed header containing shape and dtype information, and a metadata section at the start of the file contains an index of all tensors and their offsets.

Internally the model parameters for GPT-2 are stored in the following key/value format:

{
    "wpe.weight"             : np.array([1024, 768]),
    "wte.weight"             : np.array([50257, 768]),
    ...
    "h.0.attn.bias"          : np.array([1, 1, 1024, 1024]),
    "h.0.attn.c_attn.bias"   : np.array([2304]),
    "h.0.attn.c_attn.weight" : np.array([768, 2304]),
    "h.0.attn.c_proj.bias"   : np.array([768]),
    "h.0.attn.c_proj.weight" : np.array([768, 768]),
    "h.0.ln_1.bias"          : np.array([768]),
    "h.0.ln_1.weight"        : np.array([768]),
    "h.0.ln_2.bias"          : np.array([768]),
    "h.0.ln_2.weight"        : np.array([768]),
    "h.0.mlp.c_fc.bias"      : np.array([3072]),
    "h.0.mlp.c_fc.weight"    : np.array([768, 3072]),
    "h.0.mlp.c_proj.bias"    : np.array([768]),
    "h.0.mlp.c_proj.weight"  : np.array([3072, 768]),
    ...
    "ln_f.bias"              : np.array([768]),
    "ln_f.weight"            : np.array([768])
}

Each of these is a tensor with a shape and a dtype that hold the learned parameters for that component, these are the result of the model training process.

The LayerNormParams dataclass represents the layer normalization parameters, which include a scale (g) and bias (b) for each layer.

@dataclass
class LayerNormParams:
    g: np.ndarray  # Gamma (scale)
    b: np.ndarray  # Beta (bias)

The LinearParams dataclass represents the linear projection parameters, which include a weight matrix (w) and a bias vector (b).

@dataclass
class LinearParams:
    w: np.ndarray  # Weight matrix
    b: np.ndarray  # Bias vector

The MLPParams dataclass represents the feed-forward network parameters, which include two linear layers: a first linear layer (c_fc) and a second linear layer (c_proj).

@dataclass
class MLPParams:
    c_fc: LinearParams  # First linear layer
    c_proj: LinearParams  # Second linear layer

The AttentionParams dataclass represents the attention parameters, which include a query-key-value projection (c_attn) and an output projection (c_proj).

@dataclass
class AttentionParams:
    c_attn: LinearParams  # QKV projection
    c_proj: LinearParams  # Output projection

The TransformerBlockParams dataclass represents a single transformer block, which includes a layer normalization (ln_1), a feed-forward network (mlp), an attention mechanism (attn), and a second layer normalization (ln_2).

@dataclass
class TransformerBlockParams:
    ln_1: LayerNormParams  # First layer norm
    ln_2: LayerNormParams  # Second layer norm
    mlp: MLPParams  # MLP block
    attn: AttentionParams  # Attention block

The ModelParams dataclass represents the complete model parameters, which include a token embedding matrix (wte), a position embedding matrix (wpe), a list of transformer blocks (blocks), and a final layer normalization (ln_f).

@dataclass
class ModelParams:
    wte: np.ndarray  # Token embeddings
    wpe: np.ndarray  # Position embeddings
    blocks: List[TransformerBlockParams]  # Transformer blocks
    ln_f: LayerNormParams  # Final layer norm

The HParams dataclass represents the hyperparameters of the model, which include the number of transformer layers (n_layer), the number of attention heads (n_head), and the context length (n_ctx).

@dataclass
class HParams:
    n_layer: int  # Number of transformer layers
    n_head: int  # Number of attention heads
    n_ctx: int  # Context length

We can load the model parameters from a model.safetensors file using the safe_open function. This file can be downloaded from the Hugging Face Model Hub.

tensors = {}
with safe_open(weights_path, framework="numpy") as f:
    for key in f.keys():
        tensors[key] = f.get_tensor(key)

# Build transformer blocks
blocks = []
for i in range(config["n_layer"]):
    prefix = f"h.{i}"
    block = TransformerBlockParams(
        ln_1=LayerNormParams(
            g=tensors[f"{prefix}.ln_1.weight"], b=tensors[f"{prefix}.ln_1.bias"]
        ),
        ln_2=LayerNormParams(
            g=tensors[f"{prefix}.ln_2.weight"], b=tensors[f"{prefix}.ln_2.bias"]
        ),
        mlp=MLPParams(
            c_fc=LinearParams(
                w=tensors[f"{prefix}.mlp.c_fc.weight"],
                b=tensors[f"{prefix}.mlp.c_fc.bias"],
            ),
            c_proj=LinearParams(
                w=tensors[f"{prefix}.mlp.c_proj.weight"],
                b=tensors[f"{prefix}.mlp.c_proj.bias"],
            ),
        ),
        attn=AttentionParams(
            c_attn=LinearParams(
                w=tensors[f"{prefix}.attn.c_attn.weight"],
                b=tensors[f"{prefix}.attn.c_attn.bias"],
            ),
            c_proj=LinearParams(
                w=tensors[f"{prefix}.attn.c_proj.weight"],
                b=tensors[f"{prefix}.attn.c_proj.bias"],
            ),
        ),
    )
    blocks.append(block)

# Build final model params
params = ModelParams(
    wte=tensors["wte.weight"],
    wpe=tensors["wpe.weight"],
    blocks=blocks,
    ln_f=LayerNormParams(g=tensors["ln_f.weight"], b=tensors["ln_f.bias"]),
)

Greedy Decoding

With the model architecture defined and parameters loaded, we're now ready to put everything together and generate text. The simplest approach for text generation is greedy decoding, where at each step we simply choose the token with the highest probability as predicted by our model.

The generate function below encapsulates the entire text generation process, from encoding the initial prompt to iteratively generating new tokens. This function showcases how all the components we've explored—tokenization, embedding, transformer blocks, and vocabulary projection—work together to create a functioning language model.

def generate(prompt: str, n_tokens_to_generate: int = 40) -> str:
    encoder = get_encoder("", "model")
    params, hparams = load_gpt2_weights()

    input_ids = encoder.encode(prompt)
    generated_token_ids: list[int] = []

    print(prompt, end="", flush=True)

    current_ids = list(input_ids)

    for _ in range(n_tokens_to_generate):
        logits = gpt2(current_ids, params, n_head=hparams.n_head)
        next_id = np.argmax(logits[-1, :])
        next_id_int = int(next_id)

        current_ids.append(next_id_int)
        generated_token_ids.append(next_id_int)

        token_text = encoder.decode([next_id_int])
        print(token_text, end="", flush=True)

    print()

    return encoder.decode(generated_token_ids)

The generation process starts by encoding the user's prompt into token IDs using our BPE tokenizer. We initialize an empty list to keep track of the tokens we'll generate. Then we enter a loop where, at each iteration, we:

Feed the current sequence of token IDs (the original prompt plus all tokens generated so far) through our GPT-2 model
Extract the logits for the last token position, which represent the model's prediction for what comes next
Take the argmax of these logits to select the most likely next token
Append this new token to our list of generated tokens and to the current sequence
Decode and print the new token to show the generation in real-time

After generating the requested number of tokens, we decode the full sequence of generated tokens back into text and return it. And that's it that's all it take to impmlement a naive version of a GPT-2 model. There's only about six "kernel" operations that we need to implement (softmax, gelu, layer_norm, linear, add, matmul, var, mean) and the rest is just a lot of bookkeeping to handle the data structures.

But as you notice, this model is very slow and inefficient averaging about 2-3 tokens per second on a modern CPU. There are many opportunities for both fusion and parallelization via lowering into MLIR and PTX, which we'll explore in the next section.

External Resources

MLIR Part 6 - Specializing Python with E-graphs

Mon, 17 Mar 2025 00:00:00 +0000

Specializing Python with E-graphs

We've explored progressively more sophisticated techniques for optimizing numerical computations. We started with basic MLIR concepts, moved through memory management and linear algebra, and then neural network implementations. Each layer has added new capabilities for expressing and optimizing computations. Now we're reading to build our first toy compiler for Python expressions.

In this section, we'll explore how to use the egglog library to perform term rewriting and optimization on Python expressions and compile them into MLIR.

The entire source code for this section is available on GitHub.

Equality Saturaiton and E-Graphs

Before we dive into the implementation, let's review the key concepts of equality saturation and e-graphs.

Take as an example if we have the rewrites.

x * 2 → x << 1
x*y/x → y

And we try to apply it over the expression (a * 2)/2 becomes (a << 1)/2. However we should have cancelled the 2 in the numerator and denominator and got a which results in a simpler expression. The order of rewrites is important and we want to find an optimal order of rewrites that reduces the expression to a form according to a cost function. This is called the phase ordering problem.

The egg library employs an approach that involves exhaustively applying all possible rewrites to an expression, effectively addressing the phase ordering problem through the use of an e-graph. This approach allows for the exploration of all possible rewrites, followed by the extraction of the most optimal form of the expression.

In linear algebra for example, matrix operations with NumPy like transpose, multiplication, are quite expensive because they involve touching every element of the matrix. But there is a wide range of identities that can be applied to reduce the number of operations.

Compilers like LLVM and even the linalg dialect of MLIR doesn't know about these identities and so can't necessarily abstract away the expensive operations by applying rewrites. However at a high-level (our core language) we can use e-graph to produce much more efficient tensor manipulation operations before lowering them into MLIR.

For example, the following identities are quite common in linear algebra:

$$
(A B)^T = B^T A^T
$$

$$
(A^T)^T = A
$$

Or in Python:

np.transpose(A * B) = np.transpose(B) * np.transpose(A)
np.transpose(np.transpose(A)) == A

By applying these rules, we can optimize NumPy expressions at compile time, leading to significant performance improvements. For instance, in our example, we've successfully reduced three loops—comprising one multiplication and two transposes—down to just two loops, which consist of one multiplication and one transpose. This optimization not only simplifies the computation but also enhances efficiency. In common uses of NumPy, there are numerous opportunities for such optimizations, often referred to as low-hanging fruit. These optimizations can be systematically applied to reduce the number of operations required, thereby streamlining the execution of numerical computations. This is particularly beneficial before even LLVM's auto-vectorization comes into play, as it allows us to leverage the full potential of our expressions and achieve faster execution times.

An e-graph (equality graph) is a data structure that compactly represents many equivalent expressions. Instead of maintaining a single canonical form for expressions, e-graphs maintain classes of equivalent expressions. This approach allows for more flexible and efficient term rewriting.

Let's look at a concrete example using egglog library to do basic simplification. First we have to define our expression model.

from __future__ import annotations
from egglog import *

class Num(Expr):
    def __init__(self, value: i64Like) -> None: ...
    
    @classmethod
    def var(cls, name: StringLike) -> Num: ...
    
    def __add__(self, other: Num) -> Num: ...
    
    def __mul__(self, other: Num) -> Num: ...

# Create an e-graph to store our expressions
egraph = EGraph()

# Define our expressions and give them names in the e-graph
expr1 = egraph.let("expr1", Num(2) * (Num.var("x") + Num(3)))  # 2 * (x + 3)
expr2 = egraph.let("expr2", Num(6) + Num(2) * Num.var("x"))    # 6 + 2x

# Define our rewrite rules using a decorated function
@egraph.register
def _num_rule(a: Num, b: Num, c: Num, i: i64, j: i64):
    yield rewrite(a + b).to(b + a)                    # Commutativity of addition
    yield rewrite(a * (b + c)).to((a * b) + (a * c))  # Distributive property
    yield rewrite(Num(i) + Num(j)).to(Num(i + j))     # Constant folding for addition
    yield rewrite(Num(i) * Num(j)).to(Num(i * j))     # Constant folding for multiplication

# Apply rules until no new equalities are found
egraph.saturate()

# Check if expr1 and expr2 are equivalent
egraph.check(eq(expr1).to(expr2))

# Extract the simplified form of expr1
egraph.extract(expr1)

Using the egraph.display() function we can visualize the e-graph.

The input expression before equality saturation:

Input expression before equality saturation

Then the output with all the equivalences classes is a network of expressions:

Output expression after equality saturation

From there we can extract the expression we want according to a custom cost function.

Foundation Layer

Ok now let's apply this to our basic expression compiler. Our compiler pipeline has several key stages:

Python function decoration and type annotation
Expression tree extraction
Term rewriting and optimization using e-graphs
MLIR code generation
LLVM compilation and JIT execution

The foundation layer of our compiler provides the core abstractions for representing and manipulating mathematical expressions. This layer is crucial as it forms the basis for all higher-level optimizations and transformations. Let's explore each component in detail.

Expression Model (`expr_model.py`)

At the heart of our compiler is an expression model that represents mathematical expressions as an abstract syntax tree (AST). The model is implemented using Python's dataclasses for clean and efficient representation.

Core Expression Types

The base class for all expressions is the Expr class, which provides the fundamental operations:

@dataclass(frozen=True)
class Expr:
    def __add__(self, other: Expr) -> Expr:
        return Add(self, as_expr(other))
    
    def __mul__(self, other: Expr) -> Expr:
        return Mul(self, as_expr(other))
    # ... other operations

The expression model consists of three fundamental types:

Literals: Constants in our expressions

@dataclass(frozen=True)
class FloatLiteral(Expr):
    fval: float  # Floating-point constant

@dataclass(frozen=True)
class IntLiteral(Expr):
    ival: float  # Integer constant

Symbols: Variables and function names

@dataclass(frozen=True)
class Symbol(Expr):
    name: str  # Variable or function name

Operations: Both unary and binary operations

@dataclass(frozen=True)
class UnaryOp(Expr):
    operand: Expr  # Single operand

@dataclass(frozen=True)
class BinaryOp(Expr):
    lhs: Expr  # Left-hand side
    rhs: Expr  # Right-hand side

@dataclass(frozen=True)
class Add(BinaryOp): pass      # Addition
...

@dataclass(frozen=True)
class Sin(UnaryOp): pass       # Sine

Built-in Functions (`builtin_functions.py`)

The built-in functions module provides a NumPy-like interface for mathematical operations. This makes it easier for users to write expressions in a familiar syntax while still leveraging our optimization framework. It includes common mathematical constants and helper functions for operations like absolute value.

# A mock NumPy namespace that we convert into our own expression model

import math
from mlir_egglog.expr_model import (
    sin,
    cos,
    tan,
    asin,
    acos,
    atan,
    tanh,
    sinh,
    cosh,
    sqrt,
    exp,
    log,
    log10,
    log2,
    float32,
    int64,
    maximum,
)  # noq

# Constants
e = math.e
pi = math.pi


# Define abs function
def abs(x):
    return maximum(x, -x)


def relu(x):
    return maximum(x, 0.0)


def sigmoid(x):
    return 1.0 / (1.0 + exp(-x))


__all__ = [
    "sin",
    "cos",
    "tan",
    "asin",
    "acos",
    "atan",
    "tanh",
    "sinh",
    "cosh",
    "sqrt",
    "exp",
    "log",
    "log10",
    "log2",
    "float32",
    "int64",
    "e",
    "pi",
    "maximum",
    "abs",
]

Term IR (`term_ir.py`)

The Term IR layer provides an intermediate representation optimized for term rewriting and equality saturation. A key feature of the Term IR is a cost model for different operations:

COST_BASIC_ARITH = 1   # Basic arithmetic (single CPU instruction)
COST_CAST = 2          # Type conversion operations
COST_DIV = 5           # Division
COST_POW_INTEGER = 10  # Integer power
COST_SQRT = 20         # Square root
COST_LOG = 30          # Logarithm
COST_EXP = 40          # Exponential
COST_POW = 50          # General power operation
COST_TRIG_BASIC = 75   # Basic trigonometric functions
COST_HYPERBOLIC = 180  # Hyperbolic functions

These costs are used by the e-graph optimization engine to make decisions about which transformations to apply. The costs roughly correspond to the computational complexity of each operation on modern hardware.

from __future__ import annotations

import egglog
from egglog import StringLike, i64, f64, i64Like, f64Like  # noqa: F401
from egglog import RewriteOrRule, rewrite
from typing import Generator
from mlir_egglog.expr_model import Expr, FloatLiteral, Symbol, IntLiteral
from abc import abstractmethod

def as_egraph(expr: Expr) -> Term:
    """
    Convert a syntax tree expression to an egraph term.
    """
    from mlir_egglog import expr_model

    match expr:
        # Literals and Symbols
        case FloatLiteral(fval=val):
            return Term.lit_f32(val)
        case IntLiteral(ival=val):
            return Term.lit_i64(int(val))
        case Symbol(name=name):
            return Term.var(name)

        # Binary Operations
        case expr_model.Add(lhs=lhs, rhs=rhs):
        
        # Rest of the operations
        ...

The cost model is used to guide the e-graph optimization engine to find the most cost-effective implementation according to our cost model. For example

$$
e^x \cdot e^x \cdot e^x = e^{3x}
$$

The LHS has 3 multiplications and the RHS has 1 multiplication. So the cost applied to the extraction will select the RHS.

Transformation Layer

One of the most powerful features of our compiler is its ability to symbolically interpret Python functions. This process transforms regular Python functions into our IR representation, allowing us to apply optimizations on the resulting expression tree.

The interpretation process is handled by the interpret function:

import types
import inspect

from mlir_egglog import expr_model as ir


def interpret(fn: types.FunctionType, globals: dict[str, object]):
    """
    Symbolically interpret a python function.
    """
    # Get the function's signature
    sig = inspect.signature(fn)

    # Create symbolic parameters for each of the function's arguments
    params = [n for n in sig.parameters]
    symbolic_params = [ir.Symbol(name=n) for n in params]

    # Bind the symbolic parameters to the function's arguments
    ba = sig.bind(*symbolic_params)

    # Inject our globals (i.e. np) into the function's globals
    custom_globals = fn.__globals__.copy()
    custom_globals.update(globals)

    # Create a temporary function with our custom globals
    tfn = types.FunctionType(
        fn.__code__,
        custom_globals,
        fn.__name__,
        fn.__defaults__,
        fn.__closure__,
    )
    return tfn(*ba.args, **ba.kwargs)

The function begins with parameter analysis, where it analyzes the input function's signature to determine its parameters. For each parameter, it creates a symbolic representation using our Symbol class. These symbols will be used to track variables through the expression tree.

Next, the symbolic parameters are bound to the function's argument slots, creating a mapping between parameter names and their symbolic representations. The function then injects our custom implementations of mathematical operations, such as NumPy functions, into the function's global namespace. This allows us to intercept calls to these functions and replace them with our symbolic operations.

A temporary function is created with the modified globals, while retaining the same code, name, and closure as the original function. Finally, the function is executed with the symbolic parameters, resulting in an expression tree that represents the computation.

For example, given a Python function:

def f(x, y):
    return np.sin(x) + np.cos(y)

The interpretation process will:

Create symbols for x and y
Replace np.sin and np.cos with our symbolic versions
Execute the function with symbolic inputs
Return an expression tree representing Sin(Symbol("x")) + Cos(Symbol("y"))

This symbolic interpretation is what allows us to capture Python computations in a form that can be optimized using our e-graph machinery.

IR Conversion (`ir_to_mlir.py`)

The IR to MLIR conversion layer serves as a crucial bridge between our high-level expression representation and MLIR's lower-level dialect. This conversion process is implemented in ir_to_mlir.py and involves several steps that leverage Python's dynamic execution capabilities along with AST manipulation.

The conversion pipeline begins with the convert_term_to_expr function, which transforms an IR term into our internal expression model. This function employs Python's built-in ast module to parse and manipulate the abstract syntax tree of the term. The process is particularly interesting because it uses Python's execution environment as part of the conversion process.

When a term arrives for conversion, it first goes through AST parsing. The function creates a Python AST from the string representation of the term, which allows us to manipulate the code structure before execution. A key part of this process is the mangle_assignment function, which ensures the result of the expression is properly captured in a variable named _out. This mangling step is crucial because it provides a way to extract the final result from the execution environment.

The execution environment is carefully constructed using a function_map dictionary that maps operation names to their corresponding implementations. This map includes basic arithmetic operations (Add, Sub, Mul, Div), mathematical functions (Sin, Cos, Exp, Log), and type conversion operations (CastF32, CastI64). Each of these operations is mapped to either a method from our expression model or a function from our builtin functions module.

The second major component is the convert_term_to_mlir function, which takes the converted expression and generates MLIR code. This function handles the final transformation into MLIR's textual format. It processes function arguments through the argspec parameter, creating a mapping between argument names and their MLIR representations (e.g., converting x to %arg_x). The actual MLIR generation is delegated to the MLIRGen class, which walks through the expression tree and produces corresponding MLIR operations.

For example, when converting a simple arithmetic expression like a + b * c, the pipeline would:

Parse the expression into an AST
Transform it into our internal expression model using the function map
Generate MLIR code with proper memory references and operations
Wrap the operations in a proper MLIR function structure with appropriate type annotations

def convert_term_to_expr(tree: IRTerm) -> ir.Expr:
    """
    Convert a term to an expression.
    """

    # Parse the term into an AST
    astree = ast.parse(str(tree))

    # Mangle the assignment
    astree.body[-1] = ast.fix_missing_locations(mangle_assignment(astree.body[-1]))  # type: ignore

    # Execute the AST
    globals: dict[str, Any] = {}
    exec(compile(astree, "<string>", "exec"), function_map, globals)

    # Get the result
    result = globals["_out"]
    return result


def convert_term_to_mlir(tree: IRTerm, argspec: str) -> str:
    """
    Convert a term to MLIR.
    """

    expr = convert_term_to_expr(tree)
    argnames = map(lambda x: x.strip(), argspec.split(","))
    argmap = {k: f"%arg_{k}" for k in argnames}
    source = MLIRGen(expr, argmap).generate()
    return source

Optimization Layer

Now we can start to write our own rewrite rules to apply over our expression tree.

The birewrite_subsume helper function is a generator that yields rewrite rules for the e-graph. It takes two terms and yields a rewrite rule that converts the first term to the second, making the first term unable to be matched against or extracted. We use this to unidirectionally convert generic Terms into specialized binary and unary operations.

def birewrite_subsume(a: Term, b: Term) -> Generator[RewriteOrRule, None, None]:
    yield rewrite(a, subsume=True).to(b)
    yield rewrite(b).to(a)

The basic simplification module implements fundamental mathematical rewrites that form the foundation of our term rewriting system. These rules are organized in the basic_math ruleset and include several key categories of transformations:

Term Translation Rules: These rules allow conversion between generic Terms and their specialized forms (Add, Mul, Div, Pow)
Identity Rules: Rules for handling mathematical identities like $x + 0 = x$ and $x \cdot 1 = x$
Associativity Rules: Rules that handle the associative properties of operations like $(x + y) + z = x + (y + z)$
Power Rules: Special handling for powers, including cases like $x^0 = 1$ and $x^1 = x$
Arithmetic Simplification: Rules that simplify common arithmetic patterns like $x + x = 2 \cdot x$

Each rule is implemented using egglog's rewrite system.

from mlir_egglog.term_ir import Term, Add, Mul, Div, Pow, PowConst, birewrite_subsume
from egglog import RewriteOrRule, ruleset, rewrite, i64, f64
from typing import Generator


@ruleset
def basic_math(
    x: Term, y: Term, z: Term, i: i64, f: f64
) -> Generator[RewriteOrRule, None, None]:
    # Allow us to translate Term into their specializations
    yield from birewrite_subsume(x + y, Add(x, y))
    yield from birewrite_subsume(x * y, Mul(x, y))
    yield from birewrite_subsume(x / y, Div(x, y))
    yield from birewrite_subsume(x**y, Pow(x, y))

    # x + 0 = x (integer case)
    yield rewrite(Add(x, Term.lit_i64(0))).to(x)
    # x + 0.0 = x (float case)
    yield rewrite(Add(x, Term.lit_f32(0.0))).to(x)
    # 0.0 + x = x (float case)
    yield rewrite(Add(Term.lit_f32(0.0), x)).to(x)

    # x * 1 = x
    yield rewrite(Mul(x, Term.lit_i64(1))).to(x)

    # x * 0 = 0
    yield rewrite(Mul(x, Term.lit_i64(0))).to(Term.lit_i64(0))

    # (x + y) + z = x + (y + z)
    yield rewrite(Add(x, Add(y, z))).to(Add(Add(x, y), z))

    # (x * y) * z = x * (y * z)
    yield rewrite(Mul(x, Mul(y, z))).to(Mul(Mul(x, y), z))

    # x + x = 2 * x
    yield rewrite(Add(x, x)).to(Mul(Term.lit_i64(2), x))

    # x * x = x^2
    yield rewrite(Mul(x, x)).to(Pow(x, Term.lit_i64(2)))

    # (x^y) * (x^z) = x^(y + z)
    yield rewrite(Pow(x, y) * Pow(x, z)).to(Pow(x, Add(y, z)))

    # x^i = x * x^(i - 1)
    yield rewrite(Pow(x, Term.lit_i64(i))).to(PowConst(x, i))

    # x^0 = 1
    yield rewrite(PowConst(x, 0)).to(Term.lit_f32(1.0))

    # x^1 = x
    yield rewrite(PowConst(x, 1)).to(x)

    # x^i = x * x^(i - 1)
    yield rewrite(PowConst(x, i)).to(Mul(x, PowConst(x, i - 1)), i > 1)

Similar to the basic simplification module, the trigonometric simplification module provides a comprehensive set of rules for simplifying expressions involving trigonometric and hyperbolic functions. The trig_simplify ruleset implements several important categories of transformations:

Fundamental Identities: Core trigonometric identities like $ \sin^2(x) + \cos^2(x) = 1 $
Double Angle Formulas: Rules for simplifying expressions like $ \sin(x + y) $ and $ \cos(x + y) $
Hyperbolic Identities: Similar rules for hyperbolic functions, including identities for $ \sinh $, $ \cosh $, and $ \tanh $

These rules are particularly important for optimizing numerical computations involving trigonometric functions, which are common in scientific computing and machine learning applications. The module carefully balances the tradeoff between expression simplification and computational efficiency, using the cost model defined in the Term IR to guide its decisions.

from mlir_egglog.term_ir import Sin, Cos, Sinh, Cosh, Tanh, Term, Pow, Add
from egglog import ruleset, i64, f64
from egglog import rewrite


@ruleset
def trig_simplify(x: Term, y: Term, z: Term, i: i64, fval: f64):
    # Fundamental trig identities
    # sin²(x) + cos²(x) = 1
    two = Term.lit_i64(2)
    yield rewrite(Add(Pow(Sin(x), two), Pow(Cos(x), two))).to(Term.lit_f32(1.0))

    # Double angle formulas
    yield rewrite(Sin(x + y)).to(Sin(x) * Cos(y) + Cos(x) * Sin(y))
    yield rewrite(Sin(x - y)).to(Sin(x) * Cos(y) - Cos(x) * Sin(y))
    yield rewrite(Cos(x + y)).to(Cos(x) * Cos(y) - Sin(x) * Sin(y))
    yield rewrite(Cos(x - y)).to(Cos(x) * Cos(y) + Sin(x) * Sin(y))

    # Hyperbolic identities
    yield rewrite(Sinh(x) * Cosh(y) + Cosh(y) * Sinh(x)).to(Sinh(x + y))
    yield rewrite(Cosh(x) * Cosh(y) + Sinh(x) * Sinh(y)).to(Cosh(x + y))
    yield rewrite((Tanh(x) + Tanh(y)) / (Term.lit_i64(1) + Tanh(x) * Tanh(y))).to(
        Tanh(x + y)
    )

Egglog Optimizer (`egglog_optimizer.py`)

The optimization engine ties together all the rewrite rules and provides the main interface for applying optimizations to Python functions. It consists of several key components:

Rule Composition: The ability to combine multiple rulesets either sequentially or in parallel
Expression Extraction: Logic for converting between the Python AST and the term representation
Optimization Pipeline: A structured approach to applying rules until reaching a fixed point
MLIR Generation: Final conversion of the optimized expression to MLIR code

The optimizer uses the e-graph data structure to efficiently explore equivalent expressions and find the most cost-effective implementation according to our cost model.

import inspect
from types import FunctionType

from egglog import EGraph, RewriteOrRule, Ruleset
from egglog.egraph import UnstableCombinedRuleset

from mlir_egglog.term_ir import Term, as_egraph
from mlir_egglog.python_to_ir import interpret
from mlir_egglog import builtin_functions as ns
from mlir_egglog.expr_model import Expr
from mlir_egglog.ir_to_mlir import convert_term_to_mlir

# Rewrite rules
from mlir_egglog.basic_simplify import basic_math
from mlir_egglog.trig_simplify import trig_simplify

OPTS: tuple[Ruleset | RewriteOrRule, ...] = (basic_math, trig_simplify)


def extract(ast: Expr, rules: tuple[RewriteOrRule | Ruleset, ...], debug=False) -> Term:
    root = as_egraph(ast)

    egraph = EGraph()
    egraph.let("root", root)

    # The user can compose rules as (rule1 | rule2) to apply them in parallel
    # or (rule1, rule2) to apply them sequentially
    for opt in rules:
        if isinstance(opt, Ruleset):
            egraph.run(opt.saturate())
        elif isinstance(opt, UnstableCombinedRuleset):
            egraph.run(opt.saturate())
        else:
            # For individual rules, create a temporary ruleset
            temp_ruleset = Ruleset("temp")
            temp_ruleset.append(opt)
            egraph.run(temp_ruleset.saturate())

    extracted = egraph.extract(root)

    # if debug:
    #     egraph.display()

    return extracted


def compile(
    fn: FunctionType, rewrites: tuple[RewriteOrRule | Ruleset, ...] = OPTS, debug=True
) -> str:
    # Convert np functions accordinging to the namespace map
    exprtree = interpret(fn, {"np": ns})
    extracted = extract(exprtree, rewrites, debug)

    # Get the argument spec
    argspec = inspect.signature(fn)
    params = ",".join(map(str, argspec.parameters))

    return convert_term_to_mlir(extracted, params)

These modules work together to provide a powerful system for optimizing mathematical expressions, particularly those involving trigonometric and transcendental functions. The system is extensible, allowing new rules to be added easily, and provides a solid foundation for building more specialized optimizations on top.

The egglog optimizer supports two ways to compose rewrite rules: parallel and sequential composition. When rules are combined using the | operator (parallel composition), they are applied simultaneously in the same iteration of the e-graph saturation process. This allows multiple transformations to be explored concurrently. In contrast, when rules are combined using a tuple or sequence (sequential composition), they are applied one after another, with each rule set running to saturation before moving to the next. This sequential approach can be useful when certain transformations should only be attempted after others have completed.

# Example 1: Parallel Composition
# Both rulesets are applied simultaneously in each iteration
parallel_rules = simplify_adds | simplify_muls
egraph = EGraph()
egraph.run(parallel_rules.saturate())

# Example 2: Sequential Composition
# simplify_adds runs to completion before simplify_muls starts
sequential_rules = (simplify_adds, simplify_muls)
egraph = EGraph()
for ruleset in sequential_rules:
    egraph.run(ruleset.saturate())

MLIR Generation (`mlir_gen.py`)

The MLIR code generator is responsible for transforming our optimized expression trees into executable MLIR code. The generator follows a systematic approach to produce vectorized kernels that can efficiently process N-dimensional arrays. Let's examine the key components and design principles:

The generator produces a function that follows this template:

func.func @kernel_worker(
    %arg0: memref<?xf32>,
    %arg1: memref<?xf32>
) {
    // Kernel body
}

The generated kernel accepts two memref arguments - an input and output buffer - and processes them element-wise using affine loops. This design allows for efficient vectorized operations on arrays of any dimension.

func.func @kernel_worker(
    %arg0: memref<?xf32>,
    %arg1: memref<?xf32>
) attributes {llvm.emit_c_interface} {
    %c0 = arith.constant 0 : index
    
    // Get dimension of input array
    %dim = memref.dim %arg0, %c0 : memref<?xf32>
    
    // Process each element in a flattened manner
    affine.for %idx = %c0 to %dim {
        // Kernel body
    }
    return
}

Expression Translation

The MLIRGen class implements a multi-pass translation strategy that begins with subexpression expansion, where the generator unfolds the expression tree into a complete set of subexpressions using the unfold method. This process ensures that common subexpressions are identified and can be reused. Next, the generator employs topological ordering, sorting subexpressions by complexity, using string length as a proxy to ensure that simpler expressions are evaluated before more complex ones that might depend on them. Finally, the code generation pipeline is executed, which first loads input variables from the memref, generates intermediate computations for subexpressions, and stores the final result back to the output memref.

The generator employs a smart caching mechanism to avoid redundant computations:

def walk(self, expr: ir.Expr):
    if expr in self.cache:
        return
    def lookup(e):
        return self.cache.get(e) or as_source(e, self.vars, lookup)
    self.cache[expr] = as_source(expr, self.vars, lookup)

This caching strategy ensures that each subexpression is computed exactly once, common subexpressions are reused through MLIR's SSA (Static Single Assignment) form, and the generated code maintains optimal efficiency.

MLIR Dialect Usage

Our generator then walks over the expression tree and maps our high-level expressions to appropriate MLIR dialects:

Arithmetic operations use the arith dialect (e.g., arith.addf, arith.mulf)
Mathematical functions use the math dialect (e.g., math.sin, math.exp)
Memory operations use the memref dialect for array access
Loop structures use the affine dialect for optimized iteration

For example, a Python expression like sin(x) + cos(y) would be translated into:

%sin = math.sin %arg_x : f32
%cos = math.cos %arg_y : f32
%result = arith.addf %sin, %cos : f32

The generator handles type conversions automatically, standardizing floating-point operations to f32 and using i32 or i64 for integer operations as appropriate. When needed, explicit type casts are generated, such as arith.sitofp for converting integers to floating-point values. This type system ensures type safety while maintaining compatibility with MLIR's strong typing requirements.

from textwrap import indent
from typing import Callable
from mlir_egglog import expr_model as ir

KERNEL_NAME = "kernel_worker"

# Numpy vectorized kernel that supports N-dimensional arrays
kernel_prologue = f"""
func.func @{KERNEL_NAME}(
    %arg0: memref<?xf32>,
    %arg1: memref<?xf32>
) attributes  \{\{
    %c0 = arith.constant 0 : index
    
    // Get dimension of input array
    %dim = memref.dim %arg0, %c0 : memref<?xf32>
    
    // Process each element in a flattened manner
    affine.for %idx = %c0 to %dim \{\{
"""

kernel_epilogue = """
    }
    return
}
"""


class MLIRGen:
    """
    Generate textual MLIR from a symbolic expression.
    """

    root: ir.Expr
    cache: dict[ir.Expr, str]
    subexprs: dict[str, str]
    vars: list[str]  # local variables

    def __init__(self, root: ir.Expr, argmap: dict[str, str]):
        # Use the keys from argmap as the variable names
        self.root = root
        self.cache = {}
        self.vars = list(argmap.keys())
        self.subexprs = {}

    def generate(self):
        """
        Generate MLIR code for the root expression.
        """
        subexprs = list(self.unfold(self.root))
        subexprs.sort(key=lambda x: len(str(x)))

        buf = []
        # First load input arguments from memref
        for var in self.vars:
            buf.append(f"%arg_{var} = affine.load %arg0[%idx] : memref<?xf32>")

        for i, subex in enumerate(subexprs):
            # Skip if this is just a variable reference
            if isinstance(subex, ir.Symbol) and subex.name in self.vars:
                continue

            # Recurse and cache the subexpression
            self.walk(subex)
            orig = self.cache[subex]

            # Generate a unique name for the subexpression
            k = f"%v{i}"
            self.cache[subex] = k
            self.subexprs[k] = orig

            # Append the subexpression to the buffer
            buf.append(f"{k} = {orig}")

        self.walk(self.root)
        res = self.cache[self.root]

        # Handle the output
        buf.append(f"affine.store {res}, %arg1[%idx] : memref<?xf32>")

        # Format the kernel body
        kernel_body = indent("\n".join(buf), "    " * 2)
        return kernel_prologue + kernel_body + kernel_epilogue

    def unfold(self, expr: ir.Expr):
        """
        Unfold an expression into a set of subexpressions.
        """
        visited = set()
        all_subexprs = set()
        to_visit = [expr]
        while to_visit:
            current = to_visit.pop()
            all_subexprs.add(current)
            if current in visited:
                continue
            visited.add(current)
            to_visit.extend(get_children(current))

        return all_subexprs

    def walk(self, expr: ir.Expr):
        """
        Walk an expression recursively and generate MLIR code for subexpressions,
        caching the intermediate expressions in a lookup table.
        """
        if expr in self.cache:
            return

        def lookup(e):
            return self.cache.get(e) or as_source(e, self.vars, lookup)

        self.cache[expr] = as_source(expr, self.vars, lookup)


def get_children(expr: ir.Expr):
    """Get child expressions for an AST node."""
    match expr:
        case ir.BinaryOp():
            return {expr.lhs, expr.rhs}
        case ir.UnaryOp():
            return {expr.operand}
        case ir.FloatLiteral() | ir.IntLiteral() | ir.Symbol():
            return set()
        case _:
            raise NotImplementedError(f"Unsupported expression type: {type(expr)}")


def as_source(
    expr: ir.Expr, vars: list[str], lookup_fn: Callable[[ir.Expr], str]
) -> str:
    """
    Convert expressions to MLIR source code using arith and math dialects.
    """
    match expr:
        # Literals and Symbols
        case ir.FloatLiteral(fval=val):
            return f"arith.constant {val:e} : f32"
        case ir.IntLiteral(ival=val):
            return f"arith.constant {val} : i32"
        case ir.Symbol(name=name) if name in vars:
            return f"%arg_{name}"
        case ir.Symbol(name=name):
            return f"%{name}"

        # Binary Operations
        case ir.Add(lhs=lhs, rhs=rhs):
            return f"arith.addf {lookup_fn(lhs)}, {lookup_fn(rhs)} : f32"
        case ir.Mul(lhs=lhs, rhs=rhs):
            return f"arith.mulf {lookup_fn(lhs)}, {lookup_fn(rhs)} : f32"
        case ir.Div(lhs=lhs, rhs=rhs):
            return f"arith.divf {lookup_fn(lhs)}, {lookup_fn(rhs)} : f32"
        case ir.Maximum(lhs=lhs, rhs=rhs):
            return f"arith.maximumf {lookup_fn(lhs)}, {lookup_fn(rhs)} : f32"

        # Unary Math Operations
        case (
            ir.Sin()
            | ir.Cos()
            | ir.Log()
            | ir.Sqrt()
            | ir.Exp()
            | ir.Sinh()
            | ir.Cosh()
            | ir.Tanh()
        ) as op:
            op_name = type(op).__name__.lower()
            return f"math.{op_name} {lookup_fn(op.operand)} : f32"
        case ir.Neg(operand=op):
            return f"arith.negf {lookup_fn(op)} : f32"

        # Type Casting
        case ir.CastF32(operand=op):
            return f"arith.sitofp {lookup_fn(op)} : i64 to f32"
        case ir.CastI64(operand=op):
            return f"arith.fptosi {lookup_fn(op)} : f32 to i64"

        case _:
            raise NotImplementedError(f"Unsupported expression type: {type(expr)}")

MLIR Backend (`mlir_backend.py`)

The MLIR backend to our compiler is responsible for transforming our high-level MLIR code through various lowering stages until it reaches LLVM IR and finally executable code. Let's walk through the key components and design principles:

The backend supports two primary compilation targets:

class Target(enum.Enum):
    OPENMP = "openmp"      # Parallel execution using OpenMP
    BASIC_LOOPS = "loops"  # Sequential execution with basic loops

This allows the compiler to generate either parallel code using OpenMP for multi-threaded execution or simpler sequential code depending on the application's needs.

The compilation process is organized into several distinct phases, each applying specific MLIR optimization passes:

Common Initial Transformations:

COMMON_INITIAL_OPTIONS = (
    "--debugify-level=locations",
    "--inline",
    "-affine-loop-normalize",
    "-affine-parallelize",
    "-affine-super-vectorize",
    "--affine-scalrep",
    "-lower-affine",
    "-convert-vector-to-scf",
    "-convert-linalg-to-loops",
)

These passes handle function inlining, loop normalization, vectorization, and initial dialect conversions.

Target-Specific Lowering:

OpenMP Path: Converts structured control flow to OpenMP operations and then to LLVM

OPENMP_OPTIONS = (
    "-convert-scf-to-openmp",
    "-convert-openmp-to-llvm",
    "-convert-vector-to-llvm",
    "-convert-math-to-llvm",
    # ... additional lowering passes
)

Basic Loops Path: Direct conversion to sequential LLVM IR

BASIC_LOOPS_OPTIONS = (
    "-convert-scf-to-cf",
    "-convert-vector-to-llvm",
    "-convert-math-to-llvm",
    # ... additional lowering passes
)

Final LLVM IR Generation:

MLIR_TRANSLATE_OPTIONS = (
    "--mlir-print-local-scope",
    "--mlir-to-llvmir",
    "--verify-diagnostics",
)

The MLIRCompiler class orchestrates the entire compilation process through three main stages:

MLIR to LLVM Dialect (to_llvm_dialect):
- Converts high-level MLIR operations to the LLVM dialect
- Applies target-specific optimizations (OpenMP or basic loops)
- Handles memory layout and type conversions
LLVM Dialect to LLVM IR (mlir_translate_to_llvm_ir):
- Translates the LLVM dialect representation to textual LLVM IR
- Preserves debug information and verifies the generated code
LLVM IR to Bitcode (llvm_ir_to_bitcode):
- Converts textual LLVM IR to binary LLVM bitcode
- Prepares the code for final execution

The backend uses temporary files for intermediate representations and provides debugging capabilities through the debug flag:

def _run_shell(self, cmd, in_mode, out_mode, src):
    with (
        NamedTemporaryFile(mode=f"w{in_mode}") as src_file,
        NamedTemporaryFile(mode=f"r{out_mode}") as out_file,
    ):
        # Execute compilation command and handle I/O

Then the compiler spit out the LLVM IR and we can use the llvmlite library to load it and execute it inside of the Python process, allowing us to dynamically load the compiled machine code.

LLVM Runtime (`llvm_runtime.py`)

The LLVM runtime provides the final layer of our compilation pipeline, handling the dynamic loading and execution of compiled LLVM code within Python. This component uses llvmlite to interface with LLVM and manages the Just-In-Time (JIT) compilation process.

LLVM Initialization

The runtime begins with a cached initialization of LLVM components:

@cache
def init_llvm():
    llvm.initialize()
    llvm.initialize_all_targets()
    llvm.initialize_all_asmprinters()

This initialization is cached to ensure it occurs only once per Python session, which sets up the core LLVM functionality, all available target architectures, and the assembly printers necessary for code generation.

The runtime creates an LLVM execution engine that manages the JIT compilation process:

def create_execution_engine():
    target = llvm.Target.from_default_triple()
    target_machine = target.create_target_machine()
    backing_mod = llvm.parse_assembly("")
    engine = llvm.create_mcjit_compiler(backing_mod, target_machine)
    return engine

This setup determines the host machine's target architecture, creates a target machine instance for code generation, initializes an empty LLVM module as a backing store, and creates an MCJIT compiler instance for optimized code execution.

The runtime provides two levels of module compilation:

Direct Module Compilation:

def compile_mod(engine, mod):
    mod.verify()                     # Verify module correctness
    engine.add_module(mod)           # Add to execution engine
    engine.finalize_object()         # Finalize compilation
    engine.run_static_constructors() # Initialize static data
    return mod

IR String Compilation:

def compile_ir(engine, llvm_ir):
    mod = llvm.parse_assembly(llvm_ir)  # Parse IR text
    return compile_mod(engine, mod)      # Compile module

This runtime layer bridges the gap between LLVM's low-level compilation infrastructure and Python's high-level execution environment, allowing our compiled kernels to run efficiently within the Python process.

import llvmlite.binding as llvm
import llvmlite
from functools import cache


@cache
def init_llvm():
    print(llvmlite.__version__)
    llvm.initialize()
    llvm.initialize_all_targets()
    llvm.initialize_all_asmprinters()


def compile_mod(engine, mod):
    mod.verify()
    engine.add_module(mod)
    engine.finalize_object()
    engine.run_static_constructors()
    return mod


def create_execution_engine():
    target = llvm.Target.from_default_triple()
    target_machine = target.create_target_machine()
    backing_mod = llvm.parse_assembly("")
    engine = llvm.create_mcjit_compiler(backing_mod, target_machine)
    return engine


def compile_ir(engine, llvm_ir):
    mod = llvm.parse_assembly(llvm_ir)
    return compile_mod(engine, mod)

JIT Engine (`jit_engine.py`)

The jit_engine.py module is the orchestrator of our compiler pipeline, tying together all the components into a seamless compilation process. It manages the entire lifecycle from Python function to executable machine code, handling optimization, code generation, and runtime execution.

The JITEngine class provides three main levels of compilation:

Frontend Compilation (run_frontend):
```
def run_frontend(
    self,
    fn: FunctionType,
    rewrites: tuple[RewriteOrRule | Ruleset, ...] | None = None,
) -> str:
```
The run_frontend method takes a Python function along with optional rewrite rules, applies the egglog optimizer to perform term rewriting, and generates optimized MLIR code.

Backend Compilation (run_backend):

def run_backend(self, mlir_src: str) -> bytes:
    mlir_compiler = MLIRCompiler(debug=False)
    mlir_omp = mlir_compiler.to_llvm_dialect(mlir_src)
    llvm_ir = mlir_compiler.mlir_translate_to_llvm_ir(mlir_omp)

The run_backend method converts MLIR to the LLVM dialect, translates it to LLVM IR, handles platform-specific optimizations, and ultimately returns the address of the compiled function.

Full JIT Compilation (jit_compile):

def jit_compile(
    self,
    fn: FunctionType,
    rewrites: tuple[RewriteOrRule | Ruleset, ...] | None = None,
) -> bytes:
    mlir = self.run_frontend(fn, rewrites)
    address = self.run_backend(mlir)
    return address

The jit_compile method combines both frontend and backend compilation, providing a single entry point for the entire compilation process.

In order to use the OpenMP rutnime we need to load the system-specific OpenMP library into the Python process. Which we can do through the ctypes library once we know the corect path of the shared library.

def find_omp_path():
    if sys.platform.startswith("linux"):
        omppath = ctypes.util.find_library("libgomp.so")
    elif sys.platform.startswith("darwin"):
        omppath = ctypes.util.find_library("iomp5")
    else:
        raise RuntimeError(f"Unsupported platform: {sys.platform}")
    return omppath

The engine handles several critical LLVM-related tasks:

Initialization:

def __init__(self):
    init_llvm()
    omppath = find_omp_path()
    ctypes.CDLL(omppath, mode=os.RTLD_NOW)
    self.ee = create_execution_engine()

Initializes LLVM infrastructure
Loads OpenMP runtime
Creates the execution engine

The class serves as the glue that binds our compiler's components together, providing an interface between Python code and optimized machine code execution. It handles the complexity of multi-stage compilation, platform-specific requirements, and runtime optimization.

from __future__ import annotations

import ctypes
import ctypes.util
import os
import sys
from types import FunctionType
from egglog import RewriteOrRule, Ruleset

import llvmlite.binding as llvm

from mlir_egglog.llvm_runtime import (
    create_execution_engine,
    init_llvm,
    compile_mod,
)
from mlir_egglog.mlir_gen import KERNEL_NAME
from mlir_egglog.mlir_backend import MLIRCompiler, Target
from mlir_egglog.egglog_optimizer import compile, OPTS


def find_omp_path():
    if sys.platform.startswith("linux"):
        omppath = ctypes.util.find_library("libgomp.so")
    elif sys.platform.startswith("darwin"):
        omppath = ctypes.util.find_library("iomp5")
    else:
        raise RuntimeError(f"Unsupported platform: {sys.platform}")
    return omppath


class JITEngine:
    def __init__(self):
        init_llvm()
        omppath = find_omp_path()
        ctypes.CDLL(omppath, mode=os.RTLD_NOW)

        self.ee = create_execution_engine()

    def run_frontend(
        self,
        fn: FunctionType,
        rewrites: tuple[RewriteOrRule | Ruleset, ...] | None = None,
    ) -> str:
        actual_rewrites = rewrites if rewrites is not None else OPTS
        return compile(fn, rewrites=actual_rewrites, debug=False)

    def run_backend(self, mlir_src: str) -> bytes:
        mlir_compiler = MLIRCompiler(debug=False)

        mlir_omp = mlir_compiler.to_llvm_dialect(mlir_src, target=Target.BASIC_LOOPS)
        llvm_ir = mlir_compiler.mlir_translate_to_llvm_ir(mlir_omp)

        print(llvm_ir)
        print("Parsing LLVM assembly.")

        try:
            # Clean up the LLVM IR by ensuring proper line endings and formatting
            llvm_ir = llvm_ir.strip()

            # Clean up problematic attribute strings (hack for divergence in modern LLVM IR syntax with old llvmlite)
            llvm_ir = llvm_ir.replace("captures(none)", " ")
            llvm_ir = llvm_ir.replace("memory(argmem: readwrite)", "")
            llvm_ir = llvm_ir.replace("memory(none)", "")
            llvm_ir += "\n"

            mod = llvm.parse_assembly(llvm_ir)
            mod = compile_mod(self.ee, mod)

            # Resolve the function address
            func_name = f"_mlir_ciface_{KERNEL_NAME}"
            address = self.ee.get_function_address(func_name)

            assert address, "Function must be compiled successfully."
            return address
        except Exception as e:
            print(f"Error during LLVM IR parsing/compilation: {str(e)}")
            print("LLVM IR that failed to parse:")
            print(llvm_ir)
            raise

    def jit_compile(
        self,
        fn: FunctionType,
        rewrites: tuple[RewriteOrRule | Ruleset, ...] | None = None,
    ) -> bytes:
        mlir = self.run_frontend(fn, rewrites)
        address = self.run_backend(mlir)
        return address

Dispatcher (`dispatcher.py`)

The Dispatcher serves as the user-facing interface of our compiler, providing a decorator to transform regular Python functions into optimized vectorized kernels. It handles the compilation process and manages the execution of compiled functions.

The Dispatcher class manages the lifecycle of compiled functions:

class Dispatcher:
    _compiled_func: bytes | None      # Compiled function address
    _compiler: JITEngine | None       # JIT compilation engine
    py_func: types.FunctionType       # Original Python function
    rewrites: tuple[RewriteOrRule, ...] | None  # Optimization rules

The compilation process is handled through a simple interface by invoking the compiler's jit_compile method.

def compile(self):
    self._compiler = JITEngine()
    binary = self._compiler.jit_compile(self.py_func, self.rewrites)
    self._compiled_func = binary
    return binary

This method creates a new JIT engine instance, compiles the Python function with the specified rewrites, and stores the compiled binary for future execution. The dispatcher implements a cached calling mechanism to avoid recompiling the function on subsequent calls. When we call our compiled function with a numpy array the dispatcher will retreives the underlying input arrays and allocates a new empty output array of the same shape. Then it will convert the numpy array to a memref descriptor and pass it to the compiled function.

def __call__(self, *args, **kwargs):
    # Get the input array and its shape
    input_array = args[0]
    original_shape = input_array.shape

    # Flatten the input array
    flattened_input = input_array.flatten()
    flattened_output = np.empty_like(flattened_input)

    # Convert to memrefs
    memrefs = [
        as_memref_descriptor(flattened_input, ctypes.c_float),
        as_memref_descriptor(flattened_output, ctypes.c_float)
    ]

The dispatcher then lookups the function pointer from the MCJIT compiled memory and calls it with the memref descriptors as arguments.

# Create function prototype for ctypes
prototype = ctypes.CFUNCTYPE(None, *[ctypes.POINTER(type(x)) for x in memrefs])

# Execute compiled function
cfunc = prototype(self._compiled_func)
cfunc(*[ctypes.byref(x) for x in memrefs])

Now to use our compiler to compile a function we can use the @kernel decorator on our own functions.

import llvmlite
import numpy as np
llvmlite.opaque_pointers_enabled = True

from mlir_egglog import kernel

@kernel("float32(float32)")
def fn(a):
    return np.sin(a) * np.cos(a) + np.cos(a) * np.sin(a)

out = fn(np.array([1.0], dtype=np.float32))
print(out)

Now this is a very simple example compiler, the symbolic interpretation approach is fundamentaly limited because it can only handle flat functions with no control flow operations and requires us to manually specify the argument types, and only supports a limited set of operations. But it's a good starting point for seeing something that works end to end to use MLIR and e-graphs for optimization.

External Resources

MLIR Part 5 - Neural Networks

Sat, 15 Mar 2025 00:00:00 +0000

Neural Networks

In our journey through MLIR and modern compiler technology, we've explored how to build efficient systems for numerical computation. Now, we turn our attention to one of the most important applications of these systems: deep learning. Before diving into how MLIR can optimize neural network computations, it's crucial to understand how neural networks work from first principles.

This section presents a ground-up implementation of a neural network library in pure Python. While this implementation prioritizes clarity over performance, it serves as an excellent foundation for understanding the optimizations that MLIR can provide. By building everything from scratch, we'll gain deep insights into:

The mathematical foundations of neural networks
How automatic differentiation enables learning
The computational patterns that make neural networks ideal for hardware acceleration
Why frameworks like PyTorch and TensorFlow are structured the way they are

In later sections, we'll transform this simple implementation into highly optimized CUDA kernels using MLIR. This progression from a clear but naive implementation to a high-performance compiled version will demonstrate the power of modern compiler technology in deep learning.

The complete source code for this section is available in a separate repository for reference.

Neural networks are everywhere these days, I won't explain too much about why they're useful but if you've used any of the popular libraries like Jax, PyTorch, or TensorFlow, you know they make it easy to build and train complex models. Understanding how these frameworks work under the hood is invaluable. In this section, we'll build a very minimal neural network library from first principles, providing insight into the core mechanisms that power modern deep learning.

Gradients and Optimization

At the heart of neural network training lies the concept of gradients. Think of a gradient as a compass that points in the direction of steepest increase for a function. For a function with multiple inputs $f(x_1, x_2, ..., x_n)$, the gradient $\nabla f$ is a vector containing the rate of change in each direction:

$$\nabla f = \begin{bmatrix}
\frac{\partial f}{\partial x_1} \
\frac{\partial f}{\partial x_2} \
\vdots \
\frac{\partial f}{\partial x_n}
\end{bmatrix}$$

Each component $\frac{\partial f}{\partial x_i}$ tells us how much the function would change if we slightly adjusted that input while keeping all others constant. This information is crucial for training neural networks.

In neural network training, we want to minimize a loss function $L(\theta)$ that measures how well our model performs. The parameters $\theta$ include all the weights and biases in the network - often thousands or millions of values. The gradient $\nabla L(\theta)$ tells us how to adjust each parameter to reduce the loss:

$$
\theta_{t+1} = \theta_t - \alpha \nabla L(\theta_t)
$$

This is gradient descent in action: we repeatedly take small steps (controlled by the learning rate $\alpha$) in the direction opposite to the gradient, gradually finding parameter values that minimize the loss.

Computing these gradients efficiently is crucial. While we could use numerical approximations:

$$
\frac{\partial f}{\partial x_i} \approx \frac{f(x + h\mathbf{e}_i) - f(x)}{h}
$$

where $h$ is a small number and $\mathbf{e}_i$ is the unit vector in direction $i$, this approach is both slow and numerically unstable. Instead, we use automatic differentiation, which computes exact gradients by systematically applying the chain rule through a computation graph.

The chain rule states that for composite functions, derivatives multiply:

$$
\frac{d}{dx}(f(g(x))) = f'(g(x)) \cdot g'(x)
$$

In higher dimensions, this becomes:

$$
\frac{\partial f}{\partial x_i} = \sum_j \frac{\partial f}{\partial y_j} \frac{\partial y_j}{\partial x_i}
$$

where $y_j$ are intermediate values in our computation. This is the foundation of backpropagation, which we'll implement in our neural network library.

Neural Network Theory

A neural network is fundamentally a function that learns to map inputs to outputs through a series of adjustable transformations. The basic building block is the artificial neuron, which mimics how biological neurons process information:

It receives multiple input signals ($x_1, x_2, ..., x_n$)
Each input is weighted by a strength parameter ($w_1, w_2, ..., w_n$)
The weighted inputs are summed together with a bias term ($b$)
The result is passed through an activation function ($\sigma$)

Mathematically, this process is described as:

$$
z = \sum_{i=1}^{n} w_i x_i + b
$$

$$
a = \sigma(z)
$$

where $z$ is the weighted sum (often called the pre-activation), and $a$ is the neuron's output (or activation).

Multiple neurons are organized into layers, and layers are stacked to form a network. In a fully-connected feed-forward neural network, each neuron connects to every neuron in the next layer. For a layer $l$, we can write this compactly in matrix form:

$$
\mathbf{Z}^{[l]} = \mathbf{W}^{[l]} \mathbf{A}^{[l-1]} + \mathbf{b}^{[l]}
$$
$$
\mathbf{A}^{[l]} = \sigma(\mathbf{Z}^{[l]})
$$

where:

$\mathbf{W}^{[l]}$ is the weight matrix for layer $l$
$\mathbf{A}^{[l-1]}$ contains the activations from the previous layer
$\mathbf{b}^{[l]}$ is the bias vector
$\sigma$ applies the activation function to each element

The choice of activation function is crucial as it introduces non-linearity that allows the network to learn complex patterns. Without non-linearity, a neural network would behave like a linear model, regardless of the number of layers it has. This is because the composition of linear functions is still a linear function. Non-linear activation functions enable the network to approximate complex functions and capture intricate relationships in the data. They allow the model to learn from errors and adjust weights in a way that can represent a wider variety of functions. Common choices of activation functions are:

ReLU (Rectified Linear Unit): $\sigma(z) = \max(0, z)$
- Simple and computationally efficient
- Helps prevent vanishing gradients
- Most widely used in modern networks
Sigmoid: $\sigma(z) = \frac{1}{1 + e^{-z}}$
- Squashes values to range [0,1]
- Historically popular but prone to vanishing gradients
- Still useful for binary classification
Tanh: $\sigma(z) = \tanh(z) = \frac{e^z - e^{-z}}{e^z + e^{-z}}$
- Similar to sigmoid but ranges [-1,1]
- Often performs better than sigmoid
- Still can suffer from vanishing gradients
SwiGLU: $\sigma(z) = \text{ReLU}(zW_1 + b_1)V + b_2$
- Introduced in the GLU (Gated Linear Unit) family
- Often used in the Transformer architecture
- Provides a balance between non-linearity and computational efficiency

SwiGLU has become the default choice in many modern networks. I won't go into the details of the GLU family here, but if you're interested in learning more, I recommend checking out the GLU paper. For our purposes, we'll use ReLU as our activation function because it's simpler.

Automatic Differentiation

Automatic differentiation is the engine that powers neural network learning. Unlike numerical differentiation (which approximates derivatives) or symbolic differentiation (which manipulates mathematical expressions), automatic differentiation computes exact derivatives by tracking operations in a computation graph.

Our implementation centers on the Value class, which wraps a scalar value and records the operations performed on it:

class Value:
    def __init__(self, data, _children=(), _op="", label=""):
        self.data = data
        self.grad = 0.0
        self.label = label
        self._backward = lambda: None
        self._prev = set(_children)
        self._op = _op

Each operation (like addition or multiplication) creates a new Value and defines how gradients should flow backward. For example, here's how addition works:

def __add__(self, other):
    other = other if isinstance(other, Value) else Value(other)
    out = Value(self.data + other.data, (self, other), "+")

    def _backward():
        # The gradient flows equally to both inputs
        self.grad += out.grad
        other.grad += out.grad

    out._backward = _backward
    return out

For multiplication, the gradient follows the product rule - each input's gradient is scaled by the other input's value:

def __mul__(self, other):
    other = other if isinstance(other, Value) else Value(other)
    out = Value(self.data * other.data, (self, other), "*")

    def _backward():
        # Each input's gradient is scaled by the other's value
        self.grad += other.data * out.grad
        other.grad += self.data * out.grad

    out._backward = _backward
    return out

The backward pass is initiated by calling backward(), which:

Performs a topological sort of the computation graph
Sets the gradient of the output to 1.0
Propagates gradients backward through the graph

def backward(self):
    # Sort nodes in topological order
    topo = []
    visited = set()

    def topo_sort(v):
        if v not in visited:
            visited.add(v)
            for child in v._prev:
                topo_sort(child)
            topo.append(v)

    topo_sort(self)

    # Backpropagate gradients
    self.grad = 1
    for v in reversed(topo):
        v._backward()

To see this in action, let's create a simple computation graph for the expression relu(a * b + c):

# Create input values
a = Value(2.0, label="a")
b = Value(-3.0, label="b")
c = Value(10.0, label="c")

# Build computation graph
d = a * b
d.label = "d"
e = d + c
e.label = "e"
f = e.relu()
f.label = "f"

Now we can compute the gradients of the output with respect to each input:

print("Gradients after backward pass:")
print(f"a.grad = {a.grad}")
print(f"b.grad = {b.grad}")
print(f"c.grad = {c.grad}")
print(f"d.grad = {d.grad}")
print(f"e.grad = {e.grad}")
print(f"f.grad = {f.grad}")

The resulting computation graph is shown in Figure 1. Each node represents a value, and edges show how values are combined through operations. When we call f.backward(), gradients flow backward through this graph, allowing us to compute how each input affects the final output.

Figure 1: Visualization of a computation graph showing how operations are connected and gradients flow backward.

Backpropagation

Backpropagation is the algorithm that enables neural networks to learn from data by efficiently computing gradients of the loss function with respect to the network parameters. It applies the chain rule of calculus to propagate error gradients backward through the network, from the output layer to the input layer.

The process begins with a forward pass, where input data is fed through the network to produce predictions. The loss function $L$ quantifies the difference between these predictions and the true target values. For a mean squared error loss, this is:

$$
L = \frac{1}{n} \sum_{i=1}^{n} (y_i - \hat{y}_i)^2
$$

where $y_i$ are the true values and $\hat{y}_i$ are the predicted values.

The goal of training is to minimize this loss by adjusting the network parameters (weights and biases). This requires computing the gradient of the loss with respect to each parameter:

$$
\frac{\partial L}{\partial w_{ij}^{[l]}}
\text{ and }
\frac{\partial L}{\partial b_i^{[l]}}
$$

for each weight $w_{ij}^{[l]}$ and bias $b_i^{[l]}$ in layer $l$.

Backpropagation computes these gradients efficiently by working backward through the network. For the output layer $L$, we first compute the error term:

$$
\delta^{[L]} = \nabla_a L \odot \sigma'(z^{[L]})
$$

where $\nabla_a L$ is the gradient of the loss with respect to the output activations, $\sigma'(z^{[L]})$ is the derivative of the activation function evaluated at the pre-activation values $z^{[L]}$, and $\odot$ denotes element-wise multiplication.

For hidden layers, the error term is computed recursively:

$$
\delta^{[l]} = ((w^{[l+1]})^T \delta^{[l+1]}) \odot \sigma'(z^{[l]})
$$

where $(w^{[l+1]})^T$ is the transpose of the weight matrix for layer $l+1$.

Finally, the gradients of the loss with respect to the parameters are:

$$
\frac{\partial L}{\partial w_{ij}^{[l]}} = a_j^{[l-1]} \delta_i^{[l]}
$$

$$
\frac{\partial L}{\partial b_i^{[l]}} = \delta_i^{[l]}
$$

where $a_j^{[l-1]}$ is the activation of neuron $j$ in layer $l-1$.

In our implementation, these calculations are handled automatically by the Value class and its operations. When we call loss.backward(), the gradients are computed and stored in the grad attribute of each parameter.

Building Neural Network Components

With our automatic differentiation engine in place, we can build neural network components. The Module class serves as the base for all neural network modules:

class Module:
    """Base class for all neural network modules."""

    def zero_grad(self):
        """Sets gradients of all parameters to zero."""
        for p in self.parameters():
            p.grad = 0

    def parameters(self):
        """Returns a list of all parameters in the module."""
        return []

The Neuron class implements a single neuron that computes a weighted sum of inputs plus a bias, optionally followed by a non-linear activation function:

class Neuron(Module):
    """A single neuron with multiple inputs and one output."""

    def __init__(self, nin, nonlin=True):
        self.w = [Value(random.uniform(-1, 1)) for _ in range(nin)]
        self.b = Value(0)
        self.nonlin = nonlin

    def __call__(self, x):
        act = sum((wi * xi for wi, xi in zip(self.w, x)), self.b)
        return act.relu() if self.nonlin else act

    def parameters(self):
        return self.w + [self.b]

The Layer class groups neurons together to process inputs in parallel:

class Layer(Module):
    """A layer of neurons, where each neuron has the same number of inputs."""

    def __init__(self, nin, nout, **kwargs):
        self.neurons = [Neuron(nin, **kwargs) for _ in range(nout)]

    def __call__(self, x):
        out = [n(x) for n in self.neurons]
        return out[0] if len(out) == 1 else out

    def parameters(self):
        return [p for n in self.neurons for p in n.parameters()]

Finally, the MLP (Multi-Layer Perceptron) class combines layers into a complete network:

class MLP(Module):
    """Multi-layer perceptron (fully connected feed-forward neural network)."""

    def __init__(self, nin, nouts):
        sz = [nin] + nouts
        self.layers = [
            Layer(sz[i], sz[i + 1], nonlin=i != len(nouts) - 1)
            for i in range(len(nouts))
        ]

    def __call__(self, x):
        for layer in self.layers:
            x = layer(x)
        return x

    def parameters(self):
        return [p for layer in self.layers for p in layer.parameters()]

This modular design makes it easy to create networks of any size. For example, a small network for binary classification might look like:

# Create a network with:
# - 2 input features
# - 8 neurons in first hidden layer
# - 8 neurons in second hidden layer
# - 1 output neuron
model = MLP(nin=2, nouts=[8, 8, 1])

The architecture is visualized in Figure 2, showing how neurons are organized into layers and layers are connected to form the complete network.

Figure 2: Visualization of our neural network architecture showing multiple layers of neurons.

We can create deeper networks by adding more layers, as shown in Figure 3. Each additional layer allows the network to learn more complex features. Early layers typically learn simple patterns (like edges in images), while deeper layers combine these to recognize more complex patterns (like objects or concepts).

Figure 3: A deeper neural network with multiple hidden layers, showing how layers can be stacked to increase model capacity.

Optimization and Training

To train our neural network, we need an optimizer that updates parameters based on gradients. Our SGD (Stochastic Gradient Descent) optimizer is remarkably simple:

class SGD:
    """
    Stochastic Gradient Descent optimizer.
    """

    def __init__(self, parameters, lr=0.01):
        self.parameters = parameters
        self.lr = lr

    def zero_grad(self):
        """Set all parameter gradients to zero."""
        for p in self.parameters:
            p.grad = 0

    def step(self):
        """
        Updates each parameter as: p = p - lr * p.grad
        """
        for p in self.parameters:
            p.data -= self.lr * p.grad

The optimizer stores references to model parameters, provides a method to zero gradients before each forward pass, and updates parameters using the gradient descent rule:

$$
\theta_{t+1} = \theta_t - \alpha \nabla_\theta L(\theta_t)
$$

where $\theta$ represents the parameters, $\alpha$ is the learning rate, and $\nabla_\theta L(\theta_t)$ is the gradient of the loss function with respect to the parameters.

While more sophisticated optimizers like Adam or RMSProp offer better convergence properties by adapting the learning rate for each parameter based on historical gradient information, SGD illustrates the core principle of gradient-based optimization.

The training process is encapsulated in the Trainer class, which handles data batching, forward and backward passes, parameter updates, and metric tracking:

import random
import matplotlib.pyplot as plt
from tinynn.engine import Value


class Trainer:
    def __init__(self, model, optimizer, loss_fn=None):
        self.model = model
        self.optimizer = optimizer
        self.loss_fn = loss_fn or self._mse_loss

        # Training history
        self.losses = []
        self.accuracies = []

    def _mse_loss(self, pred, target):
        """Mean squared error loss function."""
        return (pred - target) * (pred - target)

    def train(
        self, X, y, n_epochs=100, batch_size=32, verbose=True, early_stopping=True
    ):
        """
        Train the model on the given dataset.

        Args:
            X: Features (list or numpy array)
            y: Target values (list or numpy array)
            n_epochs: Number of training epochs
            batch_size: Mini-batch size
            verbose: Whether to print progress
            early_stopping: Whether to stop early on perfect accuracy

        Returns:
            Dictionary containing training history
        """
        print("Training neural network...")

        for epoch in range(n_epochs):
            # Track metrics for this epoch
            total_loss = 0.0
            correct = 0

            # Shuffle the data
            indices = list(range(len(X)))
            random.shuffle(indices)

            # Mini-batch training
            for start_idx in range(0, len(X), batch_size):
                end_idx = min(start_idx + batch_size, len(X))
                batch_indices = indices[start_idx:end_idx]

                # Zero gradients
                self.optimizer.zero_grad()

                # Accumulate loss and accuracy over the batch
                batch_loss = Value(0.0)

                for idx in batch_indices:
                    # Convert numpy features to Value objects
                    x_vals = [Value(X[idx][0]), Value(X[idx][1])]

                    # Forward pass
                    pred = self.model(x_vals)
                    pred_value = pred[0] if isinstance(pred, list) else pred

                    # Binary cross-entropy loss with tanh activation
                    target = 1.0 if y[idx] == 1 else -1.0  # Use -1/1 targets for tanh

                    # Calculate loss
                    loss = self.loss_fn(pred_value, target)

                    # Accumulate loss
                    batch_loss = batch_loss + loss

                    # Check accuracy
                    pred_class = 1 if pred_value.data > 0 else 0
                    if pred_class == y[idx]:
                        correct += 1

                # Scale loss by batch size
                batch_loss = batch_loss * (1.0 / len(batch_indices))

                # Backward pass
                batch_loss.backward()

                # Update parameters
                self.optimizer.step()

                # Track total loss
                total_loss += batch_loss.data

            # Record metrics
            avg_loss = total_loss / max(1, (len(X) // batch_size))
            accuracy = correct / len(X)
            self.losses.append(avg_loss)
            self.accuracies.append(accuracy)

            # Print progress every 10 epochs
            if verbose and (epoch + 1) % 10 == 0:
                print(
                    f"Epoch {epoch+1}/{n_epochs}: Loss={avg_loss:.4f}, Accuracy={accuracy:.4f}"
                )

            # Early stopping if we reach perfect accuracy
            if early_stopping and accuracy == 1.0 and avg_loss < 0.01:
                print(f"Early stopping at epoch {epoch+1} with 100% accuracy!")
                break

        print("Training complete!")
        print(f"Final accuracy: {self.accuracies[-1]:.4f}")

        return {"losses": self.losses, "accuracies": self.accuracies}

    def plot_training_progress(self, save_path="output/training_progress.png"):
        """Plot and save the training progress."""
        plt.figure(figsize=(12, 5))

        plt.subplot(1, 2, 1)
        plt.plot(self.losses)
        plt.title("Training Loss")
        plt.xlabel("Epoch")
        plt.ylabel("Loss")

        plt.subplot(1, 2, 2)
        plt.plot(self.accuracies)
        plt.title("Training Accuracy")
        plt.xlabel("Epoch")
        plt.ylabel("Accuracy")

        plt.tight_layout()
        plt.savefig(save_path)
        plt.close()

For each epoch, the trainer shuffles the data, processes mini-batches, computes loss and gradients, updates parameters, and tracks metrics like loss and accuracy. This structured approach to training makes it easy to experiment with different models and datasets while maintaining a consistent training procedure.

L2 Regularization

Regularization techniques are essential in machine learning to prevent overfitting, where a model performs well on training data but poorly on unseen data. L2 regularization, also known as weight decay, is one of the most common regularization methods for neural networks.

The core idea of L2 regularization is to add a penalty term to the loss function that discourages large weights:

$$
L_{regularized} = L_{original} + \lambda \sum_{w \in \text{weights}} w^2
$$

where $\lambda$ is the regularization strength, a hyperparameter that controls the trade-off between fitting the training data and keeping the weights small.

The gradient of this regularization term with respect to each weight is:

$$
\frac{\partial}{\partial w} \left( \lambda w^2 \right) = 2\lambda w
$$

This means that during the weight update step, each weight is not only adjusted based on the gradient of the original loss but also shrunk proportionally to its magnitude:

$$
w_{t+1} = w_t - \alpha \left( \frac{\partial L_{original}}{\partial w_t} + 2\lambda w_t \right)
= (1 - 2\alpha\lambda)w_t - \alpha\frac{\partial L_{original}}{\partial w_t}
$$

This has the effect of pushing weights toward zero, unless there is strong evidence from the data that they should be large. The result is a simpler model that is less likely to overfit.

Implementing L2 regularization in our framework is straightforward. We can modify our loss function to include the regularization term:

def _mse_loss_with_l2(self, pred, target, lambda_reg=0.01):
    """Mean squared error loss function with L2 regularization."""
    # Original MSE loss
    mse_loss = (pred - target) * (pred - target)
    
    # L2 regularization term
    l2_reg = Value(0.0)
    for p in self.model.parameters():
        l2_reg = l2_reg + p * p
    l2_reg = l2_reg * lambda_reg
    
    # Combined loss
    return mse_loss + l2_reg

Alternatively, we can implement L2 regularization directly in the optimizer by modifying the weight update rule:

def step(self, lambda_reg=0.01):
    """Updates each parameter with L2 regularization."""
    for p in self.parameters:
        # L2 regularization: weight decay
        p.data -= self.lr * (p.grad + 2 * lambda_reg * p.data)

L2 regularization has several benefits:

It helps prevent overfitting by penalizing large weights
It makes the model more robust to noise in the training data
It can improve generalization to unseen data
It can help with numerical stability during training

The regularization strength $\lambda$ is a hyperparameter that needs to be tuned. If $\lambda$ is too small, the regularization effect will be negligible; if it's too large, the model may underfit the data. Cross-validation is typically used to find an optimal value for $\lambda$.

End-to-End Usage

To demonstrate our library in action, we train a neural network on a simple classification task: the "moons" dataset from scikit-learn. This dataset consists of two interleaving half-circles, requiring a non-linear decision boundary to separate the classes:

from sklearn.datasets import make_moons
import numpy as np
import matplotlib.pyplot as plt

from tinynn.engine import Value
from tinynn.nn import MLP
from tinynn.optim import SGD
from tinynn.trainer import Trainer

# Generate the dataset
X, y = make_moons(n_samples=100, noise=0.1, random_state=42)

# Create a neural network: 2 inputs -> 32 -> 32 -> 16 -> 1 output
model = MLP(nin=2, nouts=[32, 32, 16, 1])

# Create an optimizer
optimizer = SGD(model.parameters(), lr=0.005)

# Create trainer
trainer = Trainer(model, optimizer)

# Train the model
trainer.train(X, y, n_epochs=500, batch_size=10, verbose=True)

Key training concepts:

Batch Size: Determines how many training examples are processed together in each forward/backward pass. Smaller batches introduce more noise in gradient updates (which can help escape local minima) but converge more slowly. Larger batches provide more stable updates but may get stuck in suboptimal solutions.

Epochs: One complete pass through the training dataset. Multiple epochs are needed for the model to learn effectively. The optimal number depends on factors like dataset size, model complexity, and optimization parameters.

Training Loss: Measures how well the model's predictions match the true values. We use Mean Squared Error (MSE):

$$
MSE = \frac{1}{n}\sum_{i=1}^n(y_{pred_i} - y_{target_i})^2
$$

MSE is particularly suitable for our binary classification task because:

It heavily penalizes large errors through the squared term
It provides smooth gradients for optimization
It's simple to implement and understand

Accuracy: The proportion of correct predictions. While intuitive, accuracy should be considered alongside other metrics, as it can be misleading with imbalanced datasets.

The training progress is shown in Figure 4, where we can see both the loss decreasing and accuracy improving over time:

Figure 4: Training progress showing how loss decreases and accuracy improves as the model learns.

Our simple model learns to separate the two classes effectively, as shown by the decision boundary visualization in Figure 5:

Figure 5: The learned decision boundary shows how our model separates the two classes with a non-linear boundary.

Optimization Opportunities

Neural network training presents numerous opportunities for parallelization across multiple dimensions. The most obvious is batch parallelism, where multiple training examples can be processed simultaneously through the network. Each example in a batch can be computed independently during the forward pass, and their gradients can be accumulated in parallel during backpropagation. Additionally, within each layer, matrix multiplications and element-wise operations can be parallelized across neurons and feature dimensions, creating a rich hierarchy of parallel computation that modern hardware can exploit.

This inherent parallelism modern GPUS ideal for deep learning workloads. Unlike CPUs, which are optimized for sequential processing with complex control flow, GPUs contain thousands of simpler cores designed specifically for parallel arithmetic operations. This architecture aligns perfectly with neural network computations—matrix multiplications, convolutions, and element-wise operations can all be distributed across these cores, leading to orders of magnitude speedup compared to CPU implementations. Modern GPUs also feature specialized tensor cores that accelerate mixed-precision matrix operations commonly found in deep learning.

The memory hierarchy of GPUs is another crucial factor in their deep learning performance. High-bandwidth memory and sophisticated caching mechanisms allow GPUs to feed data to their numerous processing cores efficiently, while shared memory enables fast communication between threads working on the same computation. This is particularly important for deep learning, where memory access patterns are predictable and regular, allowing for optimal utilization of the memory subsystem. Combined with their massive parallel processing capability, these memory characteristics make GPUs the backbone of modern deep learning infrastructure, enabling the training of increasingly large and complex models. We'll move onto that next.

External Resources

MLIR Part 4 - Linear Algebra in MLIR

Fri, 14 Mar 2025 00:00:00 +0000

Linear Algebra in MLIR

The Linalg dialect is a core idea in the MLIR ecosystem, it was built to make high-level tensor computations easier and more efficient. Essentially, it's all about simplifying the way we handle complex mathematical operations in a way that can be translated into fast, optimized code. At its core, the Linalg dialect uses a straightforward, declarative approach. This means it lays out operations and transformations in a way that keeps the math intact while also allowing for a variety of optimizations. It provides high-level linear algebra operations like pointwise calculations, matrix multiplications, and convolutions as single operations.

`linalg.generic`

The most generic operation in the Linalg dialect is linalg.generic. This operation allows us to define a generic tensor manipulation operations over indices. It is the most generic operation and all other operations are defined as specializations of this operation. You probably won't use this directly much, but it's useful to discuss first because it's the most fundamental operation.

#map_1d_identity = affine_map<(d0) -> (d0)>

func.func @add_tensors(%arg0: tensor<10xf32>, %arg1: tensor<10xf32>) -> tensor<10xf32> {
  %result = tensor.empty() : tensor<10xf32>
  %0 = linalg.generic {
    // attributes
      indexing_maps = [
        #map_1d_identity,
        #map_1d_identity,
        #map_1d_identity
       ],
      iterator_types = [
        "parallel"
      ]
    } 
    // input tensors
    ins(%arg0, %arg1 : tensor<10xf32>, tensor<10xf32>) 
    // output tensor
    outs(%result : tensor<10xf32>) 
    // loop region
    {
    ^bb0(%arg2: f32, %arg3: f32, %arg4: f32):
      %1 = arith.addf %arg2, %arg3 : f32
      linalg.yield %1 : f32
    } -> tensor<10xf32>
  return %0 : tensor<10xf32>
}

Let's break down each component of this linalg.generic operation:

indexing_maps: This attribute defines how input and output tensors are accessed. Here we have 3 maps:
- First map for first input tensor (%arg0)
- Second map for second input tensor (%arg1)
- Third map for output tensor (%result)
All use #map_1d_identity which is defined as affine_map<(d0) -> (d0)>, meaning each element maps directly to the corresponding element (no coordinate transformations).
iterator_types: Specifies the type of iteration for each dimension. Here we have:
- ["parallel"]: Single dimension marked as parallel, meaning iterations can be executed in any order or concurrently.
There are three possible iterator types in linalg:
- parallel: Iterations can be executed in any order or concurrently (like element-wise operations)
- reduction: Iterations contribute to a single result value (like summing along an axis)
- window: Iterations access a sliding window of elements (like convolutions)
ins(%arg0, %arg1 : tensor<10xf32>, tensor<10xf32>):
- Specifies the input tensors and their types
- Both are 1D tensors of 10 float32 elements
outs(%result : tensor<10xf32>):
- Specifies the output tensor and its type
- Also a 1D tensor of 10 float32 elements
The region (loop body):
```
{
^bb0(%arg2: f32, %arg3: f32, %arg4: f32):
  %1 = arith.addf %arg2, %arg3 : f32
  linalg.yield %1 : f32
}
```
- Takes scalar values from input tensors (%arg2, %arg3) and output tensor (%arg4)
- Performs floating point addition
- Yields result back using linalg.yield

This would perform the standard vectorized addition of two tensors element-wise, just like in NumPy:

np.array([1,2,3]) + np.array([2,3,4])
# array([3, 5, 7])

If this seems like a lot, don't worry it is. There are much simpler ways to write this that compile down to the same thing.

`linalg.map`

The same operation can be written is a generic linalg.map operation which abstracts away the precise details of the loop nest and index manipulations, instead directly applying the arith.addf operation to the input tensors.

module {
  func.func @addv(%arg0: tensor<10xf32>, %arg1: tensor<10xf32>, %out: memref<10xf32>) {
    %out2 = tensor.empty() : tensor<10xf32>
    %result = linalg.map { arith.addf } ins(%arg0, %arg1 : tensor<10xf32>, tensor<10xf32>) outs(%out2 : tensor<10xf32>)

    %l = bufferization.to_memref %result : tensor<10xf32> to memref<10xf32>
    memref.copy %l, %out : memref<10xf32> to memref<10xf32>

    return
  }
}

There are also named operations for common arithmetic map operations that are named specializations of the linalg.map operation.

linalg.add
linalg.mul
linalg.div
linalg.sub

`linalg.reduce`

The linalg.reduce operation is a powerful primitive that can be used to implement various reduction operations.

func.func @add_tensor() -> (f64) {
  %_ssa_0 = tensor.empty () : tensor<3xf64>
  %out = tensor.empty () : tensor<f64>
  %reduce = linalg.reduce { arith.addf } ins(%_ssa_0:tensor<3xf64>) outs(%out:tensor<f64>) dimensions = [0]
  %result = tensor.extract %reduce [] : tensor<f64>
  return %result : f64
}

In NumPy this operation can be written as:

import numpy as np
np.multiply.reduce([2,3,5]) # 30

`linalg.matmul`

We can also define a generic matrix multiplication operation in terms of direct tensor contractions. The matrix multiplication operation shown in the MLIR code can be written in conventional tensor notation as:

$$
C_{ij} = \sum_{k=1}^{10} A_{ik} B_{kj}
$$

Where:

$A$ is the 8×10 input matrix (memref<8x10xf32>)
$B$ is the 10×16 input matrix (memref<10x16xf32>)
$C$ is the 8×16 output matrix (memref<8x16xf32>)
$i$ ranges from 1 to 8
$j$ ranges from 1 to 16
$k$ is the summation index ranging from 1 to 10

This matches the MLIR implementation where:

The parallel iterator types correspond to the free indices $i$ and $j$
The reduction iterator type corresponds to the summation over $k$
The indexing maps (i, j, k) -> (i, k), (i, j, k) -> (k, j), and (i, j, k) -> (i, j) correspond to accessing $A_{ik}$, $B_{kj}$, and $C_{ij}$ respectively

func.func @matmul(
    %A: memref<8x10xf32>,
    %B: memref<10x16xf32>,
    %C: memref<8x16xf32>
) {
    linalg.generic {
        indexing_maps = [
            affine_map<(i, j, k) -> (i, k)>,
            affine_map<(i, j, k) -> (k, j)>,
            affine_map<(i, j, k) -> (i, j)>
        ],
        iterator_types = [
            "parallel",
            "parallel",
            "reduction"
        ]
    } ins(%A, %B : memref<8x10xf32>, memref<10x16xf32>) outs(%C : memref<8x16xf32>) {
        ^bb0(%lhs_one: f32, %rhs_one: f32, %init_one: f32):
            %tmp0 = arith.mulf %lhs_one, %rhs_one : f32
            %tmp1 = arith.addf %init_one, %tmp0 : f32
            linalg.yield %tmp1 : f32
    }
    return
}

Or in the much more succinct form using linalg.matmul operation.

func.func @matmul(
    %A: memref<8x10xf32>,
    %B: memref<10x16xf32>,
    %C: memref<8x16xf32>
) {
    linalg.matmul ins(%A, %B : memref<8x10xf32>, memref<10x16xf32>) outs(%C : memref<8x16xf32>)
    return
}

The tensor operations are then lowered into a sequence of loops using either the affine.for or scf.for operations using the convert-linalg-to-loops or convert-linalg-to-affine-loops passes.

func.func @matmul(%arg0: memref<8x10xf32>, %arg1: memref<10x16xf32>, %arg2: memref<8x16xf32>) {
  affine.for %arg3 = 0 to 8 {
    affine.for %arg4 = 0 to 16 {
      affine.for %arg5 = 0 to 10 {
        %0 = affine.load %arg0[%arg3, %arg5] : memref<8x10xf32>
        %1 = affine.load %arg1[%arg5, %arg4] : memref<10x16xf32>
        %2 = affine.load %arg2[%arg3, %arg4] : memref<8x16xf32>
        %3 = arith.mulf %0, %1 : f32
        %4 = arith.addf %2, %3 : f32
        affine.store %4, %arg2[%arg3, %arg4] : memref<8x16xf32>
      }
    }
  }
  return
}

func.func @matmul(%arg0: memref<8x10xf32>, %arg1: memref<10x16xf32>, %arg2: memref<8x16xf32>) {
  %c0 = arith.constant 0 : index
  %c8 = arith.constant 8 : index
  %c1 = arith.constant 1 : index
  %c16 = arith.constant 16 : index
  %c10 = arith.constant 10 : index
  scf.for %arg3 = %c0 to %c8 step %c1 {
    scf.for %arg4 = %c0 to %c16 step %c1 {
      scf.for %arg5 = %c0 to %c10 step %c1 {
        %0 = memref.load %arg0[%arg3, %arg5] : memref<8x10xf32>
        %1 = memref.load %arg1[%arg5, %arg4] : memref<10x16xf32>
        %2 = memref.load %arg2[%arg3, %arg4] : memref<8x16xf32>
        %3 = arith.mulf %0, %1 : f32
        %4 = arith.addf %2, %3 : f32
        memref.store %4, %arg2[%arg3, %arg4] : memref<8x16xf32>
      }
    }
  }
  return
}

Broadcasting

Broadcasting in MLIR's Linalg dialect allows tensors of different shapes to be combined in operations, similar to NumPy's broadcasting rules. The smaller tensor is implicitly expanded to match the shape of the larger tensor along broadcast dimensions. This is particularly useful for operations like adding a vector to each row/column of a matrix or applying scalar operations to tensors.

Let's look at some common broadcasting patterns:

func.func @broadcast_1d_to_2d(%arg0: tensor<3xf32>) -> tensor<3x3xf32> {
  // Create an empty output tensor
  %init = tensor.empty() : tensor<3x3xf32>
  
  // Broadcast the input tensor along dimension 1 (columns)
  %result = linalg.broadcast 
    ins(%arg0: tensor<3xf32>)
    outs(%init: tensor<3x3xf32>)
    dimensions = [1]
    
  return %result : tensor<3x3xf32>
}

In NumPy this operation can be written as:

arg0 = np.array([1,2,3])
result = np.broadcast_to(arg0, (3,3))
# array([[1, 2, 3],
#        [1, 2, 3],
#        [1, 2, 3]])

We can also combine broadcasting with other operations. For example, adding a vector to each row of a matrix:

func.func @add_vector_to_matrix(
    %matrix: tensor<3x4xf32>,
    %vector: tensor<4xf32>
) -> tensor<3x4xf32> {
  %init = tensor.empty() : tensor<3x4xf32>
  
  // First broadcast the vector
  %broadcasted = linalg.broadcast
    ins(%vector: tensor<4xf32>)
    outs(%init: tensor<3x4xf32>)
    dimensions = [0]
    
  // Then add the broadcasted result to the matrix
  %result = linalg.map { arith.addf }
    ins(%matrix, %broadcasted: tensor<3x4xf32>, tensor<3x4xf32>)
    outs(%init: tensor<3x4xf32>)
    
  return %result : tensor<3x4xf32>
}

This is the equivalent to the common NumPy operation:

matrix = np.ones((3,4))
vector = np.array([1,2,3,4])
result = matrix + vector
# array([[2., 3., 4., 5.],
#        [2., 3., 4., 5.],
#        [2., 3., 4., 5.]])

Kernel Fusion

Kernel fusion is an important optimization technique that combines multiple operations into a single operation, reducing memory bandwidth requirements and improving performance. The Linalg dialect provides built-in support for fusing elementwise operations through its optimization passes.

Let's look at a simple example where we have two operations - addition followed by multiplication - that we want to fuse together. First, we'll write these as separate operations:

module {
  func.func @addmul(%arg0: tensor<10xf32>, %arg1: tensor<10xf32>, %arg2: tensor<10xf32>) -> tensor<10xf32> {
    // First create an empty tensor for intermediate results
    %0 = tensor.empty() : tensor<10xf32>
    
    // Add operation
    %1 = linalg.add ins(%arg0, %arg1 : tensor<10xf32>, tensor<10xf32>)
                    outs(%0 : tensor<10xf32>) -> tensor<10xf32>

    // Create another empty tensor for the multiplication result
    %2 = tensor.empty() : tensor<10xf32>
    
    // Multiply operation
    %3 = linalg.mul ins(%1, %arg2 : tensor<10xf32>, tensor<10xf32>)
                    outs(%2 : tensor<10xf32>) -> tensor<10xf32>

    return %3 : tensor<10xf32>
  }
}

Here we have two distinct operations: linalg.add followed by linalg.mul. Each operation requires reading from memory and writing back to memory, which can be inefficient.

Through MLIR's optimization passes, we can fuse these operations into a single kernel that performs both operations in one pass over the data:

#map = affine_map<(d0) -> (d0)>
module {
  func.func @addmul(%arg0: tensor<10xf32>, %arg1: tensor<10xf32>, %arg2: tensor<10xf32>) -> tensor<10xf32> {
    %0 = tensor.empty() : tensor<10xf32>
    %1 = linalg.generic {indexing_maps = [#map, #map, #map, #map],
        iterator_types = ["parallel"]} ins(%arg0, %arg1, %arg2 : tensor<10xf32>,
        tensor<10xf32>, tensor<10xf32>) outs(%0 : tensor<10xf32>) {
    ^bb0(%in: f32, %in_0: f32, %in_1: f32, %out: f32):
      %2 = arith.addf %in, %in_0 : f32
      %3 = arith.mulf %2, %in_1 : f32
      linalg.yield %3 : f32
    } -> tensor<10xf32>
    return %1 : tensor<10xf32>
  }
}

To get some intuition for how this works, let's look at the equivalent Python code:

# Unfused version - two separate loops
def unfused_addmul(a, b, c):
    # First loop - addition
    temp = []
    for i in range(len(a)):
        temp.append(a[i] + b[i])
    
    # Second loop - multiplication
    result = []
    for i in range(len(temp)):
        result.append(temp[i] * c[i])
    
    return result

# Fused version - single loop
def fused_addmul(a, b, c):
    result = []
    for i in range(len(a)):
        # Combine add and multiply in one loop iteration
        result.append((a[i] + b[i]) * c[i])
    return result

a = [1.0, 2.0, 3.0, 4.0, 5.0]
b = [1.0, 1.0, 1.0, 1.0, 1.0]
c = [2.0, 2.0, 2.0, 2.0, 2.0]

# Both produce same result but fused version only loops once
result = fused_addmul(a, b, c)  # [(1+1)*2, (2+1)*2, (3+1)*2, ...]

The fused version combines both operations into a single linalg.generic operation that reads each input only once and writes the final result directly. This eliminates the intermediate tensor allocation and memory accesses.

To perform this fusion, we need to apply a specific sequence of optimization passes:

--canonicalize: Performs general cleanups and simplifications
--linalg-fuse-elementwise-ops: Fuse elementwise operations
--cse: Common Subexpression Elimination to clean up redundant operations
--linalg-generalize-named-ops: Converts named ops (like linalg.add) to generic form
--convert-linalg-to-loops: Converts the fused operations to explicit loops

We can run these passes and output the fused addmul operation to fused_ops.mlir, reducing the time complexity from two loops over $n$ to a single loop over $n$.

mlir-opt separate_ops.mlir \
  --canonicalize \
  --linalg-fuse-elementwise-ops \
  --cse \
  --linalg-generalize-named-ops \
  --linalg-fuse-elementwise-ops \
  --convert-linalg-to-loops \
  -o fused_ops.mlir

This sequence of passes ensures that operations are properly fused and then lowered to a form that can be efficiently executed. The fusion optimization is particularly important in deep learning workloads where chains of elementwise operations are common.

Tiling

Loop tiling is a crucial optimization technique that improves memory access patterns and cache utilization. In modern computer architectures, memory access is often the bottleneck rather than computation. When processing large matrices or tensors, if we access memory in a linear fashion, we may constantly need to fetch new data from main memory, which is much slower than cache memory.

Tiling breaks down large computations into smaller blocks that better fit into cache memory. For example, in matrix multiplication, instead of computing the entire row-column dot product at once (which might exceed cache size), we break it into smaller tiles that can reside in cache memory. This reduces cache misses and improves performance.

This optimization is particularly important for GPU architectures, where memory hierarchy and access patterns significantly impact performance. GPUs have a complex memory hierarchy including global memory, shared memory (similar to cache), and registers. By tiling computations to match the GPU's hardware characteristics—like shared memory size and warp size—we can dramatically improve performance. For instance, in CUDA programming, a common pattern is to load a tile of data into shared memory, synchronize threads, and then have each thread work on elements within that tile. More on this in the later section on GPU programming.

Here's an example of using MLIR to perform loop tiling on a matrix multiplication operation. We'll start with a simple tensor-based matmul and transform it into tiled affine loops.

module {
  func.func @matmul(%arg0: tensor<10x10xf32>, %arg1: tensor<10x10xf32>,
                    %arg2: tensor<10x10xf32>) -> tensor<10x10xf32> {
    %0 = linalg.matmul 
           ins(%arg0, %arg1 : tensor<10x10xf32>, tensor<10x10xf32>)
           outs(%arg2 : tensor<10x10xf32>) -> tensor<10x10xf32>
    return %0 : tensor<10x10xf32>
  }
}

To transform this into tiled loops, we need several transformation passes:

--convert-tensor-to-linalg: Converts tensor operations to linalg dialect
--linalg-generalize-named-ops: Converts named operations (like matmul) into generic linalg operations
--one-shot-bufferize="bufferize-function-boundaries": Converts tensor operations to use buffers
--buffer-deallocation-pipeline: Handles buffer deallocation
--convert-bufferization-to-memref: Converts buffer operations to memref operations
--convert-linalg-to-affine-loops: Lowers linalg operations to affine loops
--affine-loop-tile="tile-size=5": Tiles the affine loops with size 5
--canonicalize --cse: Cleanup passes

Here's the complete transformation pipeline:

mlir-opt tiling.mlir \
  --convert-tensor-to-linalg \
  --linalg-generalize-named-ops \
  --one-shot-bufferize="bufferize-function-boundaries" \
  --buffer-deallocation-pipeline \
  --convert-bufferization-to-memref \
  --convert-linalg-to-affine-loops \
  --affine-loop-tile="tile-size=5" \
  --canonicalize \
  --cse \
  -o tiling-transformed.mlir

This produces the following tiled implementation:

#map = affine_map<(d0) -> (d0)>
#map1 = affine_map<(d0) -> (d0 + 5)>
module {
  func.func @matmul(%arg0: memref<10x10xf32, strided<[?, ?], offset: ?>>, %arg1:
  memref<10x10xf32, strided<[?, ?], offset: ?>>, %arg2: memref<10x10xf32,
  strided<[?, ?], offset: ?>>) -> memref<10x10xf32, strided<[?, ?], offset: ?>>
  {
    affine.for %arg3 = 0 to 10 step 5 {
      affine.for %arg4 = 0 to 10 step 5 {
        affine.for %arg5 = 0 to 10 step 5 {
          affine.for %arg6 = #map(%arg3) to #map1(%arg3) {
            affine.for %arg7 = #map(%arg4) to #map1(%arg4) {
              affine.for %arg8 = #map(%arg5) to #map1(%arg5) {
                %0 = affine.load %arg0[%arg6, %arg8] : memref<10x10xf32, strided<[?, ?], offset: ?>>
                %1 = affine.load %arg1[%arg8, %arg7] : memref<10x10xf32, strided<[?, ?], offset: ?>>
                %2 = affine.load %arg2[%arg6, %arg7] : memref<10x10xf32, strided<[?, ?], offset: ?>>
                %3 = arith.mulf %0, %1 : f32
                %4 = arith.addf %2, %3 : f32
                affine.store %4, %arg2[%arg6, %arg7] : memref<10x10xf32, strided<[?, ?], offset: ?>>
              }
            }
          }
        }
      }
    }
    %alloc = memref.alloc() : memref<10x10xf32>
    %cast = memref.cast %alloc : memref<10x10xf32> to memref<10x10xf32, strided<[?, ?], offset: ?>>
    memref.copy %arg2, %alloc : memref<10x10xf32, strided<[?, ?], offset: ?>> to memref<10x10xf32>
    return %cast : memref<10x10xf32, strided<[?, ?], offset: ?>>
  }
}

The tiled output shows the original 10x10 matrix multiplication broken into smaller 5x5 tiles, which can help improve cache utilization and locality of memory accesses.

External References

MLIR Part 3 - Affine Dialect and OpenMP

Thu, 13 Mar 2025 00:00:00 +0000

Affine Dialect and OpenMP

The affine dialect in MLIR provides abstractions for expressing loops and array accesses that are amenable to parallel execution. Unlike the scf dialect we've seen before, the affine dialect enables advanced loop transformations and automatic parallelization. It's esesntially "first class loops" which is something we always used to layer on top of our LLVM.

The affine dialect many advantages, including automatic parallelization opportunities, built-in vectorization capabilities, sophisticated loop optimizations, a natural expression of array computations, and integration with OpenMP.

Polyhedral Optimization Model

The polyhedral model is a mathematical framework that represents loop nests and their computations as geometric objects in multi-dimensional spaces.

At its core, the polyhedral model represents the execution of statements inside loop nests as points in a multi-dimensional space. Each point corresponds to a specific instance of a statement in the execution, defined by its iteration coordinates. This representation enables program analysis and transformation techniques by converting complex loop optimization problems into geometric operations on polyhedra.

The key components of the polyhedral model include iteration domains, access relations, and scheduling functions. Iteration domains define the set of all iterations executed by a loop nest, represented as a set of integer points bounded by affine constraints. Access relations map iteration points to the memory locations accessed by each statement. Scheduling functions determine the order of execution for iteration points, enabling transformations that preserve program semantics while improving performance characteristics.

MLIR provides the affine that incorporates polyhedral concepts as first-class citizens. This hybrid design optimizes the representation, analysis, and transformation of high-level dataflow graphs and target-specific code for high-performance data-parallel systems.

There are three core concepts we have to understand:

Affine maps: Multi-dimensional quasi-linear functions that map dimensions and symbols to results. For example, (d0, d1, d2, s0) → (d0 + d1, s0 * d2) represents a two-dimensional affine map that maps dimension arguments d0, d1, d2 and symbol argument s0 to two results.
Integer sets: Constraints on dimensions and symbols represented as affine inequalities and equalities. For instance, (i)[N, M] : (i >= 0, -i + N >= 0, N - 5 == 0, -i + M + 1 >= 0) represents the set of values i such that 0 <= i < N, N = 5, and i <= M + 1.
Affine operations: Operations such as affine.for, affine.if, and affine.parallel that leverage affine maps and integer sets to represent loop nests and conditionals with affine constraints.

Rather than front-load the theory, let's just look at some examples.

Matrix Multiplication

The classic matrix product of two matrices $A_{ij}$ and $B_{jk}$ is:

$$
C_{ik} = (A B)_{ik} = \sum_{j=1}^{N} A_{ij}B_{jk}
$$

Expressing this in MLIR as an explicit loop nest would look like this:

func.func @matmul(%A: memref<?x?xf32>, %B: memref<?x?xf32>, %C: memref<?x?xf32>) {
  %c0 = arith.constant 0 : index
  %c1 = arith.constant 1 : index

  %M = memref.dim %A, %c0 : memref<?x?xf32>
  %N = memref.dim %B, %c1 : memref<?x?xf32>
  %K = memref.dim %A, %c1 : memref<?x?xf32>

  // Sequential implementation
  affine.for %i = 0 to %M {
    affine.for %j = 0 to %N {
      affine.for %k = 0 to %K {
        %a = affine.load %A[%i, %k] : memref<?x?xf32>
        %b = affine.load %B[%k, %j] : memref<?x?xf32>
        %c = affine.load %C[%i, %j] : memref<?x?xf32>
        %prod = arith.mulf %a, %b : f32
        %sum = arith.addf %c, %prod : f32
        affine.store %sum, %C[%i, %j] : memref<?x?xf32>
      }
    }
  }
  return
}

Notice that the two loops over %i and %j have no dependencies between different iterations of these loops. Using the -affine-parallelize pass, this can be transformed into:

func.func @matmul_parallel(%A: memref<?x?xf32>, %B: memref<?x?xf32>, %C: memref<?x?xf32>) {
  %c0 = arith.constant 0 : index
  %c1 = arith.constant 1 : index

  %M = memref.dim %A, %c0 : memref<?x?xf32>
  %N = memref.dim %B, %c1 : memref<?x?xf32>
  %K = memref.dim %A, %c1 : memref<?x?xf32>

  // Parallel implementation
  affine.parallel (%i, %j) = (0, 0) to (%M, %N) {
    affine.for %k = 0 to %K {
      %a = affine.load %A[%i, %k] : memref<?x?xf32>
      %b = affine.load %B[%k, %j] : memref<?x?xf32>
      %c = affine.load %C[%i, %j] : memref<?x?xf32>
      %prod = arith.mulf %a, %b : f32
      %sum = arith.addf %c, %prod : f32
      affine.store %sum, %C[%i, %j] : memref<?x?xf32>
    }
  }
  return
}

The affine.parallel operation represents a way to express that multiple iterations of a loop can be executed independently and potentially simultaneously. Think of it like saying "these calculations can happen in any order, or all at once" - similar to how you might divide up work among multiple workers who don't need to communicate with each other.

More precisely, affine.parallel defines a set of nested loops where:

Each iteration is independent of all other iterations
The iterations can be executed in any order or simultaneously
The operation produces results through reductions (like summing up values) where the order of combining results doesn't matter

Technically, it creates a "hyper-rectangular parallel band," which means it can represent multiple nested parallel loops, each characterized by its own induction variables (loop counters), lower and upper bounds, step sizes (indicating how much to increment each iteration), and reduction operations (defining how to combine results from different iterations).

The body of the parallel region must end with affine.yield which specifies how to combine results from different iterations using operations like addition or multiplication. For loops that execute zero times, the result is the identity value for that operation (0 for addition, 1 for multiplication).

Affine Maps (`affine.apply`)

Affine maps are a key component of the affine dialect, representing multi-dimensional affine transformations. They provides us a way to describe the mapping of loop indices to memory access patterns, which is essential for optimizing memory layouts and access patterns in high-performance computing.

Let's look at a comprehensive example that demonstrates various uses of affine.apply:

// Define some reusable affine maps
#tile_map = affine_map<(d0) -> (d0 floordiv 32)>
#offset_map = affine_map<(d0)[s0] -> (d0 + s0)>
#complex_map = affine_map<(d0, d1)[s0] -> (d0 * 2 + d1 floordiv 4 + s0)>

func.func @affine_apply_examples() {
  // Create some test indices
  %c0 = arith.constant 0 : index
  %c42 = arith.constant 42 : index
  %c128 = arith.constant 128 : index
  
  // Example 1: Simple tiling calculation
  // Calculate which tile a given index belongs to (tile size = 32)
  %tile_idx = affine.apply #tile_map(%c42)
  
  // Example 2: Inline affine map for offset calculation
  %offset = affine.apply affine_map<(i) -> (i + 10)>(%c42)
  
  // Example 3: Using a symbol parameter
  %shifted = affine.apply #offset_map(%c42)[%c128]
  
  // Example 4: Multiple dimensions and a symbol
  %complex = affine.apply #complex_map(%c42, %c128)[%c0]
  
  // Example 5: Composition of affine applies
  %temp = affine.apply affine_map<(i) -> (i * 2)>(%c42)
  %final = affine.apply affine_map<(i) -> (i + 5)>(%temp)
  
  return
}

// Example showing how affine.apply can be used in a practical loop context
func.func @tiled_loop(%arg0: memref<256xf32>) {
  %c0 = arith.constant 0 : index
  %c256 = arith.constant 256 : index
  %c32 = arith.constant 32 : index

  // Outer loop iterates over tiles
  affine.for %i = 0 to 256 step 32 {
    // Inner loop processes elements within the tile
    affine.for %j = 0 to 32 {
      %idx = affine.apply affine_map<(d0, d1) -> (d0 + d1)>(%i, %j)
      %val = memref.load %arg0[%idx] : memref<256xf32>
      // Process value...
      memref.store %val, %arg0[%idx] : memref<256xf32>
    }
  }
  return
}

The tiled_loop function shows how affine.apply can be used in a real-world scenario to implement tiled processing of an array. The outer loop steps by the tile size, and affine.apply is used to calculate the bounds for the inner loop that processes each tile.

Some key points about affine maps include that floordiv performs integer division rounding down, and the syntax (d0)[s0] indicates one dimension parameter d0 and one symbol parameter s0. Additionally, affine maps can only contain addition, subtraction, multiplication by constants, division by constants, modulo by constants, and floordiv/ceildiv by constants. The result type is always index.

Affine Optimization Passes

The MLIR optimizer provides a rich set of passes specifically designed for the affine dialect. These passes can automatically transform code to improve performance through various optimization techniques. Let's explore some of the most important ones:

Loop invariant code motion: This transformation moves loop invariant code (code that does not depend on the loop index) outside the loop. This can help expose parallelism by moving code that is not dependent on the loop index to the outer loop.

// Before
func.func @before(%A: memref<10xf32>, %B: memref<10xf32>) {
  %c0 = arith.constant 0 : index
  %c10 = arith.constant 10 : index
  %c1 = arith.constant 1 : index
  
  affine.for %i = 0 to 10 {
    %x = arith.constant 42.0 : f32  // This is loop invariant!
    %v = memref.load %A[%i] : memref<10xf32>
    %sum = arith.addf %v, %x : f32
    memref.store %sum, %B[%i] : memref<10xf32>
  }
  return
}

// After
func.func @after(%A: memref<10xf32>, %B: memref<10xf32>) {
  %c0 = arith.constant 0 : index
  %c10 = arith.constant 10 : index
  %c1 = arith.constant 1 : index
  
  %x = arith.constant 42.0 : f32  // Moved outside the loop
  affine.for %i = 0 to 10 {
    %v = memref.load %A[%i] : memref<10xf32>
    %sum = arith.addf %v, %x : f32
    memref.store %sum, %B[%i] : memref<10xf32>
  }
  return
}

Loop skewing: This transformation changes the iteration space by shifting iterations based on the values of other loop indices. This can help expose parallelism by transforming dependencies.

// Before - Dependencies prevent parallelization
func.func @before(%A: memref<10x10xf32>) {
  affine.for %i = 1 to 10 {
    affine.for %j = 1 to 10 {
      %v1 = affine.load %A[%i-1, %j] : memref<10x10xf32>
      %v2 = affine.load %A[%i, %j-1] : memref<10x10xf32>
      %sum = arith.addf %v1, %v2 : f32
      affine.store %sum, %A[%i, %j] : memref<10x10xf32>
    }
  }
}

// After skewing - Inner loop can now be parallelized
func.func @after(%A: memref<10x10xf32>) {
  affine.for %i = 1 to 10 {
    affine.for %j = %i to %i + 9 {
      %i_new = affine.apply affine_map<(d0, d1) -> (d0)>(%i, %j)
      %j_new = affine.apply affine_map<(d0, d1) -> (d1 - d0)>(%i, %j)
      %v1 = affine.load %A[%i_new-1, %j_new] : memref<10x10xf32>
      %v2 = affine.load %A[%i_new, %j_new-1] : memref<10x10xf32>
      %sum = arith.addf %v1, %v2 : f32
      affine.store %sum, %A[%i_new, %j_new] : memref<10x10xf32>
    }
  }
}

Loop interchange: This transformation changes the nesting order of loops, which can improve cache locality and expose parallelism.

// Before - Column-major access pattern
func.func @before(%A: memref<16x16xf32>, %B: memref<16x16xf32>) {
  affine.for %i = 0 to 16 {
    affine.for %j = 0 to 16 {
      %v = affine.load %A[%j, %i] : memref<16x16xf32>
      affine.store %v, %B[%j, %i] : memref<16x16xf32>
    }
  }
}

// After - Row-major access pattern (better locality)
func.func @after(%A: memref<16x16xf32>, %B: memref<16x16xf32>) {
  affine.for %j = 0 to 16 {
    affine.for %i = 0 to 16 {
      %v = affine.load %A[%j, %i] : memref<16x16xf32>
      affine.store %v, %B[%j, %i] : memref<16x16xf32>
    }
  }
}

Loop fusion: This transformation combines adjacent loops to improve locality and reduce loop overhead.

// Before fusion
func.func @before(%A: memref<10xf32>, %B: memref<10xf32>, %C: memref<10xf32>) {
  affine.for %i = 0 to 10 {
    %v1 = affine.load %A[%i] : memref<10xf32>
    %v2 = arith.mulf %v1, %v1 : f32
    affine.store %v2, %B[%i] : memref<10xf32>
  }
  
  affine.for %i = 0 to 10 {
    %v3 = affine.load %B[%i] : memref<10xf32>
    %v4 = arith.addf %v3, %v3 : f32
    affine.store %v4, %C[%i] : memref<10xf32>
  }
}

// After fusion
func.func @after(%A: memref<10xf32>, %B: memref<10xf32>, %C: memref<10xf32>) {
  affine.for %i = 0 to 10 {
    %v1 = affine.load %A[%i] : memref<10xf32>
    %v2 = arith.mulf %v1, %v1 : f32
    affine.store %v2, %B[%i] : memref<10xf32>
    %v3 = arith.addf %v2, %v2 : f32
    affine.store %v3, %C[%i] : memref<10xf32>
  }
}

Loop tiling: This transformation breaks a loop into smaller chunks to improve cache locality.

// Before tiling
func.func @before(%A: memref<32x32xf32>) {
  affine.for %i = 0 to 32 {
    affine.for %j = 0 to 32 {
      %v = affine.load %A[%i, %j] : memref<32x32xf32>
      // ... computation ...
      affine.store %v, %A[%i, %j] : memref<32x32xf32>
    }
  }
}

// After tiling (tile size 8x8)
func.func @after(%A: memref<32x32xf32>) {
  affine.for %ti = 0 to 32 step 8 {
    affine.for %tj = 0 to 32 step 8 {
      affine.for %i = #map(%ti) to #map(%ti + 8) {
        affine.for %j = #map(%tj) to #map(%tj + 8) {
          %v = affine.load %A[%i, %j] : memref<32x32xf32>
          // ... computation ...
          affine.store %v, %A[%i, %j] : memref<32x32xf32>
        }
      }
    }
  }
}

These optimizations are available in the mlir-opt tool:

-affine-loop-coalescing - Merge consecutive loops into a single loop.
-affine-loop-fusion - Merge loops with the same bounds and steps.
-affine-loop-invariant-code-motion - Move loop invariant code outside the loop.
-affine-loop-normalize - Normalize loop bounds and steps.
-affine-loop-tile - Tile loops.
-affine-loop-unroll - Unroll loops.
-affine-loop-unroll-jam - Unroll loops and jam them together.
-affine-parallelize - Parallelize loops.
-affine-pipeline-data-transfer - Pipeline non-blocking data transfers between explicitly managed levels of the memory hierarchy
-affine-scalrep - Replace affine memref accesses by scalars by forwarding stores to loads and eliminating redundant loads
-affine-simplify-structures - Simplify affine expressions in maps/sets and normalize memrefs
-affine-super-vectorize - Vectorize to a target independent n-D vector abstraction

There is also the -convert-affine-for-to-gpu, which we'll use later, which converts affine loops to GPU kernels which can target multiple GPU architectures.

Convolution Kernels

Now that we understand the basic optimizations available in the affine dialect, let's look at a more practical example: implementing a 2D convolution. This operation is fundamental in image processing and deep learning, where it's used for feature extraction and pattern recognition.

The mathematical formula for 2D convolution is:

$$
(A * K)_{ij} = \sum_{u} \sum_{v} K_{uv} A_{(i+u)(j+v)}
$$

module {
  func.func @conv_2d(%input: memref<128x128xf32>, %filter: memref<16x16xf32>, %output: memref<113x113xf32>) {
    // Loop over the output matrix dimensions (113x113)
    affine.for %i = 0 to 113 {
      affine.for %j = 0 to 113 {
        // Use affine.parallel to accumulate values into %acc using iter_args
        %zero = arith.constant 0.0 : f32
        %acc = affine.for %fi = 0 to 16 iter_args(%acc = %zero) -> (f32) {
          %acc_inner = affine.for %fj = 0 to 16 iter_args(%acc_inner = %acc) -> (f32) {
            // Load filter value
            %filter_val = affine.load %filter[%fi, %fj] : memref<16x16xf32>

            // Load corresponding input value from the input matrix
            %input_val = affine.load %input[%i + %fi, %j + %fj] : memref<128x128xf32>

            // Multiply input value with filter value
            %prod = arith.mulf %input_val, %filter_val : f32

            // Add product to the accumulator
            %new_acc = arith.addf %acc_inner, %prod : f32
            affine.yield %new_acc : f32
          }
          affine.yield %acc_inner : f32
        }

        // Store the accumulated result in the output matrix
        affine.store %acc, %output[%i, %j] : memref<113x113xf32>
      }
    }
    return
  }
}

To properly optimize and parallelize affine operations, we need a specific sequence of passes:

mlir-opt conv_2d.mlir \
  --affine-loop-normalize \
  --affine-parallelize \
  -lower-affine \
  --convert-scf-to-cf \
  --convert-cf-to-llvm \
  --convert-math-to-llvm \
  --convert-arith-to-llvm \
  --finalize-memref-to-llvm \
  --convert-func-to-llvm \
  --reconcile-unrealized-casts \
  -o conv_2d_opt.mlir

# Translate to LLVM IR
mlir-translate conv_2d_opt.mlir -mlir-to-llvmir -o conv_2d.ll

# Compile to object file
llc -filetype=obj --relocation-model=pic conv_2d.ll -o conv_2d.o

# Compile to shared library
clang -shared -fopenmp -o libconv2d.dylib conv_2d.o

Here the -lower-affine pass lowers the affine dialect to combinations of the scf and arith dialects.

To use our parallelized code from Python, we've created a helper module to handle 2D array conversions between NumPy and MLIR MemRef descriptors. The module provides utilities for converting NumPy arrays and running the compiled MLIR code:

import ctypes
import numpy as np
from ctypes import c_void_p, c_longlong, Structure


class MemRef2DDescriptor(Structure):
    """Structure matching MLIR's 2D MemRef descriptor"""

    _fields_ = [
        ("allocated", c_void_p),  # Allocated pointer
        ("aligned", c_void_p),  # Aligned pointer
        ("offset", c_longlong),  # Offset in elements
        ("shape", c_longlong * 2),  # Array shape (2D)
        ("stride", c_longlong * 2),  # Strides in elements
    ]


def numpy_to_memref2d(arr):
    """Convert a 2D NumPy array to a MemRef descriptor"""
    if not arr.flags["C_CONTIGUOUS"]:
        arr = np.ascontiguousarray(arr)

    desc = MemRef2DDescriptor()
    desc.allocated = arr.ctypes.data_as(c_void_p)
    desc.aligned = desc.allocated
    desc.offset = 0
    desc.shape[0] = arr.shape[0]
    desc.shape[1] = arr.shape[1]
    desc.stride[0] = arr.strides[0] // arr.itemsize
    desc.stride[1] = arr.strides[1] // arr.itemsize

    return desc


def run_conv2d():
    """Run 2D convolution using MLIR compiled module"""
    # Create input arrays
    input_matrix = np.ones((10, 10), dtype=np.float32)
    conv_filter = np.arange(9, dtype=np.float32).reshape(3, 3)
    result = np.zeros((8, 8), dtype=np.float32)

    # Load compiled module
    module = ctypes.CDLL("./libconv2d.dylib")

    # Prepare MemRef descriptors
    input_memref = numpy_to_memref2d(input_matrix)
    filter_memref = numpy_to_memref2d(conv_filter)
    result_memref = numpy_to_memref2d(result)

    # Set function argument types
    module.conv_2d.argtypes = [
        *[type(x) for x in input_memref._fields_],
        *[type(x) for x in filter_memref._fields_],
        *[type(x) for x in result_memref._fields_],
    ]

    # Call the function
    module.conv_2d(
        *[getattr(input_memref, field[0]) for field in input_memref._fields_],
        *[getattr(filter_memref, field[0]) for field in filter_memref._fields_],
        *[getattr(result_memref, field[0]) for field in result_memref._fields_]
    )

    return result


if __name__ == "__main__":
    result = run_conv2d()
    print(result)

OpenMP

While the affine dialect provides abstractions for parallel execution, sometimes we want more direct control over parallelization. This is where OpenMP comes in. OpenMP is a directive-based model that provides explicit control over parallel execution, making it a popular choice in high-performance computing.

Let's look at a simple example in C that demonstrates OpenMP parallelization:

#include <stdlib.h>
#include <stdio.h>
#include <omp.h>

int kernel(float *input, float *output) {
    #pragma omp parallel
    {
        #pragma omp for
        for (int i = 0; i < 10; i++) {
            output[i] = input[i] * 2.0f;
        }
    }
}

int main() {
    float input[10] = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10};
    float output[10];
    kernel(input, output);
    for (int i = 0; i < 10; i++) {
        printf("%f ", output[i]);
    }
    return 0;
}

When compiled with OpenMP support (clang -fopenmp), this program will parallelize the loop across multiple threads. The same computation can be expressed in MLIR with the OpenMP dialect:

Parallel Regions (omp.parallel)

OpenMP organizes parallel execution through the concept of parallel regions. In MLIR, these are represented by the omp.parallel construct, which creates a team of threads that can execute code concurrently. This provides a more explicit way to control parallelization compared to the automatic parallelization we saw with the affine dialect.

The region is terminated with an omp.terminator operation, which is required for all OpenMP regions.

Worksharing Loops (omp.wsloop)

For parallel loops, the OpenMP dialect provides the omp.wsloop operation, which specifies that loop iterations will be executed in parallel by threads in the current context. Worksharing loops are typically used within parallel regions to distribute loop iterations across available threads:

omp.wsloop {
  omp.loop_nest (%i1, %i2) : index = (%c0, %c0) to (%c10, %c10) step (%c1, %c1) {
    %a = load %arrA[%i1, %i2] : memref<?x?xf32>
    %b = load %arrB[%i1, %i2] : memref<?x?xf32>
    %sum = arith.addf %a, %b : f32
    store %sum, %arrC[%i1, %i2] : memref<?x?xf32>
    omp.yield
  }
}

This example shows a nested loop being parallelized to add two matrices. The omp.loop_nest operation inside the omp.wsloop represents the nested loop structure with iteration variables, bounds, and steps.

Synchronization with Barriers (omp.barrier)

For thread synchronization, the OpenMP dialect provides the omp.barrier operation, which specifies an explicit barrier at the point where it appears. This ensures that all threads in a team reach the barrier before any thread proceeds:

// Code executed by all threads
omp.barrier
// Code executed after all threads reach the barrier

The omp.barrier operation is a simple operation without inputs or outputs, and its assembly format just includes the name and any attributes.

`omp` Dialect

Let's translate the above C code of a parallel loop to MLIR:

func.func private @kernel(%input: memref<10xf32>, %output: memref<10xf32>) {
  %loop_ub = llvm.mlir.constant(9 : i32) : i32
  %loop_lb = llvm.mlir.constant(0 : i32) : i32
  %loop_step = llvm.mlir.constant(1 : i32) : i32

  omp.parallel {
      omp.wsloop {
        omp.loop_nest (%i) : i32 = (%loop_lb) to (%loop_ub) inclusive step (%loop_step) {
          %ix = arith.index_cast %i : i32 to index
          %input_val = memref.load %input[%ix] : memref<10xf32>
          %two = arith.constant 2.0 : f32
          %result = arith.mulf %input_val, %two : f32
          memref.store %result, %output[%ix] : memref<10xf32>
          omp.yield
        }
      }
    omp.barrier
    omp.terminator
  }

  return
}

And then we can have a main function that calls the kernel over a static defined input:

memref.global constant @input : memref<10xf32> = dense<[1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0]>

// Define external references to printf and kernel
llvm.func @printf(!llvm.ptr, ...) -> i32
func.func private @kernel(%input: memref<10xf32>, %output: memref<10xf32>) -> ()

func.func @main() {
  %input = memref.get_global @input : memref<10xf32>
  %output = memref.alloc() : memref<10xf32>

  func.call @kernel(%input, %output) : (memref<10xf32>, memref<10xf32>) -> ()

  %lb = index.constant 0
  %ub = index.constant 10 
  %step = index.constant 1

  %fs = llvm.mlir.addressof @fmt : !llvm.ptr

  scf.for %iv = %lb to %ub step %step {
    %el = memref.load %output[%iv] : memref<10xf32>
    llvm.call @printf(%fs, %el) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, f32) -> i32
  }

  return
}

// Define a constant string for the format specifier
llvm.mlir.global private constant @fmt("%f\0A\00") {addr_space = 0 : i32}

As an aside, variadic functions in MLIR allow for flexible argument passing, similar to C. A common pattern we'll use is calling functions like printf, which can take a variable number of arguments. In the main function, we're calling the printf function (which is variadic) to print the result. The following is equivalent to printf("%f\n", el) in C, demonstrating how to use printf in MLIR.

// Define external printf function from stdio.h
llvm.func @printf(!llvm.ptr, ...) -> i32

// Define a constant string for the format specifier
llvm.mlir.global private constant @fmt("%f\0A\00") {addr_space = 0 : i32}

// Call the variadic printf function with the format specifier and type specialized arguments
%fs = llvm.mlir.addressof @fmt : !llvm.ptr
%el = llvm.mlir.constant(1.0 : f32) : f32
llvm.call @printf(%fs, %el) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, f32) -> i32

Here's the full example with the parallel loop and the main function:

memref.global constant @input : memref<10xf32> = dense<[1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0]>

llvm.func @printf(!llvm.ptr, ...) -> i32
llvm.mlir.global private constant @fmt("%f\0A\00") {addr_space = 0 : i32}

func.func private @kernel(%input: memref<10xf32>, %output: memref<10xf32>) {
  %loop_ub = llvm.mlir.constant(9 : i32) : i32
  %loop_lb = llvm.mlir.constant(0 : i32) : i32
  %loop_step = llvm.mlir.constant(1 : i32) : i32

  omp.parallel {
      omp.wsloop {
        omp.loop_nest (%i) : i32 = (%loop_lb) to (%loop_ub) inclusive step (%loop_step) {
          %ix = arith.index_cast %i : i32 to index
          %input_val = memref.load %input[%ix] : memref<10xf32>
          %two = arith.constant 2.0 : f32
          %result = arith.mulf %input_val, %two : f32
          memref.store %result, %output[%ix] : memref<10xf32>
          omp.yield
        }
      }
    omp.barrier
    omp.terminator
  }

  return
}

func.func private @main() {
  %input = memref.get_global @input : memref<10xf32>
  %output = memref.alloc() : memref<10xf32>

  call @kernel(%input, %output) : (memref<10xf32>, memref<10xf32>) -> ()

  %lb = index.constant 0
  %ub = index.constant 10 
  %step = index.constant 1

  %fs = llvm.mlir.addressof @fmt : !llvm.ptr

  scf.for %iv = %lb to %ub step %step {
    %el = memref.load %output[%iv] : memref<10xf32>
    llvm.call @printf(%fs, %el) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, f32) -> i32
  }

  return
}

SCF to OpenMP Conversion Pass

The -convert-scf-to-openmp pass automatically converts parallel loops from the SCF dialect into equivalent OpenMP operations. This pass is particularly useful when you want to target OpenMP execution without manually writing OpenMP dialect code.

For example, an SCF parallel loop like this:

scf.parallel (%i) = (%c0) to (%c100) step (%c1) {
  %val = memref.load %A[%i] : memref<100xf32>
  %result = arith.addf %val, %val : f32
  memref.store %result, %B[%i] : memref<100xf32>
  scf.yield
}

Will be converted to OpenMP operations:

omp.parallel {
  omp.wsloop for (%i) : i32 = (%c0) to (%c100) step (%c1) {
    %val = memref.load %A[%i] : memref<100xf32>
    %result = arith.addf %val, %val : f32
    memref.store %result, %B[%i] : memref<100xf32>
    omp.yield
  }
  omp.terminator
}

The pass handles several important conversions, including the transformation of scf.parallel operations into omp.parallel regions that contain omp.wsloop, while preserving loop bounds and step sizes. Additionally, reduction operations in SCF are mapped to OpenMP reductions, and nested parallel loops are properly managed. This conversion is typically utilized as part of a larger lowering pipeline, which is often followed by -convert-openmp-to-llvm to generate LLVM IR that can be executed with OpenMP runtime support.

External Resources

MLIR Part 2 - Memory in MLIR

Wed, 12 Mar 2025 00:00:00 +0000

Memory in MLIR

MLIR's memory architecture represents a balance between high-level abstractions and low-level efficiency. At its core, MLIR provides three primary ways to represent data: Tensors for immutable, abstract operations; MemRefs for concrete memory buffers; and LLVM-level constructs for fine-grained control. This three-layer approach allows developers to work at their preferred level of abstraction while maintaining the ability to precisely control memory when needed.

While Tensors enable clean, mathematical expressions of computations, MemRefs provide a bridge to actual memory operations, and LLVM constructs offer direct control over memory layout and access patterns. This design is based on MLIR's philosophy of progressive lowering, where high-level concepts can be systematically transformed into more concrete representations as needed for optimization and execution.

In short, Tensors are pure mathematical objects, MemRefs are concrete memory buffers, and LLVM constructs are low-level memory operations, and vectors are refrences to multiple register values that we can manipulate simultaneously. Let's start with the highest level abstraction and work our way down.

Tensors

Tensors in MLIR are immutable, high-level data structures without explicit memory locations. They represent structured data in a computation-oriented manner desigend for use in matrix-style computations often found in machine learning and linear algebra.

// 4-D static tensor with 10x10x10x10 elements of type f32
!TensorType1 = tensor<10 x 10 x 10 x 10 x f32>

// 4-D dynamic tensor with N x M x 10 x 10 elements of type f32
!TensorType2 = tensor<? x ? x 10 x 10 x f32>

// dummy example constants
%N = index.constant 2
%M = index.constant 3
%X = arith.constant 42.0 : f32

// allocate a tensor with the shape of the last 2 dimensions
%A = tensor.empty(%N, %M) : tensor<? x ? x 10 x 10 x f32>

// allocate a zero tensor with the shape of the last 2 dimensions
%B = tensor.empty() : tensor<10 x 10 x 10 x 10 x f32>

// create a tensor with the given values
%C = tensor.from_elements %X, %X, %X  : tensor<3xf32>

// Common tensor operations
%D = tensor.extract %A[%N, %M, %N, %M] : !TensorType2
%E = tensor.insert %X into %A[%N, %M, %N, %M] : !TensorType2

Tensor operations facilitate mathematical transformations in a clean, side-effect-free manner that makes analysis and optimization straightforward. For example, the identity matrix can be represented as:

\[
A_{ij} = \begin{cases}
1 & \text{if } i = j \\
0 & \text{otherwise}
\end{cases}
\]

func.func @identity(%m : index, %n : index) {
  %out = tensor.generate %m, %m {
  ^bb0(%i : index, %j : index):
      %ni = arith.index_cast %i : index to i32
      %nj = arith.index_cast %j : index to i32
      %elem = arith.cmpi eq, %ni, %nj : i32
      %elem_i32 = arith.extui %elem : i1 to i32
      tensor.yield %elem_i32 : i32
  } : tensor<?x?xi32>
  return
}

MemRefs

MemRefs are MLIR's primary abstraction for representing memory buffers. They serve as a bridge between high-level array concepts (like NumPy arrays) and low-level memory operations. A MemRef essentially represents a pointer to a region of memory with additional metadata about its structure.

A MemRef consists of several core components, these are divided into metadata and data.

Allocated Pointer: Points to the data buffer (used for deallocation)
Aligned Pointer: Points to properly aligned data
Offset: Distance (in elements) between aligned pointer start and first accessible element
Shape: Array of integers describing dimensions
Strides: Array of integers describing memory layout

In MLIR, a MemRef type is declared using syntax like:

memref<1024xf32>  // 1D array of 1024 float32 elements
memref<4x4xf64>   // 2D array of 4x4 float64 elements

Creating a Simple Array Addition Kernel

Let's create a simple example that adds two arrays using MLIR MemRefs:

module {
  func.func @array_add(%arg0: memref<1024xf32>, %arg1: memref<1024xf32>, %arg2: memref<1024xf32>) 
      attributes {llvm.emit_c_interface} {
    %c0 = arith.constant 0 : index
    %c1024 = arith.constant 1024 : index
    %c1 = arith.constant 1 : index
    
    scf.for %arg3 = %c0 to %c1024 step %c1 {
      %0 = memref.load %arg0[%arg3] : memref<1024xf32>
      %1 = memref.load %arg1[%arg3] : memref<1024xf32>
      %2 = arith.addf %0, %1 : f32
      memref.store %2, %arg2[%arg3] : memref<1024xf32>
    }

    return
  }
}

Then to compile the above MLIR code to an executable we can use the following commands:

mlir-opt array_add.mlir \
  -finalize-memref-to-llvm \
  -convert-scf-to-cf \
  -convert-cf-to-llvm \
  -convert-arith-to-llvm \
  -convert-func-to-llvm \
  -o array_add_opt.mlir

mlir-translate array_add_opt.mlir \
  -mlir-to-llvmir \
  -o array_add_opt.ll

llc -filetype=obj --relocation-model=pic arary_add.ll -o arary_add.o
clang -shared -fPIC arary_add.o -o array_add.so

NumPy Array Memory Layout

Before we integrate with Python, it's important to understand how NumPy arrays are laid out in memory:

Data Buffer: Contiguous memory block holding the actual values
Shape: Tuple describing array dimensions
Strides: Tuple describing steps (in bytes) to move in each dimension
Dtype: Data type of elements

When you allocate a NumPy array it essentially creates a PyObject wrapper around a raw memory buffer with metadata about the shape, strides, and dtype of the array. We can move this memory back and forth between Python and the JIT compiled LLVM logic without copying the data.

import ctypes
import numpy as np

a = np.array([[1, 2, 3], [4, 5, 6]], dtype=np.float32)
print(a.shape)          # (2, 3)
print(a.strides)        # (12, 4)
print(a.dtype)          # float32
print(a.itemsize)       # 4
print(a.ctypes.data)    # 0x7f926d6e2b20 (base pointer to the memory buffer)

# Get a ctypes pointer
print(a.ctypes.data_as(ctypes.POINTER(ctypes.c_float)))

By default numpy arrays are C-contiguous, which means that the memory is laid out in a row-major order. This is the most common memory layout and is the default for most NumPy operations. To calculate the memory address of the [i, j] element in a matrix we can use the following formula:

\[
\text{address} = \text{base_address} + (i \times \text{strides}[0] + j \times \text{strides}[1])
\]

For example, a row-major strided layout for memref<3x4xf32> is the same as both the following fully expanded memrefs (which are identical):

memref<3x4xf32, strided<[4, 1], offset: 0>>
memref<3x4xf32, affine_map<(i, j) -> (i, j)>>

Converting NumPy Arrays to MemRefs

To use NumPy arrays with our MLIR code, we need to create a bridge between NumPy's memory layout and MLIR's MemRef structure. We can do this by creating a Python class that matches MLIR's MemRef descriptor layout:

import numpy as np
from ctypes import c_void_p, c_longlong, Structure


class MemRefDescriptor(Structure):
    """Structure matching MLIR's MemRef descriptor"""

    _fields_ = [
        ("allocated", c_void_p),  # Allocated pointer
        ("aligned", c_void_p),  # Aligned pointer
        ("offset", c_longlong),  # Offset in elements
        ("shape", c_longlong * 1),  # Array shape (1D in this case)
        ("stride", c_longlong * 1),  # Strides in elements
    ]


def numpy_to_memref(arr):
    """Convert a NumPy array to a MemRef descriptor"""
    if not arr.flags["C_CONTIGUOUS"]:
        arr = np.ascontiguousarray(arr)

    desc = MemRefDescriptor()
    desc.allocated = arr.ctypes.data_as(c_void_p)
    desc.aligned = desc.allocated
    desc.offset = 0
    desc.shape[0] = arr.shape[0]
    desc.stride[0] = 1

    return desc

The MemRefDescriptor class mirrors the memory layout that MLIR expects:

allocated: Points to the start of the allocated memory
aligned: Points to aligned memory (often same as allocated)
offset: Number of elements to offset from the start
shape: Array dimensions (1D array in our example)
stride: Steps between elements in each dimension

The numpy_to_memref function handles the conversion by:

Ensuring the array is contiguous in memory
Creating a MemRef descriptor
Setting up the pointers to the NumPy array's data
Configuring the shape and stride information

This conversion allows us to pass NumPy arrays to MLIR functions without copying the underlying data. Let's see how to use this in practice with our array addition example.

Integrating MLIR with Python

There are two main approaches to using MLIR code from Python: compiling to a shared library and loading it, or JIT-compiling the MLIR code at runtime. Let's explore both approaches using our array addition example.

Loading Pre-compiled MLIR Code

The first approach is to compile our MLIR code into a shared library that can be loaded from Python using ctypes. This requires compiling the MLIR code ahead of time:

# Compile MLIR to shared library
mlir-opt array_add.mlir \
  --convert-tensor-to-linalg \
  --convert-linalg-to-loops \
  --convert-scf-to-cf \
  --convert-cf-to-llvm \
  --convert-math-to-llvm \
  --convert-arith-to-llvm \
  --convert-func-to-llvm \
  --convert-index-to-llvm \
  --finalize-memref-to-llvm \
  --reconcile-unrealized-casts \
  -o array_add_opt.mlir

mlir-translate --mlir-to-llvmir array_add_opt.mlir > array_add.ll
llc -filetype=obj array_add.ll -o array_add.o
clang -shared -fPIC array_add.o -o libarray_add.dylib

Then we can load and use the compiled library from Python:

import ctypes
import numpy as np
from np_memref import MemRefDescriptor, numpy_to_memref


def main():
    # Load the shared library
    lib = ctypes.CDLL("./libarray_add.dylib")

    # Get the C interface function
    array_add = lib._mlir_ciface_array_add
    array_add.argtypes = [
        ctypes.POINTER(MemRefDescriptor)
    ] * 3  # input1, input2, output
    array_add.restype = None

    # Create sample input arrays
    size = 1024
    a = np.ones(size, dtype=np.float32)
    b = np.ones(size, dtype=np.float32) * 2
    c = np.zeros(size, dtype=np.float32)

    # Convert arrays to MemRef descriptors
    a_desc = numpy_to_memref(a)
    b_desc = numpy_to_memref(b)
    c_desc = numpy_to_memref(c)

    # Call the function
    array_add(ctypes.byref(a_desc), ctypes.byref(b_desc), ctypes.byref(c_desc))

    # Verify results
    expected = a + b
    np.testing.assert_array_almost_equal(c, expected)
    print("Array addition successful!")
    print(f"First few elements: {c[:5]}")  # Should show [3.0, 3.0, 3.0, 3.0, 3.0]


if __name__ == "__main__":
    main()

This approach is simpler and more suitable for production use since the compilation is done ahead of time. The compiled library can be distributed with your Python package and loaded at runtime.

JIT Compiling MLIR at Runtime

The second approach is to JIT-compile the MLIR code at runtime using llvmlite (Python bindings for LLVM). This gives more flexibility since the MLIR code can be generated or modified at runtime:

import os
import subprocess
import numpy as np
from ctypes import CFUNCTYPE, POINTER
from np_memref import MemRefDescriptor, numpy_to_memref

import llvmlite

# Disable typed pointers for LLVM 15+ compatibility
llvmlite.opaque_pointers_enabled = True

import llvmlite.binding as llvm  # noqa: E402

# Initialize LLVM
llvm.initialize()
llvm.initialize_native_target()
llvm.initialize_native_asmprinter()


def compile_mlir_to_llvm(mlir_file_path):
    """Compile MLIR code to LLVM IR using mlir-opt and mlir-translate"""
    # Run mlir-opt to lower to LLVM dialect
    opt_cmd = [
        "mlir-opt",
        mlir_file_path,
        "--convert-tensor-to-linalg",
        "--convert-linalg-to-loops",
        "--convert-scf-to-cf",
        "--convert-cf-to-llvm",
        "--convert-math-to-llvm",
        "--convert-arith-to-llvm",
        "--convert-func-to-llvm",
        "--convert-index-to-llvm",
        "--finalize-memref-to-llvm",
        "--reconcile-unrealized-casts",
    ]

    try:
        opt_result = subprocess.run(opt_cmd, capture_output=True, text=True, check=True)
    except subprocess.CalledProcessError as e:
        print("Error running mlir-opt:")
        print("STDOUT:", e.stdout)
        print("STDERR:", e.stderr)
        raise

    # Run mlir-translate to convert to LLVM IR
    translate_cmd = ["mlir-translate", "--mlir-to-llvmir"]
    try:
        translate_result = subprocess.run(
            translate_cmd,
            input=opt_result.stdout,
            capture_output=True,
            text=True,
            check=True,
        )
    except subprocess.CalledProcessError as e:
        print("Error running mlir-translate:")
        print("STDOUT:", e.stdout)
        print("STDERR:", e.stderr)
        raise

    return translate_result.stdout


def create_execution_engine():
    """Create an ExecutionEngine suitable for JIT"""
    target = llvm.Target.from_default_triple()
    target_machine = target.create_target_machine()
    backing_mod = llvm.parse_assembly("")
    engine = llvm.create_mcjit_compiler(backing_mod, target_machine)
    return engine


def compile_and_load_mlir(mlir_file_path):
    """Compile MLIR code and load it into a JIT engine"""
    # Convert MLIR to LLVM IR
    llvm_ir = compile_mlir_to_llvm(mlir_file_path)

    # Create module from LLVM IR
    mod = llvm.parse_assembly(llvm_ir)
    mod.verify()

    # Create execution engine and add module
    engine = create_execution_engine()
    engine.add_module(mod)
    engine.finalize_object()

    return engine, mod


def main():
    # Get path to MLIR file
    current_dir = os.path.dirname(os.path.abspath(__file__))
    mlir_file = os.path.join(current_dir, "array_add.mlir")

    # Compile and load the MLIR code
    engine, mod = compile_and_load_mlir(mlir_file)

    # Get function pointer to the compiled function
    func_ptr = engine.get_function_address("_mlir_ciface_array_add")

    # Create the ctypes function wrapper
    array_add = CFUNCTYPE(
        None,
        POINTER(MemRefDescriptor),
        POINTER(MemRefDescriptor),
        POINTER(MemRefDescriptor),
    )(func_ptr)

    # Create test arrays
    size = 1024
    a = np.ones(size, dtype=np.float32)
    b = np.ones(size, dtype=np.float32) * 2
    c = np.zeros(size, dtype=np.float32)

    # Convert arrays to MemRef descriptors
    a_desc = numpy_to_memref(a)
    b_desc = numpy_to_memref(b)
    c_desc = numpy_to_memref(c)

    # Call the JIT-compiled function
    array_add(a_desc, b_desc, c_desc)

    # Verify results
    expected = a + b
    np.testing.assert_array_almost_equal(c, expected)
    print("Array addition successful!")
    print(f"First few elements: {c[:5]}")  # Should show [3.0, 3.0, 3.0, 3.0, 3.0]


if __name__ == "__main__":
    main()

The JIT compilation approach offers several advantages. First, MLIR code can be generated or modified at runtime. Second, there is no need to manage separate compiled libraries. Finally, it allows for optimization for the specific CPU architecture at runtime. However, this approach also has some drawbacks. There is compilation overhead at startup, a more complex setup with dependencies on MLIR tools, and the need to handle compilation errors at runtime.

Low-level LLVM Structures

In addition to the higher-level MLIR constructs, MLIR also provides a low-level LLVM dialect that allows for more direct control over memory layout and operations. Structs from LLVM dialect can be used to create custom types in MLIR. For example in C we would write:

struct Pair {
  int a;
  float b;
};

In MLIR we can define the same struct as follows:

!Pair = !llvm.struct<(i32, f32)>
%1 = llvm.mlir.zero : !Pair

This creates a new type alias !Pair which is a struct with two fields: an i32 and a f32. The %1 variable is then an instance of this struct with all fields initialized to zero.

LLVM arrays provide fixed-size sequential storage of elements. They can be created using the following syntax:

// Array of 10 integers
!IntArray = !llvm.array<10 x i32>

// Array of 4 pairs (using the struct defined above)
!PairArray = !llvm.array<4 x !Pair>

// Create and initialize an array
%arr = llvm.mlir.constant(dense<[1, 2, 3, 4]> : tensor<4xi32>) : !llvm.array<4 x i32>

// Access array elements
%idx = llvm.mlir.constant(2 : i32) : i32
%element = llvm.extractvalue %arr[2] : !llvm.array<4 x i32>

// Update array elements
%new_arr = llvm.insertvalue %element, %arr[0] : !llvm.array<4 x i32>

Unlike higher-level MLIR constructs like MemRefs, LLVM arrays are more rigid and closely mirror the behavior of arrays in C. They have a fixed size known at compile time and don't carry any metadata about their structure.

Vectors

MLIR's vector dialect provides a low-level abstraction for SIMD (Single Instruction, Multiple Data) operations. While it's closely aligned with hardware vector capabilities, it's not strictly limited to what the target architecture supports, thanks to LLVM's vector operation lowering and optimization capabilities.

Vectors in MLIR can be:

Single-dimensional: representing traditional SIMD registers (usually operating over 2, 4, 8 elements)
Multi-dimensional: representing higher-order vector operations

// Single-dimensional vectors
vector<4xf32>     // 4-element vector of float32
vector<8xi32>     // 8-element vector of int32

// Multi-dimensional vectors
vector<2x4xf32>   // 2x4 matrix of float32 as vectors
vector<2x2x4xf32> // 3D vector arrangement

MLIR provides vector operations that map efficiently to hardware instructions:

// Vector arithmetic
%c = vector.add %a, %b : vector<4xf32>
%d = vector.mul %a, %b : vector<4xf32>

// Vector shuffles and extracts
%e = vector.extract %c[0] : vector<4xf32>
%f = vector.shuffle %c, %d [0, 1, 4, 5] : vector<4xf32>, vector<4xf32>

// Vector fold/reduction operations
%sum = vector.reduction <add>, %c : vector<4xf32> into f32

While MLIR's vector dialect provides operations that may not directly correspond to hardware capabilities, LLVM handles the lowering process by directly mapping to hardware vectors (e.g., AVX, NEON), splitting into smaller vectors, and scalarization when necessary.

For example, a vector<8xf32> operation might be mapped directly to AVX on x86, split into two NEON operations on ARM, or scalarized on architectures without vector support.

Bufferization

Bufferization in MLIR is the process of converting ops with tensor semantics to ops with memref semantics. The process of converting computations on the mathematical tensor construct to computations on physical memory buffers.

There are two low-level operations that are used to convert tensors to memrefs. They do what they say on the tin.

bufferization.to_memref - Convert a tensor to a memref
bufferization.to_tensor - Convert a memref to a tensor

%out1 = bufferization.to_memref %result : tensor<10xf32> to memref<10xf32>
%out2 = bufferization.to_tensor %result : memref<10xf32> to tensor<10xf32>

The bufferization.materialize_in_destination operation is used to convert a tensor to a memref in the destination buffer. This is equivalent to converting the tensor to a memref and then storing the result in the destination buffer but without the intermediate step. This is often the final step of a kernel that uses an externally allocated buffer.

bufferization.materialize_in_destination %0 in restrict writable %C : (tensor<10xf32>, memref<10xf32>) -> ()

Now there are also passes that can do this conversion automatically. The one-shot-bufferize pass is a pass that can be used to convert all tensor operations to memref operations. Importantly this will not by default bufferize function boundaries (i.e. the input and output of a function are not bufferized), so we need to add the bufferize-function-boundaries flag to the pass.

mlir-opt -one-shot-bufferize="bufferize-function-boundaries"

A simple example demonstrates the transformation:

// Before bufferization
func.func @example(%arg0: tensor<8xf32>, %idx: index) -> tensor<8xf32> {
  %f = arith.constant 5.000000e+00 : f32
  %result = tensor.insert %f into %arg0[%idx] : tensor<8xf32>
  return %result : tensor<8xf32>
}

// After bufferization
func.func @example(%arg0: memref<8xf32>, %idx: index) -> memref<8xf32> {
  %f = arith.constant 5.000000e+00 : f32
  memref.store %f, %arg0[%idx] : memref<8xf32>
  return %arg0 : memref<8xf32>
}

In this case, the tensor insert operation was able to be bufferized in-place, reusing the input buffer for the output.

C-compatible wrappers

When we want to call a function from C, we need to emit a C-compatible wrapper. This is done using the llvm.emit_c_interface attribute. Normally when we bufferize a function we unroll all the memref fields into a single arguments. This is not desirable when we want to call the function from C where we would typically pass the memrefs as void pointers to structs.

func.func @add_vector_to_matrix(%A: memref<3xf32>) -> memref<3xf32> attributes {llvm.emit_c_interface} {
  return %A : memref<3xf32>
}

This will emit a C-compatible wrapper for the function which is expanded into two functions.

module {
  llvm.func @fun(%arg0: !llvm.ptr, %arg1: !llvm.ptr, %arg2: i64, %arg3: i64, %arg4: i64) -> !llvm.struct<(ptr, ptr, i64, array<1 x i64>, array<1 x i64>)> attributes {llvm.emit_c_interface} {
    %0 = llvm.mlir.poison : !llvm.struct<(ptr, ptr, i64, array<1 x i64>, array<1 x i64>)>
    %1 = llvm.insertvalue %arg0, %0[0] : !llvm.struct<(ptr, ptr, i64, array<1 x i64>, array<1 x i64>)>
    %2 = llvm.insertvalue %arg1, %1[1] : !llvm.struct<(ptr, ptr, i64, array<1 x i64>, array<1 x i64>)>
    %3 = llvm.insertvalue %arg2, %2[2] : !llvm.struct<(ptr, ptr, i64, array<1 x i64>, array<1 x i64>)>
    %4 = llvm.insertvalue %arg3, %3[3, 0] : !llvm.struct<(ptr, ptr, i64, array<1 x i64>, array<1 x i64>)>
    %5 = llvm.insertvalue %arg4, %4[4, 0] : !llvm.struct<(ptr, ptr, i64, array<1 x i64>, array<1 x i64>)>
    llvm.return %5 : !llvm.struct<(ptr, ptr, i64, array<1 x i64>, array<1 x i64>)>
  }
  llvm.func @_mlir_ciface_fun(%arg0: !llvm.ptr, %arg1: !llvm.ptr) attributes {llvm.emit_c_interface} {
    %0 = llvm.load %arg1 : !llvm.ptr -> !llvm.struct<(ptr, ptr, i64, array<1 x i64>, array<1 x i64>)>
    %1 = llvm.extractvalue %0[0] : !llvm.struct<(ptr, ptr, i64, array<1 x i64>, array<1 x i64>)>
    %2 = llvm.extractvalue %0[1] : !llvm.struct<(ptr, ptr, i64, array<1 x i64>, array<1 x i64>)>
    %3 = llvm.extractvalue %0[2] : !llvm.struct<(ptr, ptr, i64, array<1 x i64>, array<1 x i64>)>
    %4 = llvm.extractvalue %0[3, 0] : !llvm.struct<(ptr, ptr, i64, array<1 x i64>, array<1 x i64>)>
    %5 = llvm.extractvalue %0[4, 0] : !llvm.struct<(ptr, ptr, i64, array<1 x i64>, array<1 x i64>)>
    %6 = llvm.call @fun(%1, %2, %3, %4, %5) : (!llvm.ptr, !llvm.ptr, i64, i64, i64) -> !llvm.struct<(ptr, ptr, i64, array<1 x i64>, array<1 x i64>)>
    llvm.store %6, %arg0 : !llvm.struct<(ptr, ptr, i64, array<1 x i64>, array<1 x i64>)>, !llvm.ptr
    llvm.return
  }
}

Instead now we call the @_mlir_ciface_fun function which is the C-compatible wrapper for the @fun function. Notice how it's given use two arguments, one for the input (%arg0) and one for the output (%arg1). Now we can pass our own memory buffers to the function and it will write the result back to our buffer with the code generation extracting the metadata from the memref.

External References

MLIR Part 1 - Introduction to MLIR

Mon, 10 Mar 2025 00:00:00 +0000

Introduction to MLIR

LLVM is a powerful compiler infrastructure project that has revolutionized how we build programming languages and tools. At its core, LLVM provides a collection of modular compiler and toolchain technologies that can be used to develop frontend compilers for any programming language and generate optimized code for many target architectures.

MLIR is a newer project within the LLVM ecosystem, designed to address the challenges of modern hardware accelerators and machine learning frameworks. While LLVM IR is powerful, it operates at a relatively low level. MLIR extends these concepts to support multiple levels of abstraction.

Unfortunately, the modern compiler stack is often something that one has to learn from reading RFCs, papers, and mailing lists. With this tutorial, I'll try to give a concise overview of the modern compiler stack, how MLIR fits into it, and how to integrate it into the Python machine learning ecosystem.

Throughout this series we'll cover the following topics eventually leading up to compiling a small version of the GPT2 transformer model down to efficient GPU kernels.

This tutorial assumes some knowledge of C++ and advanced Python, along with passing familiarity with NVIDIA CUDA, but should otherwise be self-contained.

Why should I care?

You probably shouldn't. Writing optimizing compilers is a very niche topic. Although it's one that now with LLVM + MLIR requires a lot less knowledge than it used to even a few years ago. So if you want to write a new AI framework or experimental programming language, it's a good time. It's not strictly neccessary to learn, but then again so few things in life are.

Why MLIR?

MLIR was designed to address the limitations of traditional compilers like LLVM and GCC, particularly when dealing with modern hardware accelerators and AI workloads. While LLVM excels at traditional CPU targets, it struggles with the diverse specialized architectures emerging in AI and machine learning.

Modern AI systems typically involve a mix of CPUs, GPUs, TPUs, and custom ASICs. MLIR's flexible architecture makes it easier to work across these different platforms, providing robust support for heterogeneous hardware.

The dialect system in MLIR can represent and optimize operations at various levels, from high-level ML tasks down to hardware-specific instructions. This means we can implement optimizations tailored to specific domains, making AI workloads run more efficiently.

Instead of needing separate compilers for each type of accelerator or framework, MLIR offers a unified infrastructure that can be extended for different use cases. Traditional compilers weren’t built with AI in mind, but MLIR has first-class support for tensor operations, neural networks, transformers, and other ML constructs.

MLIR has become the go-to tech for specialized machine learning accelerators, finding applications in signal processing, quantum computing, homomorphic encryption, FPGAs, and custom silicon. Its ability to create domain-specific compilers is a game-changer for those "weird domains" that don’t fit the traditional CPU and GPU mold. Plus, it can be easily embedded in other languages, allowing us to build domain-specific languages tailored for specific tasks—something we’ll dive into in this blog.

Key Components of the Modern Compiler Stack

LLVM: The heart of LLVM is its intermediate representation - a low-level programming language similar to assembly but with important high-level information preserved. This IR serves as a bridge between source languages and target architectures.
MLIR: MLIR is a new "multi-level" intermediate representation that is more expressive and can represent higher-level concepts like control flow, dataflow, and parallelism and be lowered into LLVM IR.
Optimization Passes: Both MLIR and LLVM provide a vast set of optimization passes that work on the IR level, allowing any language using LLVM to benefit from sophisticated optimizations. Most are written by grad students and PhDs on the latest and greatest research in compiler optimization. This is what makes LLVM such a powerful tool.
E-Graphs Equality saturation is a technique for building optimizing compilers using e-graphs, which originated from the automated theorem proving world; it operates by applying a set of rewrites using e-matching until the e-graph is saturated, continuing the saturation process until one of several halting conditions is met. After the rewriting phase, an optimal term is extracted from the e-graph based on a cost function, typically related to the size of the syntax tree or performance considerations, allowing for more efficient optimizations by exploring a broader set of potential transformations and selecting the best one based on defined criteria.

A modern compiler then weaves these components together to make up a pipeline.

Source code is parsed into a surface language.
Surface language is translated to a core language.
Core langauge can be optimized by core-to-core transformations (optionally using tools like e-graphs).
Core language is lowered to MLIR.
MLIR performs high-level optimizations
MLIR is lowered to LLVM IR
LLVM performs low-level optimizations and code generation

Many programmming langauges implement the "mid-level" IR as a way to bridge the gap between the source language and LLVM. For example, Rust, Swift, Tensorflow all follow this pattern. With MLIR we have can have a new generation of programming languages and frameworks that can reuse the same infrastructure and perhaps become more interoperable, in much the same way that LLVM has become the de facto backend for many programming languages.

Installing MLIR

Installing MLIR is a bit painful, it requires a few dependencies to be installed first.

# MacOS
brew install cmake ninja ccache

# Linux
apt-get install cmake ninja-build ccache

Then we can clone the LLVM repository and build MLIR from source. This can take a long time to build, I recommend having a cup of tea while you add entropy to the universe.

git clone https://github.com/llvm/llvm-project
mkdir llvm-project/build
cd llvm-project/build
cmake -G Ninja ../llvm \
   -DLLVM_ENABLE_PROJECTS=mlir \
   -DLLVM_BUILD_EXAMPLES=ON \
   -DLLVM_TARGETS_TO_BUILD="Native;ARM;X86" \
   -DCMAKE_BUILD_TYPE=Release \
   -DLLVM_ENABLE_ASSERTIONS=ON \
   -DCMAKE_C_COMPILER=clang -DCMAKE_CXX_COMPILER=clang++ \
   -DLLVM_CCACHE_BUILD=ON
cmake --build . --target check-mlir
cmake --build . --target install

Check the version of MLIR installed. This tutorial is using version 21.0.0.

mlir-opt --version
LLVM (http://llvm.org/):
  LLVM version 21.0.0git
  Optimized build with assertions.

At some point in the near future the Homebrew version of LLVM will be updated to include MLIR, at which point this will be a lot easier. If you're reading this at some point in a better future you can just try this and it might work.

brew install llvm

MLIR Concepts

MLIR is a programming language in its own right, it's very low-level but it contains many of the core primitives you might find in other languages. First some identifier conventions:

% prefix: SSA values (e.g. %result)
@ prefix: Functions (e.g. @fun)
^ prefix: Basic blocks (e.g. ^bb0)
# prefix: Attribute aliases (e.g. #map_1d_identity)
x delimiter: Used in shapes and between shape and type (e.g. 10xf32)
: and -> are used to indicate the type of an operation or value (e.g. %result: i32)
! prefix: Type aliases (e.g. !avx_m128 = vector<4 x f32>)
() are used to represent arguments (e.g. (%arg0, %arg1))
{} are used to represent regions
// is used for comments
<> are used to indicate type parameters (e.g. tensor<10xf32>)

Modules: The top-level container for MLIR operations.
```
module {
  // Operations
}
```
Functions: A function is a collection of operations that are executed in a specific order.
```
func.func @my_function(%arg0: i32, %arg1: i32) -> i32 {
  // Operations
}
```
Dialects: Domain-specific sets of operations and types in MLIR.

The high-level ones well use are:
- tensor: This dialect provides operations for creating and manipulating multi-dimensional arrays (tensors), enabling high-level mathematical expressions and transformations in a side-effect-free manner.
- linalg: The linear algebra (linalg) dialect offers a set of operations specifically designed for linear algebra computations, facilitating efficient implementations of matrix and vector operations.
- omp: The OpenMP (omp) dialect includes operations that support parallel programming models, allowing developers to express parallelism in a way that is compatible with OpenMP standards.
- affine: The affine dialect provides a framework for expressing affine operations and analyses, enabling optimizations that leverage the predictable behavior of affine expressions.
- gpu: The GPU dialect is specialized for GPU programming, providing operations for parallel execution on heterogeneous architectures.
The lower-level ones are:
- scf: The structured control flow (scf) dialect provides operations that represent structured control flow constructs, such as loops and conditionals, ensuring a clear and maintainable flow of execution.
- func: This dialect encompasses operations related to function definitions and calls, facilitating the organization and modularization of code through high-level function abstractions.
- memref: The memref dialect is dedicated to memory reference operations, allowing for efficient management and manipulation of memory buffers, essential for performance-critical applications.
- index: The index dialect specializes in operations for handling index computations, which are crucial for addressing elements in arrays and tensors, particularly in loop iterations and data access patterns.
- arith: The arithmetic (arith) dialect contains fundamental mathematical operations for both integer and floating-point types, including basic arithmetic, bitwise operations, and comparisons, applicable to scalars, vectors, and tensors.
Additionally we'll use some hardware specific dialects for targeting NVidia GPUs, but more on that later.
Operations: The basic unit of work in MLIR, similar to LLVM instructions but with an additional dialect namespace and possible type annotations.
```
// Example of an MLIR operation
%0 = "my_dialect.my_operation"(%arg0, %arg1) : (i32, i32) -> i32
```
In this example, my_dialect.my_operation is an operation defined in the my_dialect dialect, and %arg0 and %arg1 are arguments of type i32. It returns a result of type i32 bound to the variable %0.

A concrete example would be the "arith.addf" operation, which adds two floating point numbers.
```
%0 = arith.addf %arg0, %arg1 : f32
```
Basic Blocks: Basic blocks in MLIR are sequences of operations that execute in a linear fashion without any branching. Each basic block has a single entry point and can have multiple exit points, typically through control flow operations like branches or returns. Basic blocks are essential for structuring the flow of control in a program, allowing for clear and maintainable code organization. They enable the compiler to optimize the execution path and facilitate transformations such as inlining and loop unrolling. In MLIR, basic blocks are defined within functions and can be manipulated through various dialects to represent complex control flow constructs.
```
^bb1: // Label for the then block
%then_result = arith.muli %result, 2 : i32
return %then_result : i32
```
Unike in LLVM, basic blocks can now also take arguments, which are passed in through the ^bb1(%result : i32) syntax.
Regions: Regions are a way to group operations together. They are used to represent control flow constructs like loops and conditionals. Regions are grouped together in {} blocks and can take arguments.
```
{
  ^bb1(%result : i32):
  %then_result = arith.muli %result, 2 : i32
  return %then_result : i32
}
```
Types: A type is a classification that specifies which kind of value a variable can hold and what operations can be performed on it. Types help to enforce constraints on data, ensuring that operations are performed on compatible values.
```
%result = arith.constant 1 : i32
```
We can also defined type synonyms for convenience.
```
!avx_m128 = vector<4 x f32>
```
Passes: Transformations that operate on the MLIR dialects, optimizing and lowering them into simpler constructs.

These are arguments that can be passed to mlir-opt to transform the MLIR, the most common ones are:
- convert-func-to-llvm: Convert function-like operations to LLVM dialect
- convert-math-to-llvm: Convert math operations to LLVM dialect
- convert-index-to-llvm: Convert index operations to LLVM dialect
- convert-scf-to-cf: Convert structured control flow to CF dialect
- convert-cf-to-llvm: Convert control flow to LLVM dialect
- convert-arith-to-llvm: Convert arithmetic operations to LLVM dialect
- reconcile-unrealized-casts: Reconcile unrealized casts
- convert-memref-to-llvm: Convert memref operations to LLVM dialect
- convert-tensor-to-llvm: Convert tensor operations to LLVM dialect
- convert-linalg-to-scf: Convert linalg operations to scf.for loops
- convert-linalg-to-affine-loops: Convert linalg operations to affine.for loops
- convert-omp-to-llvm: Convert OpenMP operations to LLVM dialect
- convert-vector-to-llvm: Convert vector operations to LLVM dialect
There is also a generic -convert-to-llvm pass that will convert anything that can be converted from MLRI to LLVM IR. In practice we'll use more granular passes to convert specific dialects to LLVM.

If you need more granular control over the passes you can also specify the pass names in a comma-separated list in a --pass-pipeline string, e.g., --pass-pipeline="builtin.module(pass1,pass2)". The passes will be run sequentially in one group.

Additionally there are several use flags for debugging pass transformation. The --mlir-print-ir-after-all flag prints the IR after each pass, while --mlir-print-ir-after-change and --mlir-print-ir-after-failure provide more specific output. When using any of these print-ir flags, including --mlir-print-ir-tree-dir, the IRs are written to files in a directory tree if you don't want to parse through the terminal stdout.

Note: The order of the passes can be important, for example convert-scf-to-cf must come before convert-cf-to-llvm.

Creating and Using LLVM Modules

Let's create a simple LLVM module that returns 42 as an exit code, compile it to a shared library, and use it from Python. This example demonstrates the complete pipeline from LLVM IR to usable code.

1. Writing LLVM IR

First, create a file named simple.ll with this LLVM IR:

define i32 @main() {
    ret i32 42
}

As an analogue this program is equivalent to:

int main() {
    return 42;
}

2. Compiling to a Shared Object

We can compile this LLVM IR to a shared object using clang:

llc -filetype=obj --relocation-model=pic simple.ll -o simple.o
clang -shared -fPIC simple.o -o libsimple.so
clang simple.o -o simple # optionally create an executable

Now if you run the executable you should see the output 42 returned as the exit code to the process.

$ ./simple
$ echo $?
42

3. Using from Python

Now we can use this shared library libsimple.so from Python using ctypes:

import ctypes

module = ctypes.CDLL("./libsimple.so")

module.main.argtypes = []
module.main.restype = ctypes.c_int

print(module.main())

Running this you should see the Python logic successfully call the shared library and print the result.

$ python simple.py
42

MLIR Universe

Now for a function that returns 42, it's simple enough to write in LLVM. But non-trivial programs in LLVM is not so simple, it is indeed often too "low-level" for many applications and over the years many people have constructed higher-level abstractions on top of LLVM.

For example writing loops in LLVM is actually a bit annoying as you have to manually handle blocks, phi nodes, all for a basic loop. MLIR allows us to write high-level constructs directly and have them lowered down into LLVM in a single pass.

4. Writing MLIR

First, create a file named simple.mlir with this MLIR:

func.func @loop_add() -> (index) {
    %init = index.constant 0
    %lb = index.constant 0
    %ub = index.constant 10
    %step = index.constant 1

    %sum = scf.for %iv = %lb to %ub step %step iter_args(%acc = %init) -> (index) {
        %sum_next = arith.addi %acc, %iv : index
        scf.yield %sum_next : index
    }

    return %sum : index
}

func.func @main() -> i32 {
    %out = call @loop_add() : () -> index
    %out_i32 = arith.index_cast %out : index to i32
    func.return %out_i32 : i32
}

In C this is equivalent to:

int loop_add(int lb, int ub, int step) {
  int sum_0 = 0;
  int sum = sum_0;
  for (int iv = lb; iv < ub; iv += step) {
    sum_next = sum + iv;
    sum = sum_next;
  }
  return sum;
}

int main() {
  int out = loop_add(0, 10, 1);
  return out;
}

4. Lowering to LLVM Dialect

LLVM IR is based on Static Single Assignment, which means that every variable is assigned exactly once and every use of a variable must be dominated by its definition. In SSA, instead of variables being reassigned multiple times, each new "assignment" creates a new version of the variable, typically denoted with a numbered suffix (like %1, %2, etc.). This property makes many compiler optimizations simpler and more effective because the relationships between definitions and uses are explicit and unambiguous.

For example, in LLVM IR, you might see code like:

%1 = add i32 %a, %b
%2 = mul i32 %1, %c

Here, %1 and %2 are SSA values that can never be reassigned. When control flow requires a variable to have different values depending on the path taken (like after an if-statement), LLVM uses special "phi" nodes to merge the different possible values, maintaining the SSA property while handling dynamic program behavior.

In LLVM basic blocks are the basic unit of control flow, they are a sequence of instructions that are executed sequentially. A basic block has one entry and one exit point.

Phi nodes are special instructions in SSA-based intermediate representations that resolve multiple potential values from different control flow paths into a single value. They're essentially control-flow-aware multiplexers that select the appropriate value based on which path the program took to reach that point.

entry:
  br i1 %cond, label %then, label %else

then:
  %x.1 = add i32 1, 2
  br label %merge

else:
  %x.2 = mul i32 3, 4
  br label %merge

merge:
  %x.3 = phi i32 [ %x.1, %then ], [ %x.2, %else ]
  ret i32 %x.3

In this example, the phi node %x.3 will take the value of %x.1 (which is 3) if control flow came from the then block, or %x.2 (which is 12) if it came from the else block. The syntax [ value, predecessor_block ] specifies which value to use depending on which block was previously executed.

We can lower the high-level MLIR to LLVM dialect using mlir-opt. Essentially reducing the loop constructs to the branches over blocks statements.

mlir-opt example.mlir \
  --convert-func-to-llvm \
  --convert-math-to-llvm \
  --convert-index-to-llvm \
  --convert-scf-to-cf \
  --convert-cf-to-llvm \
  --convert-arith-to-llvm \
  --reconcile-unrealized-casts \
  -o example_opt.mlir

This will produce the following MLIR:

module {
  llvm.func @loop_add() -> i64 {
    %0 = llvm.mlir.constant(0 : i64) : i64
    %1 = llvm.mlir.constant(0 : i64) : i64
    %2 = llvm.mlir.constant(10 : i64) : i64
    %3 = llvm.mlir.constant(1 : i64) : i64
    llvm.br ^bb1(%1, %0 : i64, i64)
  ^bb1(%4: i64, %5: i64):  // 2 preds: ^bb0, ^bb2
    %6 = llvm.icmp "slt" %4, %2 : i64
    llvm.cond_br %6, ^bb2, ^bb3
  ^bb2:  // pred: ^bb1
    %7 = llvm.add %5, %4 : i64
    %8 = llvm.add %4, %3 : i64
    llvm.br ^bb1(%8, %7 : i64, i64)
  ^bb3:  // pred: ^bb1
    llvm.return %5 : i64
  }
  llvm.func @main() -> i32 {
    %0 = llvm.call @loop_add() : () -> i64
    %1 = llvm.trunc %0 : i64 to i32
    llvm.return %1 : i32
  }
}

We can use the mlir-cpu-runner to run the main function directly from MLIR code.

mlir-cpu-runner -e main -entry-point-result=i32 simple_opt.mlir

# To use the runner utils (e.g. for debug printing)
# mlir-cpu-runner -e main -entry-point-result=i32 -shared-libs=/opt/homebrew/opt/llvm/lib/libmlir_runner_utils.dylib simple_opt.mlir

5. Compiling to a Shared Object

From there is a direct translation of the MLIR to LLVM IR using mlir-translate. We can compile this MLIR to a shared object using mlir-translate:

mlir-translate simple_opt.mlir -mlir-to-llvmir -o simple.ll
llc -filetype=obj --relocation-model=pic simple.ll -o simple.o
clang -shared -fPIC simple.o -o libsimple.so

The LLVM them compiles down into assembly (in this case ARM64 assembly).

_loop_add:
sub     sp, sp, #0x30
mov     x8, #0x0
mov     x9, x8
str     x9, [sp, #0x20]
str     x8, [sp, #0x28]
b       0x100003f10
ldr     x9, [sp, #0x20]
ldr     x8, [sp, #0x28]
str     x8, [sp, #0x8]
str     x9, [sp, #0x10]
subs    x9, x9, #0xa
str     x8, [sp, #0x18]
b.ge    0x100003f4c
b       0x100003f30
ldr     x9, [sp, #0x10]
ldr     x8, [sp, #0x8]
add     x8, x8, x9
add     x9, x9, #0x1
str     x9, [sp, #0x20]
str     x8, [sp, #0x28]
b       0x100003f10
ldr     x0, [sp, #0x18]
add     sp, sp, #0x30
ret

Standard MLIR Dialects

`llvm`

The llvm dialect is the dialect that represents LLVM IR. It is the lowest level dialect in the MLIR hierarchy, it directly passes through to LLVM IR.

`scf` and `cf`

All higher-level 'scf' structures compile into 'cf' constructs.

cf.br - A branch to a basic block
cf.cond_br - A conditional branch to a basic block
cf.switch - A switch to a basic block

An unconditonal branch is a branch that always goes to the same basic block.

// A basic block
^bb0:
  cf.br ^bb1

A conditional branch is a branch that goes to a different basic block depending on a condition variable (here %c).

// A conditional branch to a basic block
^bb0:
  cf.cond_br %c, ^bb1, ^bb2

A switch is a branch that goes to a different basic block depending on a switch variable (here %i).

// A switch to a basic block
^bb0:
  cf.switch %i, ^bb1, ^bb2, ^bb3

For example we could put these constructs together to create a function that selects between two values based on a boolean flag returning one of the given arguments.

func.func @select(%a: i32, %b: i32, %flag: i1) -> i32 {
  cf.cond_br %flag, ^bb1(%a : i32), ^bb1(%b : i32)

^bb1(%x : i32) :
  return %x : i32
}

The most basic structured control flow construct is the scf.if construct.

scf.if %b  {
  // true region
} else {
  // false region
}

Like we did a above a for loop is a structured control flow construct, it has a single entry and a single exit point.

%lb = index.constant 0
%ub = index.constant 10
%step = index.constant 1

scf.for %iv = %lb to %ub step %step {
  // loop region
}

This would be lowered with the convert-scf-to-cf pass into a sequence of cf.br and cf.cond_br operations.

`arith` and `math`

The arith dialect includes basic operations like:

Integer arithmetic: addi, subi, muli, divsi (signed), divui (unsigned)
Floating point arithmetic: addf, subf, mulf, divf
Comparisons: cmpi (integer), cmpf (float)
Conversions: extsi (sign extend), extui (zero extend), trunci, fptoui, fptosi, uitofp, sitofp
Bitwise operations: andi, ori, xori

Example of arithmetic operations:

func.func @arithmetic_example(%a: i32, %b: f32) -> i32 {
    // Integer addition
    %1 = arith.constant 42 : i32
    %2 = arith.addi %a, %1 : i32

    // Float to integer conversion
    %3 = arith.fptosi %b : f32 to i32

    // Final addition
    %4 = arith.addi %2, %3 : i32
    return %4 : i32
}

The math dialect provides more complex mathematical operations:

Trigonometric: sin, cos, tan
Exponential: exp, exp2, log, log2, log10
Power functions: pow, sqrt
Special functions: erf, atan2
Constants: constant

Example using math operations:

func.func @math_example(%x: f32) -> f32 {
    // Calculate sin(x) * sqrt(x)
    %1 = math.sin %x : f32
    %2 = math.sqrt %x : f32
    %3 = arith.mulf %1, %2 : f32
    return %3 : f32
}

The passes -convert-math-to-llvm and -convert-arith-to-llvm will convert the math and arithmetic operations to basic LLVM operation equivalents.

`index`

The index dialect is specialized for handling index computations and is particularly important for array/tensor operations. An index type in MLIR is a platform-specific sized integer used for addressing and loop induction variables.

Key index operations include:

index.constant: Create an index constant
index.add: Add two indices
index.sub: Subtract two indices
index.mul: Multiply two indices
index.cmp: Compare two indices
index.divs: Signed division of indices
index.rems: Signed remainder of indices

Index operations are used to compute the offset of an element in an array. For example, the following function computes the offset of an element in a 2D array. We can treat them as natural number operations as they are always non-negative.

func.func @compute_offset(%i: index, %j: index, %stride: index) -> index {
    // Compute row-major array offset: i * stride + j
    %1 = index.mul %i, %stride
    %2 = index.add %1, %j
    return %2 : index
}

The pass -convert-index-to-llvm will convert the index dialect to the LLVM dialect.

The index type is particularly useful when working with tensors and memory layouts, as it provides a natural way to express array indices and dimensions. It's used in conjunction with the memref and tensor dialects for array access patterns. Which we'll cover next.

External Resources

MLIR Part 0 - Installing MLIR

Fri, 07 Mar 2025 00:00:00 +0000

MLIR Part 0 - Installing MLIR

Installing MLIR can be a royal pain, so here are some notes on how to do it via various methods.

From Homebrew (macOS)

The simplest way to install MLIR on macOS is through Homebrew. This will install the latest stable version of LLVM which includes MLIR tools and libraries.

brew install llvm@20

Using Apt (Ubuntu 22.04)

For Ubuntu users, the official LLVM APT repository provides pre-built packages for MLIR. This method ensures you get a properly configured build with all necessary dependencies.

wget -qO- https://apt.llvm.org/llvm-snapshot.gpg.key | tee /etc/apt/trusted.gpg.d/apt.llvm.org.asc
add-apt-repository "deb http://apt.llvm.org/jammy/ llvm-toolchain-jammy-20 main"
apt-get update
apt-get install -y libmlir-20-dev mlir-20-tools

Using `llvm.sh`

The LLVM project provides an installation script that automatically sets up the APT repository and installs LLVM/MLIR. This is a convenient method for Ubuntu/Debian systems that handles repository setup automatically.

bash -c "$(wget -O - https://apt.llvm.org/llvm.sh)"

To install a specific version of LLVM:

wget https://apt.llvm.org/llvm.sh
chmod +x llvm.sh
sudo ./llvm.sh 20

Precompiled Packages

For users who prefer to download pre-compiled Linux binaries, the LLVM project provides official release packages. These are useful when you need a specific version or want to avoid compilation time. In general these packages are best effort and may not work with your distribution / glibc setup.

Download the appropriate precompiled release package from the LLVM releases page. Look for files named:
- mlir-<version>.src.tar.xz (e.g., mlir-20.1.4.src.tar.xz)
Extract the archive to your desired location:

tar xf mlir-<version>.src.tar.xz

Add the binaries to your PATH. You can either:

Move the extracted directory to a system location:

sudo mv mlir-<version>.src /usr/local/mlir
echo 'export PATH=/usr/local/mlir/bin:$PATH' >> ~/.bashrc

Or add the current location to your PATH:

echo 'export PATH=/path/to/mlir-<version>.src/bin:$PATH' >> ~/.bashrc

Verify the installation:

mlir-opt --version

Note: While precompiled packages save build time, they may not include all optimizations that would be available in a custom build from source.

From Source (macOS)

Building from source on macOS gives you the most control over the build configuration and ensures you have the latest features. This method requires more time and disk space but provides the most flexibility.

brew install cmake cache ninja
git clone https://github.com/llvm/llvm-project.git
mkdir llvm-project/build
cd llvm-project/build
cmake -G Ninja ../llvm \
   -DLLVM_ENABLE_PROJECTS=mlir \
   -DLLVM_BUILD_EXAMPLES=ON \
   -DLLVM_TARGETS_TO_BUILD="Native" \
   -DCMAKE_BUILD_TYPE=Release \
   -DLLVM_ENABLE_ASSERTIONS=ON \
   -DCMAKE_C_COMPILER=clang -DCMAKE_CXX_COMPILER=clang++ \
   -DLLVM_CCACHE_BUILD=ON
cmake --build . -t mlir-opt mlir-translate mlir-transform-opt mlir-runner
cmake --build . -t install

From Source (Ubuntu 22.04)

Building from source on Ubuntu allows for complete customization of the MLIR build. This method is recommended for developers who need to modify MLIR or want to ensure specific optimizations are enabled.

sudo apt-get install clang lld
git clone https://github.com/llvm/llvm-project.git
mkdir llvm-project/build
cd llvm-project/build
cmake -G Ninja ../llvm \
   -DLLVM_ENABLE_PROJECTS=mlir \
   -DLLVM_BUILD_EXAMPLES=ON \
   -DLLVM_TARGETS_TO_BUILD="Native" \
   -DCMAKE_BUILD_TYPE=Release \
   -DLLVM_ENABLE_ASSERTIONS=ON \
   -DCMAKE_C_COMPILER=clang -DCMAKE_CXX_COMPILER=clang++ \
   -DLLVM_CCACHE_BUILD=ON
cmake --build . -t mlir-opt mlir-translate mlir-transform-opt mlir-runner
cmake --build . -t install

From Wheel (pip)

For Python users, pre-built wheels are available through a custom repository. This is the easiest way to get started with MLIR in Python projects.

pip install mlir -f https://github.com/makslevental/mlir-wheels/releases/expanded_assets/latest

From Wheel (Poetry)

Poetry users can install MLIR through a custom source repository. This method integrates well with Python dependency management and provides version control capabilities.

[tool.poetry.dependencies]
python = "^3.12"
mlir = { version = "latest", source = "mlir-wheels"}

[[tool.poetry.source]]
name = "mlir-wheels"
url = "https://github.com/makslevental/mlir-wheels/releases/expanded_assets/latest"
priority = "supplemental"

Then to check that it works:

poetry run mlir-opt --version

From Wheel (uv)

The uv package manager provides a modern alternative for installing MLIR wheels. This method is particularly fast and efficient for Python projects.

uv add mlir --index mlir=https://github.com/makslevental/mlir-wheels/releases/expanded_assets/latest

For uv users, you can also specify the dependencies in a pyproject.toml file. This approach provides a declarative way to manage your project's dependencies. Add the following to your pyproject.toml file:

[project]
dependencies = ["mlir"]

[tool.uv.sources]
mlir = { index = "mlir-wheels" }

[[tool.uv.index]]
name = "mlir-wheels"
url = "https://github.com/makslevental/mlir-wheels/releases/expanded_assets/latest"

Then to check that it works:

uv run mlir-opt --version

Using Conda

Conda can be used to install both MLIR and the Python bindings.

conda install conda-forge::mlir

Using Docker

For users who prefer containerized environments, pre-built Docker images are available with MLIR pre-installed that I maintain here: https://github.com/sdiehl/docker-mlir-cuda. These images come in both CUDA and non-CUDA variants, supporting both Ubuntu 22.04 and 24.04.

# Ubuntu 24.04 Images
# With CUDA
docker pull ghcr.io/sdiehl/docker-mlir-cuda:mlir20-cuda-ubuntu24.04
docker pull ghcr.io/sdiehl/docker-mlir-cuda:mlir19-cuda-ubuntu24.04

# Without CUDA
docker pull ghcr.io/sdiehl/docker-mlir-cuda:mlir20-ubuntu24.04
docker pull ghcr.io/sdiehl/docker-mlir-cuda:mlir19-ubuntu24.04

# Ubuntu 22.04 Images
# With CUDA
docker pull ghcr.io/sdiehl/docker-mlir-cuda:mlir20-cuda-ubuntu22.04
docker pull ghcr.io/sdiehl/docker-mlir-cuda:mlir19-cuda-ubuntu22.04

# Without CUDA
docker pull ghcr.io/sdiehl/docker-mlir-cuda:mlir20-ubuntu22.04
docker pull ghcr.io/sdiehl/docker-mlir-cuda:mlir19-ubuntu22.04

To run any of these images interactively:

docker run -it ghcr.io/sdiehl/docker-mlir-cuda:<tag> bash

For example, to run the CUDA-enabled MLIR 20.1.4 for Ubuntu 24.04:

docker run -it ghcr.io/sdiehl/docker-mlir-cuda:mlir20-cuda-ubuntu24.04 bash

You can also use these images as a base in your own Dockerfile:

FROM ghcr.io/sdiehl/docker-mlir-cuda:<tag>

Replace <tag> with your desired version (e.g., mlir20-cuda-ubuntu24.04). For example, to pull CUDA-enabled MLIR 20.1.4 for Ubuntu 24.04:

docker pull ghcr.io/sdiehl/docker-mlir-cuda:mlir20-cuda-ubuntu24.04

Installing MLIR Python Bindings

The MLIR Python bindings are a separate package that can be installed using your favorite Python package manager. Once you've installed the mlir-wheels index (as above), you can install the Python bindings with one of the following commands:

pip install mlir-python-bindings -f https://github.com/makslevental/mlir-wheels/releases/expanded_assets/latest

poetry add mlir-python-bindings

uv add mlir --index mlir=https://github.com/makslevental/mlir-wheels/releases/expanded_assets/latest

conda install conda-forge::mlir-python-bindings

If that doesn't work then you'll need to build them inside of the LLVM source tree from source with the DMLIR_ENABLE_BINDINGS_PYTHON flag.

sudo apt-get install -y \
  bash-completion \
  ca-certificates \
  ccache \
  clang \
  cmake \
  cmake-curses-gui \
  git \
  lld \
  man-db \
  ninja-build \
  pybind11-dev \
  python3 \
  python3-numpy \
  python3-pybind11 \
  python3-yaml \
  unzip \
  wget \
  xz-utils

git clone https://github.com/wjakob/nanobind && \
  cd nanobind && \
  git submodule update --init --recursive && \
  cmake \
    -G Ninja \
    -B build \
    -DCMAKE_CXX_COMPILER=clang++ \
    -DCMAKE_C_COMPILER=clang \
    -DCMAKE_INSTALL_PREFIX=$HOME/usr && \
  cmake --build build --target install

cmake llvm \
  -G Ninja \
  -B build \
  -DCMAKE_BUILD_TYPE=RelWithDebInfo \
  -DCMAKE_CXX_COMPILER=clang++ \
  -DCMAKE_C_COMPILER=clang \
  -DCMAKE_PREFIX_PATH=$HOME/usr \
  -DLLVM_BUILD_EXAMPLES=On \
  -DLLVM_TARGETS_TO_BUILD="Native" \
  -DLLVM_CCACHE_BUILD=On \
  -DLLVM_CCACHE_DIR=$HOME/ccache \
  -DLLVM_ENABLE_ASSERTIONS=On \
  -DLLVM_ENABLE_LLD=On \
  -DLLVM_ENABLE_PROJECTS="mlir;clang;clang-tools-extra" \
  -DLLVM_USE_SPLIT_DWARF=On \
  -DMLIR_ENABLE_BINDINGS_PYTHON=On \
  -DPython3_EXECUTABLE=/usr/bin/python3 \ # change this to your python executable
  -DMLIR_INCLUDE_INTEGRATION_TESTS=On

cmake --build build -t mlir-opt mlir-translate mlir-transform-opt mlir-runner
cmake --build build -t install

The binding are then built to:

build/tools/mlir/python_packages/mlir_core/mlir

You can then package them up with the following setup.py:

cd build/tools/mlir/python_packages/mlir_core
python setup.py bdist_wheel

And install them with:

pip install dist/mlir_core-*.whl

Or you can add them to your PYTHONPATH manually. Adjust the $HOME to be the place where you built the MLIR source tree.

export PYTHONPATH=$PYTHONPATH:$HOME/build/tools/mlir/python_packages/mlir_core

SGLang on AMD MI300X

Tue, 04 Mar 2025 00:00:00 +0000

SGLang on AMD MI300X

The best kept secret these days is that new AMD GPUs are incredibly cost efficient for doing inference. If you want the cliff-notes on getting an extremely fast inference server running on a fleet of AMD MI300X, here you go:

If you're serving high-throughput inference, your options for inference servers are essentially:

TensorRT-LLM: NVIDIA's high-performance deep learning inference library that optimizes models for deployment on GPUs, focusing on low-latency and high-throughput.
vLLM: A versatile framework for serving large language models, particularly well-suited for Kubernetes environments and high-throughput inference scenarios.
SGLang: A framework designed for efficient inference with advanced features like zero overhead batch scheduling and optimized attention kernels.

In my experience, SGLang is the easiest to get running. Although if you're using kserve to manage your Kubernetes inference service then you'll probably end up using vLLM because of network effects and lock-in.

SGLang perfmance is extremely good though, with zero overhead batch scheduling with FlashInfer attention kernels and RadixAttention for automatic KV cache reuse there's a lot of optimizations that can yield performance gains. SGLang also has an extremely fast constrained decoding algorithm if you're handlings lots of JSON output.

Setup

To get started, pull the latest SGLang image:

docker pull rocm/sglang-staging:latest

Run the container.

docker run -d \
  -it \
  --ipc=host \
  --network=host \
  --privileged \
  --device=/dev/kfd \
  --device=/dev/dri \
  --device=/dev/mem \
  --group-add render \
  --security-opt seccomp=unconfined \
  -v /home:/workspace \
  rocm/sglang-staging:latest

Then get the container id and run the following command to get a shell into the container.

docker exec -it $CONTAINER_ID bash

Then login to Hugging Face.

huggingface-cli login

Then run the following command to start the server, we'll use the DeepSeek-R1 model and quantize it to FP8.

HSA_NO_SCRATCH_RECLAIM=1 python -m sglang.launch_server \
  --model deepseek-ai/DeepSeek-R1 \
  --tp 8 \
  --quant fp8 \
  --trust-remote-code \
  --port 8000

Then run the following command to start the client.

import openai

port = 8000
client = openai.Client(base_url=f"http://127.0.0.1:{port}/v1", api_key="None")

response = client.chat.completions.create(
    model="deepseek-ai/DeepSeek-R1",
    messages=[
        {"role": "user", "content": "Who wrote the Simarillion?"},
    ],
    temperature=0,
    max_tokens=64,
)

print_highlight(f"Response: {response}")

There are also some other tricks you can do to get better performance. For example, you can disable NUMA balancing.

sudo sh -c 'echo 0 > /proc/sys/kernel/numa_balancing'

For more tuning guides, see the AMD documentation:

How to Make a Universe

Sun, 16 Feb 2025 00:00:00 +0000

How to Make a Universe

There's a new paper How to Make a Universe by Bassani and Magueijo on the quantum cosmology arXiv that proposes a curious and clever new cosmology. They propose that the fundamental constants ($c, G, \hbar, k_B, e$) are not fixed numbers, but instead evolve through a process akin to natural selection. Unlike the cosmological natural selection proposed by Smolin, this paper doesn't require any kind of anthropic reasoning, multiverses, or black hole assumptions, instead if just presuppositionally requires a universe in which the physical laws are not fixed but evolve according to a deeper mathematical structure. And most interestingly an evolution of the laws of physics and matter creation/destruction are intertwined! I'm far far outside the field anymore, but I'm always interested in clever new ideas, so I thought I'd try to digest it for a lay audience.

Their core premise is trying to understand the origin of the universe, not as a singular event meticulously preordained, but as the outcome of a process akin to natural selection, with selection happening on the fundamental laws of physics themselves. Essentially order arising from chaos, as many pre-scientific theories have proposed. They challenge the conventional view of immutable laws and constants, proposing a dynamic environment where variations in these parameters play a crucial role in shaping the cosmos we observe. The paper marries extensions of unimodular gravity with absorbing Markov chains, to paint a picture of a universe sculpted by chaos and selection.

At the heart of their model lies the idea that the "laws" of physics are not fixed entities from the beginning, but rather evolve through a period of extreme variability. This "higgledy-piggledy" phase, reminiscent of Wheeler's vision of a chaotic cosmic start, allows for the exploration of a vast space of possible physical realities. The paper explores ways to link the degree of the "lawlessness" to matter generation, in what can be seen as an implementation of Noether's theorem. They suggest this variability is not entirely random; it is driven by a deterministic process (the mechanism isn't specified) that favors certain configurations over others.

The authors introduce the distinction between local and global variables. Local variables, such as the position and momentum of particles, describe the properties of spacetime at a given point. Global variables, on the other hand, characterize the universe as a whole. These global variables, representing fundamental constants like the gravitational constant or the cosmological constant, are treated as intensive quantities. They introduce a "preferred foliation" of spacetime, which provides a "matrix" for the evolution and possible freezing of constants.

They also reinterpret the concept of "time." The authors propose that time is canonically dual to the constants of nature. Inspired by phenomenological fluid clocks (based on isentropic fluids), time becomes a "chemical potential" of fundamental constants: that is, the time dual to a certain constant (e.g., Newton's constant) dictates the rate at which the constant can change. This analogy allows them to connect variations in fundamental constants to matter creation or destruction. The rate of flow of the time dual to a constant is determined by the chemical potential of that constant. This means the violation of energy conservation is directly linked to the interaction between a matter parameter and a gravity clock (or vice versa). This provides a theoretical basis for the creation of matter in the early universe.

The other core idea in their model is the separation of matter and gravity within the chaotic early universe. While intuitively we might assume that no such distinction exists in a state of complete chaos, the authors postulate that even a modest level of separation can provide an evolutionary advantage. This requirement translates into the existence of separate local and global variables for matter and gravity, leading to a separation of the Hamiltonian into matter and gravity components.

The separation leads to a deterministic mechanism of evolution where constants of nature can evolve with time and, consequently, can lead to a change in the mass-energy of the Universe. The equation they derive for the time evolution of matter depends on the Poisson bracket between matter and gravity parts of the Hamiltonian.

The key concept in their model is the role of diffeomorphism invariance. Diffeomorphism invariance is the expression of general covariance (the laws of physics are independent of the coordinate system). The authors propose that diffeomorphism invariance emerges as a natural outcome of the selection process. By requiring the algebra of the constraints to follow the Dirac hypersurface deformation algebra in the absence of global interactions, they ensure that their framework respects this fundamental symmetry. This ultimately explains how gravity is always present, whereas matter can be optional. The upshot is that nearly diffeomorphism-invariant states are favoured as the end product of the evolutionary process.

The authors then introduce a stochastic element, inspired by the random mutations that drive biological evolution. They model these mutations using an absorbing Markov chain, where states represent different configurations of the universe with varying physical constants. The absorbing state represents a stable configuration where evolution ceases, and the laws of physics become fixed (i.e. constants become truly constant). The use of an absorbing Markov chain implies that, once the absorbing state is reached, it can no longer be left, meaning the "constants" of Nature really become constant.

Within this Markov chain, the constants of nature can jump from state to state, either becoming a function of an a variable, or converging to an a variable. This random distribution has no biases to one or other side and the chance to keep positive gains of mass creation requires a local Hamiltonian with a clear separation of matter and gravity.

The combination of the deterministic process and stochastic mutations provides a theoretical framework for cosmic natural selection. Universes with configurations conducive to matter creation and stability are favored, while those that lead to annihilation or instability are eliminated. Universes containing clear separation between matter and gravity are favoured by the evolution along the Markov chain, as are those with nearly-diffeomorphism symmetry, which is also an absorbing state.

I'm far outisde my depth as to speak to the validity or falsifiability of this model, but it's a very clever concept that at the very least is interesting and novel. The idea that we live in a universe where random mutations in physical constants were guided by a deterministic environment which favored stable matter-rich configurations and ultimately led to the nearly diffeomorphism-invariant cosmos we observe.

The FlashAttention CUDA Kernel Line by Line

Tue, 11 Feb 2025 00:00:00 +0000

The FlashAttention CUDA Kernel Line by Line

Flash Attention is a memory-efficient algorithm for computing attention in transformers. Let's break down the CUDA implementation block by block. The core innovation of Flash Attention is processing attention in blocks while maintaining numerical stability through careful tracking of maximum values and partial sums. The algorithm achieves memory efficiency by never materializing the full attention matrix while still producing mathematically equivalent results to the standard attention mechanism.

First we need some small macros. The CEIL_DIV is used to compute the ceiling of the division of two numbers.

#include <cuda.h>
#include <cuda_runtime.h>

#define CEIL_DIV(x, y) ((x) >= 0 ? (((x) + (y) - 1) / (y)) : ((x) / (y)))

Now we need the kernel declaration:

template <const int Br, const int Bc>
__global__ void flash_attn_kernel(float* Q, float* K, float* V, int N, int d, int Tr, int Tc, float scale, float* l, float* m, float* O)

This declares a CUDA kernel with template parameters Br and Bc which represent the block sizes for rows and columns. The function takes:

Q, K, V: Query, Key, and Value matrices
N: Sequence length
d: Head dimension
Tr, Tc: Number of blocks in rows and columns
scale: Scaling factor for attention scores
l, m: Auxiliary arrays for the numerically stable softmax computation
O: Output matrix

Thread and Block Index Setup

int tx = threadIdx.x;
int bx = blockIdx.x;
int by = blockIdx.y;

int qkv_off = (bx * gridDim.y * N * d) + (by * N * d);
int lm_off = (bx * gridDim.y * N) + (by * N);

This section retrieves the thread and block indices (tx, bx, by) that identify which thread is executing. It then calculates two important offset values: qkv_off for accessing the Q, K, V matrices and lm_off for accessing the auxiliary arrays l and m. These offsets ensure each block processes the correct portion of the input data.

Shared Memory Setup

extern __shared__ float smem[];
float* Qi = smem;
float* Kj = Qi + Br * d;
float* Vj = Kj + Bc * d;
float* Sij = Vj + Bc * d;
float* Oi = Sij + Br * Bc;
float* li = Oi + Br * d;
float* li_new = li + Br;
float* mi = li_new + Br;
float* mi_new = mi + Br;
float* mij_dash = mi_new + Br;

This section partitions the shared memory into different regions for:

Qi: Current block of Query matrix
Kj: Current block of Key matrix
Vj: Current block of Value matrix
Sij: Attention scores
Oi: Output accumulator
li, li_new, mi, mi_new, mij_dash: Softmax computation variables

Main Processing Loops

The kernel uses two nested loops:

Outer loop over Key/Value blocks (j)
Inner loop over Query blocks (i)

Key-Value Loading

for (int j = 0; j < Tc; j++) {
    int loads_per_thread = CEIL_DIV(d, Br);
    for (int e = 0; e < loads_per_thread; e++) {
        int idx = e * (Br * Bc) + tx;
        if (idx < Bc * d) {
            int row = idx / d;
            int col = idx % d;

            if (j * Bc + row < N) {
                Kj[row * d + col] = K[qkv_off + (j * Bc + row) * d + col];
                Vj[row * d + col] = V[qkv_off + (j * Bc + row) * d + col];
            }
        }
    }
    __syncthreads();

This section loads the current block of K and V matrices into shared memory, with bounds checking to prevent out-of-bounds access.

Let's break down the main computation loop which processes each block of queries:

Loading Query and Output Data

for (int e = 0; e < loads_per_thread; e++) {
    int idx = e * (Br * Bc) + tx;
    if (idx < Br * d) {
        int row = idx / d;
        int col = idx % d;
        if (i * Br + row < N) {
            Qi[row * d + col] = Q[qkv_off + (i * Br + row) * d + col];
            Oi[row * d + col] = O[qkv_off + (i * Br + row) * d + col];
        }
    }
}

This section loads the current block of Query matrix and Output accumulator into shared memory. Each thread may load multiple elements to ensure efficient memory access patterns. The bounds checking ensures we don't access out-of-bounds memory when N isn't perfectly divisible by the block size.

Thread Position Calculation and Max/Sum Loading

int s_row = tx / Bc;
int s_col = tx % Bc;

if (s_col == 0) {
    mi[s_row] = m[lm_off + (i * Br) + s_row];
    li[s_row] = l[lm_off + (i * Br) + s_row];
}
__syncthreads();

Each thread calculates its position in the shared memory block. The first thread in each row (s_col == 0) loads the running maximum and sum values needed for the numerically stable softmax computation.

Computing Attention Scores

float acc = 0.f;
for (int k = 0; k < d; k++)
    acc += Qi[s_row * d + k] * Kj[s_col * d + k];

acc *= scale;
Sij[s_row * Bc + s_col] = acc;

This computes the scaled dot product attention scores between the Query and Key matrices. Each thread computes one element of the attention score matrix Sij.

Numerically Stable Softmax Computation

if (s_col == 0) {
    float row_m = -INFINITY, row_l = 0.f;
    // Find max for numerical stability
    for (int c = 0; c < Bc; c++) {
        float val = Sij[s_row * Bc + c];
        if (val > row_m) {
            row_m = val;
        }
    }
    // Compute exponentials and sum
    for (int c = 0; c < Bc; c++) {
        float exp_val = expf(Sij[s_row * Bc + c] - row_m);
        Sij[s_row * Bc + c] = exp_val;
        row_l += exp_val;
    }

    // Update running max and sum
    mij_dash[s_row] = row_m;
    mi_new[s_row] = max(mi[s_row], row_m);
    li_new[s_row] = expf(mi[s_row] - mi_new[s_row]) * li[s_row] + 
                    expf(row_m - mi_new[s_row]) * row_l;
}

This implements the numerically stable softmax algorithm. For each row:

Find the maximum value for numerical stability
Compute exponentials normalized by the maximum
Sum the normalized exponentials
Update the running maximum and sum for the online softmax computation

Output Computation and Update

for (int col = s_col; col < d; col += Bc) {
    float acc = 0.f;
    for (int c = 0; c < Bc; c++)
        acc += Sij[s_row * Bc + c] * Vj[c * d + col];

    int global_row = (i * Br) + s_row;
    if (global_row < N) {
        Oi[s_row * d + col] = (1 / li_new[s_row]) * 
            ((li[s_row] * expf(mi[s_row] - mi_new[s_row]) * Oi[s_row * d + col]) + 
             (expf(mij_dash[s_row] - mi_new[s_row]) * acc));
        O[qkv_off + global_row * d + col] = Oi[s_row * d + col];
    }
}

This final section:

Computes the matrix multiplication between the softmax probabilities and the Value matrix
Updates the output using the online softmax algorithm
Each thread may compute multiple output elements (when d > Bc)
The reason for the complex update formula is to ensure numerical stability while accumulating partial results

State Update for Next Iteration

m[lm_off + (i * Br) + s_row] = mi_new[s_row];
l[lm_off + (i * Br) + s_row] = li_new[s_row];

Finally, we update the running maximum and sum values in global memory for the next iteration. This is crucial for the online softmax computation across blocks.

Training with GRPOTrainer

Fri, 07 Feb 2025 00:00:00 +0000

Training with GRPOTrainer

DeepSeek's impressive new reasoning model is powered by a key innovation called Group Relative Policy Optimization (GRPO). This clever variant of PPO not only improves the model's training convergence but also uses less memory than traditional approaches. This was one of the core idea that helped DeepSeek's new R1 model achieve state-of-the-art performance with incredibly low training costs. This article explores the basics of how to use GRPOTrainer, why it works and how it can be used in new model training.

GRPO is an online learning algorithm that improves iteratively using data generated by the model during training. The key innovation is that it eliminates the need for a critic model by estimating the baseline from group scores, significantly reducing training resources compared to PPO.

The algorithm works in four main steps:

Generating completions: For each prompt in a batch, generate G different completions using the old policy
Computing rewards: Score each completion using rule-based reward functions
Normalizing advantages: Calculate the relative advantage by normalizing rewards using the group's mean and standard deviation
Optimizing the policy: Update the model using a clipped PPO-like objective that keeps the new policy close to the old one

This approach is particularly efficient because it eliminates the need for a separate critic network, uses group statistics to establish baselines, maintains policy stability through clipping, and reduces memory usage compared to traditional PPO.

"Aha Moment"

During DeepSeek-R1's training, researchers observed what they called an "aha moment" ... which is the term they use for the emergence of sophisticated multi-step reasoning behavior through GRPO training. The model demonstrated a form of emergent chain-of-thought reasoning where it would:

Generate an initial solution approach
Automatically verify the correctness of its reasoning
Identify potential flaws or gaps in logic
Generate alternative approaches when necessary
Compare multiple solution paths before settling on a final answer

This behavior manifested particularly in mathematical and logical reasoning tasks. For example, when solving complex word problems. What made this particularly interesting was that this verification behavior emerged purely through the GRPO reward optimization process, without any explicit chain-of-thought prompting or human feedback. The group-relative advantage computation naturally encouraged the model to develop more thorough reasoning strategies, as solutions that included verification steps consistently achieved higher rewards within their comparison groups.

Four key emergent behaviors were observed that they noted in the paper:

Self-verification: The model learned to automatically check its work and validate its answers.
Extended chain-of-thought: Solutions became more detailed with explicit step-by-step reasoning.
Exploratory reasoning: The model would try multiple approaches before settling on the best solution.
Reflection: The model developed the ability to question and revise its own reasoning process.

This emergent behavior aligns with theoretical predictions about the benefits of group-relative policy optimization: by comparing multiple solution attempts within the same context group, the training process naturally selects for more robust and self-correcting reasoning patterns. The KL divergence constraint ensures these patterns develop gradually and stably, rather than through sudden policy shifts.

In simpler terms, it's like the model learned to "check its work" all on its own, similar to how a careful student might solve a math problem, then go back to make sure their answer makes sense, and try a different approach if something seems off. The training method essentially rewarded this careful, thorough approach by comparing different solution attempts side by side, like a teacher grading multiple versions of the same homework assignment and giving better scores to students who show their work and verify their answers. The model wasn't explicitly taught to do this - it just naturally developed these good study habits because they consistently led to better outcomes!

Theory

GRPO is an online learning algorithm that iteratively improves by using data generated by the model during training. The key innovation of GRPO is its approach to estimating advantages through group-based normalization and its efficient handling of KL divergence constraints.

At its core, GRPO operates by first generating multiple completions for each input prompt. For each prompt in a batch, the model generates $G$ different completions using the current policy $\pi_{\theta}$. These completions form a "group" that will be used for relative comparison, which is fundamental to how GRPO estimates advantages.

The advantage estimation process is what gives GRPO its name. For each completion, a reward $r_i$ is computed using a reward model. Instead of using a critic network to estimate advantages, GRPO normalizes rewards within each group:

$$\hat{A}_{i,t} = \frac{r_i - \text{mean}(\mathbf{r})}{\text{std}(\mathbf{r})}$$

This group-relative normalization approach is particularly effective as it naturally compares rewards relative to other completions in the same group, providing a built-in baseline for advantage estimation.

To ensure stable training, GRPO employs KL divergence estimation using Schulman's approximator. This term helps ensure the policy doesn't deviate too far from the reference policy during training. The complete GRPO loss function combines advantage maximization with this KL divergence penalty.

By eliminating the need for a separate critic model it achieves better memory efficiency. The group-relative advantage computation helps reduce variance in training, while the KL divergence term prevents policy collapse. The normalization within groups makes the method robust to reward scaling, and the single update per generation (compared to multiple updates in PPO) simplifies implementation. This design makes GRPO particularly well-suited for integration with existing language model architectures.

To put it in simpler terms, imagine GRPO as a teacher grading essays in a classroom. Instead of having a separate teaching assistant (critic model) help grade papers, the teacher looks at small groups of essays together. For each group, they rank the essays relative to each other, which ones are better or worse compared to the average of that specific group. This is like normalizing the rewards within groups.

The teacher also makes sure not to completely change their grading criteria between assignments (KL divergence constraint), they want to stay somewhat consistent with how they've graded before. This helps students understand what's expected and improve gradually rather than facing wildly different standards each time.

This approach is more efficient than traditional methods because you don't need that extra teaching assistant, and comparing essays within small groups is more manageable than trying to compare every essay to every other essay. It's like the difference between grading on a curve for each small discussion section versus trying to curve grades across the entire university!

Usage

Here's how to use GRPO via the TRL framework:

from datasets import load_dataset
from trl import GRPOConfig, GRPOTrainer

# Load your dataset
dataset = load_dataset("trl-lib/tldr", split="train")

# Configure training arguments
training_args = GRPOConfig(
    output_dir="output",
    num_train_epochs=3,
    per_device_train_batch_size=1,
    gradient_accumulation_steps=8,
    learning_rate=1e-6,
    logging_steps=10,
    num_generations=8,
    max_prompt_length=512,
    max_completion_length=256,
    temperature=0.9,
    beta=0.04,  # KL penalty coefficient
)

# Initialize trainer
trainer = GRPOTrainer(
    model="your/base/model",
    args=training_args,
    train_dataset=dataset,
    reward_funcs=reward_func,
)

# Start training
trainer.train()

The key training parameters are:

num_generations: Number of completions to generate per prompt (default: 8)
beta: KL penalty coefficient to control how far the model can deviate from reference policy (default: 0.04)
temperature: Sampling temperature for generation (default: 0.9)
max_prompt_length: Maximum length for input prompts (default: 512)
max_completion_length: Maximum length for generated completions (default: 256)

GRPO logs several important metrics during training:

completion_length: Average completion length
reward/{reward_func_name}: Reward computed by each reward function
reward: Average reward
reward_std: Average standard deviation within reward groups
kl: Average KL divergence between model and reference model

To accelerate generation, which is often the main bottleneck in online methods, you can use vLLM:

from trl import GRPOConfig

training_args = GRPOConfig(
    # ... other args ...
    use_vllm=True,
    vllm_gpu_memory_utilization=0.9,
)

You can also define custom reward functions to guide the training. The function must:

Accept prompts and completions as keyword arguments
Return a list of floats representing rewards for each completion

Example reward function that rewards longer completions:

def reward_func(completions, **kwargs):
    """Reward function that evaluates natural text quality based on multiple factors:
    - Length (with diminishing returns after target length)
    - Readability metrics
    - Sentence structure variety
    - Proper punctuation
    """
    rewards = []
    target_length = 200  # Ideal completion length
    
    for completion in completions:
        # Base score
        score = 0.0
        
        # Length reward with diminishing returns
        length = len(completion)
        if length < target_length:
            length_score = length / target_length
        else:
            length_score = 1.0 + 0.1 * math.log(length / target_length)
        score += length_score
        
        # Reward sentence variety (look for mix of short and long sentences)
        sentences = [s.strip() for s in completion.split('.') if s.strip()]
        if sentences:
            lengths = [len(s) for s in sentences]
            variance = statistics.variance(lengths) if len(lengths) > 1 else 0
            score += min(0.5, variance / 500)  # Cap variance reward
            
        # Reward proper punctuation
        if any(p in completion for p in ['.', '!', '?']):
            score += 0.3
            
        # Penalize very short sentences or fragments
        if any(len(s) < 10 for s in sentences):
            score -= 0.2
            
        rewards.append(float(score))
        
    return rewards

GRPO supports multiple reward functions - just pass them as a list:

trainer = GRPOTrainer(
    reward_funcs=[reward_func1, reward_func2],
    # rest of arguments
)

The final reward will be computed as the sum of rewards from each function.

The Case Against Crypto in 2025

Sat, 25 Jan 2025 00:00:00 +0000

The Case Against Crypto in 2025

In 2020, I wrote what became a widely-circulated critique of cryptocurrency and its implications for our financial system. At the time, I desperately hoped to be proven wrong. As a technologist who deeply believes in the potential of technology to strengthen democratic institutions, I took no pleasure in forecasting the corrosive potential of crypto assets. Unfortunately, the intervening years have borne out many of my predictions with shocking prescience.

In the years since publishing that critique, I've had the privilege of engaging with financial authorities and policymakers worldwide—from central banks and regulatory bodies to national governments and think tanks. My work has included coordinating joint letters to legislative bodies across three continents, authoring a book on the subject, and giving interviews at most global media outlets. I've done as much as humanly possible for one person to do to raise awareness of the risks posed by crypto assets because as a millennial who lived through the financial crisis I feel a twisted sense of civic responsibility to at least attempt to stave off the dark future I see unfolding.

However I must admit that despite extensive efforts to sound the alarm, the response has been stubborn resistance in the face of an overwhelming ambient culture of techno-solutionism that pervades modern life. Our democratic institutions remain paralyzed in the face of crypto's mounting threats, and the ascension of the Trump administration has only accelerated this regulatory abdication and the threat of crypto. I won't sugar-coat it, we are living through a challenging era and things may get much worse before they get better.

What originated as an obscure libertarian experiment has metastasized into an existential threat to financial stability and a political machine for far right extremists. The parallel shadow system constructed around crypto assets has reproduced precisely the systemic vulnerabilities that post-2008 reforms sought to eliminate. We have watched in real time as major crypto institutions imploded, retail investors lost their savings, and sophisticated financial instruments emerged to conceal rather than manage risk. And yet governments across the western world have done next to nothing to address these issues.

After years of persistent advocacy, I recognize that the next phase of this crucial policy debate requires new voices and broader perspectives. People who are smarter and more eloquent than me. The challenges posed by cryptocurrency demand an expanded coalition of experts spanning technology, economics, law enforcement, national security, and public policy.

For those continuing this important work, I offer this parting counsel of the things I've learned over the past four years talking to politicians, regulators, and the public. With a pivotal showdown looming in 2025, Democrats still have a narrow window to strengthen their failed approach and fight against the MAGA party's extreme anarcho-capitalist agenda. The choices made in the coming years will determine whether we finally bring this shadow financial system under control or surrender our financial stability to unrestrained speculation that may give rise to a new financial crisis or an even darker future.

Equivocation has Failed

Let's be crystal clear, that while Democrats deserve some criticism for their tepid response on the crypto problem, the Republican party bears the lion's share of responsibility for our regulatory paralysis. The GOP has been thoroughly corrupted by crypto industry money, with prominent Republican leaders actively championing deregulation while taking millions in campaign contributions from crypto super PACs. Their cynical obstruction tactics in Congress have effectively blocked any meaningful legislation, even modest consumer protection measures with broad bipartisan support. Republicans have created a legislative graveyard for crypto regulation, leaving federal agencies hamstrung and good-faith Democratic efforts dead on arrival. This systematic sabotage reflects the GOP's broader descent into market fundamentalism, where any attempt to rein in financial speculation is denounced as "stifling innovation", regardless of the clear public interest in basic oversight.

The core issue is that the Democratic party's impotent attempts at a "moderate" crypto policy position have become an embarrassing testament to political cowardice. The mealy-mouthed equivocations—that the technology is neither good nor bad, that we mustn't regulate software too heavily, that Bitcoin might have legitimate uses for marginalized groups—are intellectual fig leaves covering naked regulatory capture. While these positions might satisfy the party's donor class and business-aligned policy institutes, they represent an abdication of government's duty to protect the public.

As a result, the Democratic party's tendency toward technocratic incrementalism and regulatory restraint has created a vacuum that bad actors have eagerly filled. By treating crypto as just another financial innovation requiring modest oversight, moderates have enabled the very predatory practices they claim to oppose. Their appeals to "balanced regulation" and "promoting innovation" amount to little more than rhetorical cover for inaction in the face of widespread fraud and market manipulation.

This failure of nerve among Democratic leadership reflects a deeper rot in American politics—the capture of our regulatory apparatus by monied interests who profit from regulatory inaction. The same politicians who righteously denounce Wall Street excess are perfectly content to let crypto exchanges operate as unregulated casinos, destroying retail investors while enriching venture capitalists and hedge funds. Their studied neutrality serves only to protect the powerful while leaving ordinary citizens exposed to sophisticated financial predation.

The time for half-measures and careful moderation has long passed. The crypto industry has demonstrated, through repeated cycles of fraud and collapse, that it cannot and will not reform or regulate itself. Democratic policymakers must abandon their tepid both-sidesism and embrace aggressive regulation that treats crypto assets as what they are—unregistered securities and vehicles for financial crime. Anything less is an abdication of government's fundamental responsibility to protect the publict.

Yet there are reasons for hope. Leaders like Senator Elizabeth Warren have been steadfast champions of strong regulation and consumer protections, even in the face of fierce industry opposition and pressure from the donor class. Her tireless work to expose crypto's risks to consumers and financial stability, along with concrete legislative proposals to bring the industry under proper oversight, demonstrates the kind of principled leadership desperately needed. While a sclerotic Congress continues to drag its feet, there are still many Democrats who are willing to fight for a more aggressive regulatory response.

Shapeshifting Narratives

The crypto industry's greatest trick has been its ability to shapeshift its narrative to seduce any audience. Like a chameleon changing colors, crypto morphs into whatever its marks most desperately want to see. To libertarians, it's a weapon against government tyranny. To progressives, it's financial inclusion for the unbanked. To tech investors, it's paradigm-shifting innovation. To get-rich-quick dreamers, it's a ticket to untold wealth. The stories are as numerous as they are contradictory. When talking to regulators, crypto companies argue their tokens are mere collectibles like Beanie Babies, but to the public they present themselves as revolutionary financial instruments transforming the global economy. The sophistry and inconsistency is truly breathtaking.

However, this calculated incoherence is no accident—it's essentially a form of intellectual three-card monte designed to exhaust and confuse critics while attracting true believers of all stripes. The moment you try to pin down and critique one narrative, advocates smoothly slide to another, equally nonsensical position. Challenge Bitcoin's viability as a currency? It's actually a store of value. Question its merit as a store of value? It's really about the underlying technology. Point out the technology's fundamental limitations? Well, you just don't understand the transformative potential of web3. When web3 failed, they went back to the start and called it a currency again, and round and round they go.

The intellectual dishonesty is staggering. Bitcoin cannot simultaneously be a hedge against inflation and a high-growth speculative asset. It cannot be both a currency for daily transactions and digital gold to be hoarded. DeFi cannot replace traditional finance while depending entirely on traditional finance for its value and utility. NFTs cannot democratize art while concentrating wealth in the hands of wealthy speculators and wash traders. These contradictions don't matter because the real product being sold is the intoxicating promise of easy riches.

What makes this sophistry so insidious is how it weaponizes complexity and jargon to short-circuit critical thinking. The average person, overwhelmed by technical terminology and afraid of appearing ignorant, becomes susceptible to whatever narrative most appeals to their hopes and fears. Meanwhile, true believers can choose whichever story best fits their ideological preferences, constructing elaborate post-hoc justifications while ignoring the glaring contradictions in their position.

The end result is a kind of distributed Ponzi scheme where everyone convinces themselves they're the smart money, not the greater fool. The only consistent thread running through crypto's shifting narratives is the promise of getting rich through speculation rather than productive work. Everything else—the technology, the philosophy, the grand social vision—is merely elaborate window dressing for humanity's oldest scam: the promise of something for nothing.

Weaponized Jargon

The crypto industry has mastered the dark art of linguistic manipulation, wielding terms like "blockchain" and "tokenization" as magical incantations that mean everything and nothing at once. These words function as a kind of semantic smokescreen, allowing crypto advocates to dance between definitions whenever convenient. One moment they're describing a so-called "revolutionary" financial technology, the next a mere database—whatever serves their regulatory arbitrage du jour.

This deliberate ambiguity has proven devastatingly effective in policy circles, where aging legislators and their overwhelmed staffers grasp desperately for understanding. The average member of Congress, already struggling to operate their iPhone, stands no chance against this calculated obscurantism. They're left nodding along to incomprehensible techno-babble while the industry runs circles around meaningful oversight.

The crypto lobby has perfected this strategy of strategic ambiguity, shrouding their operations in a fog of technical jargon and shifting definitions. When pressed on specific regulations, they retreat into abstract discussions of cryptography and distributed systems. When questioned about their actual use cases, they pivot to grandiose visions of "financial inclusion" and "democratization." It's a shell game played with words instead of peas.

Almost a decade ago I led engineering teams trying to make blockchain technology work for regulated financial applications, and I can state with absolute technical certainty: the fundamental architecture is incompatible with anything except regulatory evasion and criminal enterprise. The immutable, public, and permissionless nature of these systems—the very features touted as "revolutionary"—make them unsuitable for legitimate financial infrastructure. If you remove these features to make the system work for enterprise needs, you're left with nothing more than an inefficient, overcomplicated database wrapped in buzzwords and marketing hype that could (and should) always be replaced by a simpler solution. But by keeping the discussion mired in definitional quicksand, the industry has successfully delayed this simple truth from reaching policymakers.

However let's be clear: this is a free country and no serious policy proposal involves banning cryptography, linked lists, or the word "blockchain." The crypto lobby has masterfully constructed this straw man argument to paint any regulation as technologically illiterate overreach. They deliberately conflate basic computer science concepts with their specific applications in unregistered securities and financial schemes.

The mathematical primitives underlying cryptocurrency—hash functions, public key cryptography, merkle trees—are and will remain perfectly legal. They're inert tools used across legitimate industries. But this fact is entirely irrelevant to the policy debate around crypto assets. We don't need to ban the SHA-256 hash function to effectively regulate cryptocurrency any more than we need to ban spreadsheets to prosecute accounting fraud.

For future advocates taking up this cause: don't let the industry's semantic games derail substantive policy discussions. When they retreat into abstract technical descriptions, drag the conversation back to their actual business practices. The problem isn't the technology—it's how it's being weaponized for financial misconduct. Focus relentlessly on the concrete harms: market manipulation, consumer fraud, sanctions evasion, and systemic risk.

The First Amendment protects speech, not financial schemes. We must understand that regulating crypto assets is about curtailing harmful business practices, not restricting software use. The industry's supposed constitutional concerns are a calculated distraction from straightforward securities law violations.

Political Capture

The 2024 election cycle laid bare the extent of crypto's political influence operations. The industry poured nearly $200 million into campaign advertising, targeting lawmakers who dared question their practices or advocate for consumer protections. Yet tellingly, these attack ads studiously avoided mentioning cryptocurrency itself—a tacit admission that the American public remains deeply skeptical of an industry associated with ransomware, money laundering, and financial crime.

This massive spending spree has yielded a cohort of captured politicians who reliably champion industry interests while paying lip service to "innovation" and "financial inclusion." Representatives like Ritchie Torres, Kirsten Gillibrand, Chuck Schumer, and Rohit Khanna have emerged as particularly captured advocates for the industry. Their support comes as no surprise given the enormous sums flowing into their campaigns and leadership PACs from crypto interests.

The industry's primary legislative goal is transparent—they seek to engineer regulatory arbitrage by shifting oversight to the dramatically under-resourced Commodity Futures Trading Commission. With a budget of just $365 million and 700 employees, compared to the SEC's 2.1 billion and 4,500 staff, the CFTC would be overwhelmed by the task of policing this complex and fraud-prone sector. This is precisely what crypto lobbyists want—the appearance of regulation without meaningful enforcement capability.

This cynical strategy reflects a broader corruption of American democracy by monied interests. The crypto industry's lavish spending and sophisticated influence operations eerily echo earlier eras when powerful financial interests captured the regulatory apparatus meant to constrain them. Then as now, the result is a political system that protects predatory business practices while leaving ordinary citizens exposed to sophisticated forms of financial exploitation.

In the wake of FTX's collapse and Sam Bankman-Fried's conviction, the industry has only intensified its influence peddling, raising hundreds of millions through Super PACs to push legislation that would grant it legitimacy while avoiding meaningful oversight. Key Senate races have become battlegrounds, with industry groups specifically targeting independent voices like Senators Sherrod Brown and Elizabeth Warren who have consistently stood against special interests.

The legislative agenda being advanced is particularly concerning. Both the House Financial Services and House Agriculture Committees have established dedicated digital asset subcommittees, leading to a flood of industry-friendly bills. These proposals consistently favor minimal regulation while enabling an expansion of crypto offerings that could further endanger retail investors and broader financial stability.

Most troubling is how the industry has successfully cultivated a bipartisan coalition of lawmakers deeply tied to crypto interests. These representatives consistently advance legislation designed to create the mere appearance of oversight while carefully preserving the regulatory gaps that enable predatory practices. This sophisticated capture of the legislative process threatens to permanently enshrine crypto's shadow financial system in law.

American Culture

The transformation of American culture over the past few decades reveals a troubling shift from a principle-based society to naked transactionalism, particularly among younger generations. Growing up in the crucible of late-stage capitalism has warped many Americans' fundamental understanding of value and social relationships. Where previous generations at least paid lip service to enlightenment ideals of reason, justice, and the common good, a growing segment of society now views every interaction purely through the lens of personal gain and market logic.

This mindset is particularly prevalent among millennials (my generation), who have internalized the most extreme forms of market fundamentalism. Having come of age during the 2008 financial crisis, rising inequality, and the gig economy, many have abandoned traditional liberal values in favor of a ruthlessly transactional worldview. Every relationship, every interaction, every moment becomes an opportunity for arbitrage or personal advantage. The language of "optimization" and "value extraction" has escaped the boardroom to colonize our most intimate social spaces.

The rise of cryptocurrency perfectly embodies this cultural shift. Its most vocal advocates openly reject any notion of collective good or social responsibility in favor of pure financial self-interest. The industry's marketing specifically targets young men's anxieties about status and economic security, promising them that unrestrained market speculation is the only path to dignity in an increasingly precarious world. This message resonates precisely because it validates their existing tendency to view everything—friendships, romance, civic participation—as mere transactions to be optimized.

However, this transformation is neither universal nor inevitable. Many developed nations with market economies have maintained stronger social bonds and collective values, underpinned by political and cultural institutions—hallmarks of robust liberal democracies—that promote civic virtue. Even within America, many communities uphold principles of reason, justice, and the common good, offering a potent alternative to a purely transactional and nihilistic existence.

For Democrats crafting policy responses to cryptocurrency, understanding this cultural context is crucial. A significant portion of crypto's support comes not from genuine belief in its technological merits, but from those who have fully embraced market fundamentalism as a worldview and personal identity. Traditional appeals to consumer protection or financial stability may fall flat with voters who see unfettered speculation as a moral right and reject any notion of collective good.

Yet this reality should strengthen, not weaken, Democrats' resolve to aggressively regulate cryptocurrency. The New Deal succeeded precisely because it offered a compelling alternative to pure market fundamentalism—a vision of shared prosperity and collective purpose that transcended narrow self-interest.

The paramount threat to the 21st-century body politic lies in the corrosive synthesis of extreme partisanship with anti-system politics—a 'burn it all down' mentality—and a deepening societal nihilism. This dangerous trend fosters profound cynicism, rejecting not just specific policies but the very legitimacy of democratic processes and shared societal values, thereby rendering constructive engagement and collective problem-solving nearly impossible. The antidote to this existential challenge is a robust democratic renewal, achieved by making government demonstrably work for its people once more.

Today's Democratic party must similarly champion values of reason, justice, and truth against the corrosive effects of extreme transactionalism. The crypto debate isn't just about financial regulation—it's about what kind of society we want to be.

Predatory Inclusion

The crypto industry's claims of financial inclusion represent a particularly insidious form of predatory inclusion—one that exploits legitimate concerns about financial discrimination to lure vulnerable communities into risky speculation. This narrative proves especially paralyzing for Democrats, who find themselves disarmed by accusations of "financial privilege" when raising valid regulatory concerns.

The industry cynically appropriates the language of social justice while targeting the very communities historically harmed by financial discrimination. After generations of redlining, loan denials, and predatory lending, minority communities' legitimate desire to close the wealth gap makes them especially vulnerable to crypto's false promises of financial empowerment.

This predatory inclusion manifests in deliberately exploitative practices. The industry strategically places Bitcoin ATMs in predominantly Black, Latino, and low-income neighborhoods, charging exorbitant fees while often only allowing purchases, not sales. They aggressively market get-rich-quick narratives in communities with limited financial resources and resilience, knowing full well that crypto's extreme volatility and rampant fraud puts their targets at risk of devastating losses.

What's marketed as a path to financial liberation instead becomes another vehicle for exploitation. The industry's targeting of minority communities isn't inclusion—it's predation wearing the mask of empowerment. For communities that can least afford losses, crypto's combination of volatility, fraud, and manipulated markets represents not an opportunity, but a threat to generational wealth building.

The industry's co-option of progressive language represents a calculated strategy to deflect criticism and legitimize their practices. Terms like "democratizing finance" and "financial inclusion" are wielded as shields against regulatory scrutiny, while the underlying business model continues to extract wealth from vulnerable communities. This appropriation of social justice terminology to serve profit motives undermines genuine efforts at economic empowerment and makes it harder to address real systemic inequities. The result is a cynical inversion where the language of liberation is used to enable further exploitation.

Criminality

Just as I wrote in 2021, cryptocurrency's primary real-world use case, beyond pure gambling, is enabling criminal enterprise, political corruption, and sanctions evasion on a massive scale. From North Korean hackers to Russian oligarchs, from narco-terrorists to ransomware gangs, crypto provides the financial infrastructure for modern organized crime.

The numbers are staggering. According to the FBI's 2024 Internet Crime Report, cryptocurrency was involved in 56% of the $16.6 billion in total cybercrime losses that year. Crypto-related losses reached 9.3 billion in 2024, a 66% increase from 2023. The FBI received over 140,000 complaints involving cryptocurrency from harmed individuals—more than double the number from the previous year.

Particularly concerning is the targeting of vulnerable populations. The FBI found that individuals over 60 were disproportionately victimized, accounting for roughly 33,000 complaints and $2.8 billion in losses. Complaints about cryptocurrency ATMs and kiosks nearly doubled, with losses up 31%. The bureau also documented a 59% surge in crypto-enabled extortion schemes, including "sextortion" attacks where criminals manipulate photos and videos to intimidate victims.

North Korea has turned cryptocurrency theft into a cornerstone of state financing, using armies of hackers to raid exchanges and steal billions in digital assets. These funds directly support the regime's nuclear weapons program and other illicit activities, demonstrating how crypto undermines global security. Similarly, Iranian state actors exploit cryptocurrency to evade international sanctions, funding terrorist operations across the Middle East.

Russia's invasion of Ukraine highlighted cryptocurrency's role in sanctions evasion. Despite international financial restrictions, Russian oligarchs and state entities have leveraged crypto networks to move billions of dollars, undermining the effectiveness of coordinated Western sanctions. The decentralized nature of cryptocurrency, touted as a feature by advocates, serves in practice as a critical vulnerability in the global anti-money laundering regime.

The narcotics trade has eagerly embraced cryptocurrency, with cartels using it to launder proceeds and facilitate cross-border payments. Mexican drug organizations alone are estimated to launder billions annually through crypto networks, exploiting the pseudonymous nature of transactions to obscure the flow of illegal profits. This has made the task of disrupting drug trafficking operations significantly more challenging for law enforcement.

Beyond organized crime, cryptocurrency enables an endless parade of scams targeting retail investors. The playbook is depressingly consistent: unregistered securities offerings, false promises of astronomical returns, wash trading to manipulate prices, and misappropriation of customer funds. The industry's resistance to basic financial controls and customer protections creates perfect conditions for sophisticated fraud.

Tax evasion through cryptocurrency has also emerged as a major concern for authorities. The difficulty of tracking crypto transactions, combined with widespread non-reporting of gains, creates a shadow financial system that deprives governments of legitimate revenue. This tax gap ultimately shifts the burden onto compliant citizens while undermining public services.

Perhaps most troubling is how cryptocurrency enables ransomware attacks on critical infrastructure, healthcare facilities, and local governments. Criminal groups can now easily monetize cyberattacks through untraceable ransom payments, creating an entire criminal industry that threatens public safety and national security. The Colonial Pipeline attack demonstrated how crypto-enabled ransomware can disrupt essential services across entire regions. The FBI's conclusion is unequivocal: "cryptocurrency has become an enticing means to cheat investors, launder proceeds, and engage in other illicit schemes." The only place that crypto has truly found product market fit is in enabling criminal enterprise.

Tech Institutions

The technology industry's institutions have devolved into little more than libertarian think tanks and self-congratulatory social clubs. Organizations like the IEEE, ACM and EFF, which once stood for broader societal good, now serve primarily as echo chambers for techno-utopian fantasies and regulatory resistance. Their leadership, steeped in the misguided idealism of the cypherpunk era, consistently prioritizes an absolutist view of technological freedom over any meaningful engagement with democracy or the public good.

The rank and file of the tech industry rival Wall Street bankers in their studied indifference to the societal impact of their work. Behind their carefully cultivated image of casual brilliance lies a studied indifference to the societal impact of their work. They build surveillance systems, addictive platforms, and manipulative algorithms while hiding behind the paper-thin shield of "just doing my job."

This moral abdication is ultimately a symptom of false consciousness, masked as a pragmatic progressivism that reduces labor to a mere instrument of survival under capitalism. The ruling ideology is seductive in its simplicity: tech workers, compelled to sell their labor for a wage, are absolved of all responsibility for the outcomes they produce. This framework systematically alienates the worker from the consequences of their labor, providing ideological cover for the capitalist class to pursue any profitable venture, no matter how socially destructive with no accountability.

The public's faith in tech worker restraint or corporate self-regulation is dangerously misplaced. The rank and file are simply going to keep building crypto scams, because they can, and their peers give them a permission structure that rationalizes it. The industry's workforce has proven itself entirely willing to implement whatever dystopian features maximize engagement metrics, so long as the compensation packages remain competitive. The occasional protests amount to little more than performative gestures, quickly forgotten when the next round of RSUs vest. This is an industry I am very much a part of, and we deserve every bit of society's growing contempt—we've earned our place alongside predatory lawyers and corporate lobbyists as professionals who consistently choose self-interest over social responsibility.

Securities and Exchange Commission

While Gary Gensler's SEC ultimately arrived at the correct regulatory stance on cryptocurrency, the path there was frustratingly slow and tentative. History will likely judge Gensler favorably as a principled regulator who stood firm against an onslaught of industry pressure and personal attacks, but the deliberate pace of enforcement allowed the crypto bubble to inflate far larger than necessary. A more aggressive early approach could have prevented billions in retail investor losses and curtailed the industry's growing political influence.

To his credit, Gensler maintained a consistent position that most crypto assets are unregistered securities, even as intense lobbying and congressional pressure sought to undermine this basic regulatory framework. His SEC methodically built cases against major industry players while facing severe resource constraints and coordinated resistance. The string of successful enforcement actions in 2023-24 validated his approach and helped establish essential case law.

However, this measured strategy also reflected a broader Democratic tendency toward technocratic incrementalism when bolder action was needed. A more forceful regulatory response in 2021-22, while the industry was still relatively contained, could have short-circuited its expansion into a systemic threat. Instead, the slow accumulation of case law and regulatory guidance allowed bad actors to exploit inaction while building political defenses against oversight.

The lesson for future Democratic leadership is clear—having the right policy position isn't enough. Effective regulation requires the political courage to act decisively, even in the face of powerful opposition. While Gensler deserves credit for staying the course under immense pressure, his legacy also highlights the costs of regulatory timidity when confronting emerging threats to financial stability and consumer protection. We're now left with the regulatory equivalent of trying to put out a forest fire with a garden hose.

Media

The media's coverage of cryptocurrency has proven consistently inadequate for meaningful policy discourse. While major outlets can generally report basic facts about significant events like exchange collapses or high-profile arrests, they demonstrate a concerning inability to engage with the substantive regulatory and policy implications of this technology.

This limitation manifests most prominently in what might be called the "Bloomberg consensus," epitomized by writers like Matt Levine who approach crypto with a detached intellectual curiosity that prioritizes clever analysis over public welfare. This stance—treating cryptocurrency as a fascinating experiment in market structure worthy of observation rather than a contagion requiring intervention—exemplifies the problem. When sophisticated financial instruments are being weaponized against retail investors and to undermine our democratic institutions, mere observation is no longer enough.

The New York Times' coverage proves particularly problematic, often serving as an unintentional reputation laundering service for the industry. Their tendency to present "balanced" coverage of fundamentally predatory business models grants unearned legitimacy to crypto enterprises. By treating industry talking points as equivalent to regulatory concerns, they create false equivalencies that muddy public understanding rather than clarify it.

Even well-intentioned journalists (of which there are many) face structural barriers to producing meaningful coverage. The sheer volume of concerning incidents in the cryptocurrency space makes it impossible to thoroughly investigate each case, leading to superficial coverage that fails to expose systemic issues. The complexity of cryptocurrency's technical, financial, and regulatory dimensions requires deep expertise across multiple domains, yet the modern media environment's demands for rapid content production means reporters must constantly chase the next headline rather than build deep understanding. Additionally, even when reporters uncover clear evidence of malfeasance, legal departments often require watered-down language to avoid potential litigation, making it nearly impossible to call a spade a spade. The result is coverage that barely scratches the surface while questionable practices continue to emerge unchallenged.

For those seeking to advance meaningful policy changes, traditional media engagement is increasingly ineffective, especially for reaching younger audiences. The crypto industry's sophisticated PR machine and media's limitations make it nearly impossible to get complex messages through. Instead, we need to focus on platforms where younger civicly engaged voters actually spend their time. Writing op-eds for the Financial Times and Foreign Policy is all well and good, but it won't reach the people who need to hear it in our increasingly post-literate culture.

The Dark Future

Let me paint a picture of a possible future that I believe could emerge if we do not act.

The breakdown of the international liberal order creates perfect conditions for cryptocurrency's most dystopian potential to emerge. As multilateral institutions crumble and democratic norms erode globally, we're witnessing the rise of hollow democracies—maintaining the superficial trappings of democratic process while being thoroughly captured by plutocratic interests. Cryptocurrency serves as the perfect tool for this capture, enabling untraceable flows of dark money that render campaign finance laws meaningless and electoral systems mere theater.

The historian Quinn Slobodian provides a compelling analysis in Crack-Up Capitalism, where wealthy elites seek to fragment nation states into private zones of control, while Anne Applebaum's Autocracy Inc documents the rise of modern authoritarian networks. These analyses predict a likely future: as multilateral institutions crumble and democratic norms erode globally, we see the emergence of hollow democracies—maintaining the superficial trappings of democratic process while being thoroughly captured by minority interests.

Following the Viktor Orbán playbook, these regimes maintain a thin veneer of democratic legitimacy while systematically dismantling institutional checks and balances. Cryptocurrency serves as a powerful catalyst for this transformation, providing the perfect tool for plutocrats to further capture the political process. Campaign finance laws become meaningless as untraceable crypto assets flow freely to compliant politicians. Electoral systems remain technically intact, but outcomes are increasingly predetermined through sophisticated manipulation funded by wealth and algorithmic manipulation of attention.

The wealthy crypto-holding class effectively becomes a shadow government, using their accumulated digital assets to shape policy and capture regulatory agencies. While formal democratic institutions continue to exist, they serve mainly as rubber stamps for policies that benefit this new plutocracy. Public services are gradually privatized and hollowed out, with cripled private alternatives emerging that further entrench inequality.

Most disturbing is how this system perpetuates itself through manufactured consent. Social media platforms, their algorithms optimized for engagement and controlled by autocratic and plutocratic interests, keep the public distracted with an endless stream of artificial controversies and manufactured culture wars. Critical thinking and civic engagement wither as people retreat into virtual worlds and digital communities carefully curated to maintain political apathy.

The promised crypto utopia reveals itself as a nightmare of democratic decay—not through outright authoritarianism, but through the quiet erosion of democratic substance while maintaining democratic form. Public institutions continue to exist but serve primarily as vehicles for private interests, with cryptocurrency providing the perfect tool for this capture. The death of democracy comes not through violent revolution but through the gradual hollowing out of democratic institutions until only an empty shell remains.

Future Work

I'm writing this primarily for Congressional staffers and strategists (you know who you are 👋). The political reality through 2026 demands a defensive strategy focused on preventing harmful legislation rather than pursuing immediate reform. With Republicans controlling the House, wielding effective veto power in the Senate, and now heading the SEC and DOJ, passing or enforcing robust crypto regulation is effectively impossible in the near term. Instead, Democrats must concentrate on blocking industry-written bills while building public support and preparing comprehensive oversight frameworks for when they regain control of Congress and the executive branch.

This interim period provides an opportunity to shape the broader narrative around cryptocurrency and its societal impact. The industry's unpopularity with the general public—Pew Research polling consistently shows skepticism above 60%—creates fertile ground for education about systemic risks and predatory practices. This skepticism stems from direct lived experience—millions of Americans have lost savings to crypto scams, watched friends and family members get burned by fraudulent schemes, or seen young men in their communities consumed by gambling addiction. For most Americans, cryptocurrency is just that scam their weird cousin lost his life savings on while ranting about getting rich quick. Democrats must recognize this as both a moral imperative and political opportunity—by standing firmly against industry-written bills that would enable further exploitation, they can demonstrate their commitment to protecting ordinary Americans from sophisticated financial predators.

Paradoxically, the Trump administration may also be a gift to critics, as exemplified by the shameless TRUMP memecoin launch on the eve of his inauguration. Nothing could better crystallize cryptocurrency's true nature than a president eagerly slapping his "brand" on a worthless token, nakedly designed to extract money from his most devoted followers. This isn't subtle regulatory arbitrage or complex financial innovation—it's a carnival barker hawking digital snake oil to an audience he views as marks. For those encountering cryptocurrency for the first time through this lens, the industry's protestations about "financial freedom" and "technological innovation" ring especially hollow. When a sitting president is willing to so blatantly leverage his office for a quick crypto cash grab, it becomes impossible to maintain the pretense that this technology serves any purpose beyond enabling sophisticated grift. The TRUMP token stands as a perfect crystallization of everything wrong with cryptocurrency—and now it's incredibly easy to paint the entire industry with a broad brush given the very visible examples of predation at the highest levels of government.

In the next administration, the crypto industry's aggressive lobbying and attacks on regulatory advocates should be welcomed, not feared. As Franklin Roosevelt declared of the financial interests arrayed against the New Deal: "They are unanimous in their hate for me—and I welcome their hatred." Their opposition validates the Democratic Party's role as defender of public welfare against sophisticated financial predation. Every industry attack ad and hostile congressional hearing becomes an opportunity to highlight crypto's true nature as a vehicle for exploitation.

Although there is an elephant in the room, it is a stark reality that demands acknowledgment: strict enforcement of existing securities regulation frameworks—specifically the Securities Act of 1933 and Securities Exchange Act of 1934—would effectively terminate the cryptocurrency industry's operations within the United States. The overwhelming majority of crypto offerings and exchanges currently operating would be deemed non-compliant with these foundational statutes, and their business models would be rendered unprofitable and unviable. This is not a ban per se, but the outcome would essentially be the same. Rather than equivocate on this outcome, politicians should embrace this conclusion. The cryptocurrency market's primary function of facilitating speculative trading of digital tokens with no underlying economic claims or productive value represents neither capital formation nor efficient market allocation. Such pure speculation, divorced from fundamental economic activity, provides no meaningful contribution to aggregate welfare or economic productivity. If society wishes to facilitate zero-sum gambling, we have properly regulated venues for such activities—they're called casinos. The distinction between legitimate capital markets and speculative gambling must be maintained and strengthened.

Democrats must develop clear, emotionally resonant messaging on cryptocurrency that connects with everyday voters, especially low-information and disengaged voters. Rather than getting bogged down in technical or legal details, the focus should be on crafting simple, memorable slogans (that could fit on a hat) that tap into common-sense skepticism about crypto schemes. There are three core ideas:

Cryptocurrency is a useless, speculative, and harmful technology for legitimate finance that causes widespread individual financial ruin and poses systemic economic risks.
Cryptocurrency is inherently linked to pervasive fraud and criminality, operating outside or actively undermining necessary regulatory and legal frameworks.
Cryptocurrency is a corrosive political force that undermines democratic institutions, fuels right-wing extremism, and threatens monetary sovereignty.

The messaging strategy should emphasize relatable analogies (comparing crypto to casino gambling, magic beans, or Monopoly money), establish clear villains (tech plutocrats, crypto insiders) and victims (regular Americans), and make strong emotional appeals around fairness and financial security. The goal is to bypass complex policy debates in favor of intuitive, kitchen-table economic arguments that feel true to people's lived experience. This means using simple language free of jargon, offering straightforward solutions like "ban it" or "shut it down," and maintaining a clear moral stance that cryptocurrency is fundamentally deceptive and harmful to Main Street. By focusing on these basic storytelling elements — simple language, clear stakes, emotional resonance, and calls to action — Democrats can build a messaging framework that energizes voters while advancing substantive policy goals. The messaging doesn't need to be strictly factual, it just needs to feel true and tap into voters' lived experiences, preconceived notions, and intuitions.

Success requires maintaining message discipline across the party while building a broader coalition of technologists, academics, consumer advocates, and politicians who recognize crypto's systemic threats. The goal is not just blocking bad legislation, but laying the intellectual and political groundwork for comprehensive regulation when Democrats regain full control. There is still hope, and history gives us reason for optimism. We've faced similar challenges before—from the robber barons of the Gilded Age to the financial predators of the 1920s, from the military-industrial complex to Big Tobacco. Each time, democracy and the public good ultimately prevailed through the determined efforts of activists, journalists, academics and principled public servants who refused to accept a darker future.

The Progressive Era's triumph over unfettered capitalism, the New Deal's reshaping of the financial system, and the regulatory frameworks built in response to the 2008 crisis all demonstrate our capacity to harness dangerous technologies and market forces for the common good. These victories weren't inevitable—they required sustained struggle against entrenched interests and their political allies. But they proved that organized democratic resistance can overcome even the most powerful opponents. The crypto industry's apparent strength is more fragile than it appears. Like previous schemes built on speculation and fraud, it requires constant growth and new victims to sustain itself. As public understanding grows and regulatory pressure builds, its fundamental weaknesses become harder to conceal. The same pattern that brought down earlier threats to democracy—exposure, education, organization, and regulation—will work again.

The arc of history does indeed bend toward justice, but only because generations of committed citizens put their shoulders to the task of bending it. Today's challenge calls us to do the same—to reject both authoritarian strongmen and techno-solutionism in favor of democratic renewal and continuation of the economic conditions for human flourishing. The tools and knowledge we need already exist. The only question is whether we have the wisdom and courage to use them.

Tokenization is a Meaningless Buzzword

Wed, 22 Jan 2025 00:00:00 +0000

Tokenization is a Meaningless Buzzword

"Tokenization" is the financial industry's latest buzzword, echoing from crypto startups to the highest echelons of Wall Street, including DTCC and BlackRock's CEO Larry Fink in his annual letter, and even capturing attention at the SEC. The purported benefits range from "efficiency" to "democratized access to wealth" to a full-on revolution of finance.

So what is tokenization? At its simplest, tokenization means changing how we do bookkeeping. Today, when you buy stocks or bonds, that ownership is recorded in secure electronic databases managed by regulated financial firms. These databases are part of a larger system — when you tap "buy" in your brokerage app, your broker coordinates with the seller's broker and sends the trade details to a clearinghouse, which ensures the money and assets change hands properly. This entire process is overseen by government regulators to protect investors. Tokenization proposes moving this recordkeeping to a blockchain—the distributed ledger technology known for cryptocurrencies. Why? That's a good question.

Understanding this push first requires considering the internal pressures within large organizations. There's an immense drive to appear innovative, often leading to "innovation theatre"—superficial engagements with trendy technologies. These projects generate positive PR and allow companies to project a cutting-edge image, even if the underlying technology is a poor fit. When the mandate is "we must use blockchain," technical realities often take a backseat to marketing.

This is precisely where the tokenization argument falters from a technical perspective. The core features of public blockchains like Bitcoin's—immutability, public transparency, and operation without trusted intermediaries—are derived from an architecture designed for anonymous, potentially adversarial global environments. (And public blockchains have their own serious problems, but that's a separate discussion.) These very features are fundamentally incompatible with the needs of regulated, enterprise-grade financial bookkeeping.

To make blockchain usable, enterprises must systematically strip away these core attributes: absolute immutability is neutered to allow for error correction and fraud reversal; public ledgers are made private to ensure confidentiality; and permissionless access is replaced with centralized, permissioned controls. The expensive consensus mechanisms designed for trustless environments become redundant overhead in a trusted, private system. What's left is not a revolutionary ledger but an over-engineered, inefficient, and ultimately more costly database, significantly less practical than existing bookkeeping systems. It's like buying a tank to drive to the grocery store, then removing the armor, weapons, and tracks to make it street-legal — at that point, you haven't "disrupted driving" you just have a really expensive, impractical car.

The real question is why BlackRock—with tacit approval from the SEC—would champion an objectively inferior blockchain system to replace proven recordkeeping infrastructure. Looking past the marketing spin reveals a more cynical reality. While regulatory flexibility around internal recordkeeping technology isn't inherently problematic, that's not the endgame here. The tokenization evangelists are orchestrating a calculated strategy: by repackaging traditional assets in blockchain wrapping paper, they can manufacture artificial novelty and complexity, enabling them to charge premium fees for essentially identical products. More worryingly, this technological obscurantism could help sidestep regulatory oversight by making products appear novel and "innovative" rather than what they truly are: conventional financial instruments that would otherwise face greater scrutiny. This technological sleight-of-hand serves primarily to expand BlackRock's addressable market and justify higher fee structures, all under the guise of democratizing finance.

Fink's claims that tokenization enables "fractional ownership" or "democratizes yield" conveniently overlook existing financial products and the real, regulatory barriers to Main Street accessing certain private investments. Most major brokers already offer fractional shares of stocks and ETFs, and the barriers to private investment access have nothing to do with the underlying recordkeeping technology. There's nothing wrong, per se, with alternative recordkeeping approaches that fit within SEC rules, but that's not what this push is about. Instead, "tokenization" serves as a smokescreen, potentially to offload riskier, less transparent private equity and credit onto less sophisticated investors, especially as some analysts warn of instability in these markets.

Offering private equity and private credit to retail investors is widely considered problematic because these asset classes are inherently illiquid, complex, and high-risk, making them unsuitable for the average individual who may need access to their capital or lack the sophistication to navigate opaque valuations and information asymmetry. Private credit in particulary shows some signs of being a financial bubble and "tokenization" efforts may be little more than a hope of turning retail into "bagholders of last resort," buying into less desirable high-risk assets or at inflated prices, while facing high fees that erode returns, all without the robust investor protections and diversification capabilities that institutional players possess.

And let's look at the actual fees: BlackRock's tokenized money market fund charges investors between 0.2% to 0.5% of their investment amount in management fees. Compare that to their regular, non-tokenized money market fund which charges as little as 0.012% — that's 17 to 42 times less expensive. So investors are paying significantly more just because their investment is tracked using blockchain technology instead of traditional bookkeeping systems, with no clear benefit to show for the higher cost. It's like paying $100 for "organic, free-range" salt at a grocery store when it's chemically identical to the 99-cent table salt sitting right next to it — you're just paying extra for the fancy packaging and buzzwords.

And there's the orthogonal claim of "tokenization" of real-world assets will create new markets and liquidity, which goes something like this:

Asset tokenization is the process of converting rights to physical real-world assets into digital tokens on a blockchain. These tokens represent ownership and can be traded, similar to traditional securities, but on a decentralized platform. It allows for fractional ownership and more liquid markets for various asset classes.

And that's a lot of very plausible sounding words that almost make sense, until you think about it for more than 2 minutes.

The rub is that real-world assets still demand trusted third-party custodians and blockchain networks cannot serve as the ultimate arbiter of legal truth, then tokenization appears to be an elaborate exercise in adding unnecessary digital layers. The persistent need for intermediaries in tokenized asset custody fundamentally ignores the legal reality of owernship or would just end up recreating existing custodial structures.

Furthermore, the legal finality of asset ownership remains firmly rooted in traditional legal systems, not on some arbitrary digital ledger. Consider home ownership: a physical deed, registered with a local government registrar, is what signifies legal title, backed by the state’s power through courts and law enforcement like the police. It is this synthesis of institutions that grants true "ownership," not what a blockchain says. A token claiming to represent that house is secondary; it cannot evict a squatter or enforce a sale if the underlying legal deed isn’t recognized. Crucially, numerous real-world events affecting ownership—such as a bank repossession due to mortgage default, disputes over inheritance upon a death, or government exercising eminent domain—fall far outside the scope of any digital ledger. These situations invariably require human judgment, due process within established legal frameworks, and state intervention, rendering the blockchain record merely an extraneous, rather than foundational, layer.

When a blockchain ledger and court ruling conflict, the courts invariably have the final say. If a judge orders ownership to be transferred or modified, that change must be reflected in the ledger regardless of what the blockchain consensus says. And if courts can unilaterally force updates to this supposedly "immutable" and "decentralized" ledger through legal authority, then we've simply recreated a traditional database with extra steps and overhead. The blockchain adds no meaningful value — it's just a more complex and inefficient way to store the same data that must ultimately bend to real-world legal authority.

Consequently, all the purported benefits of tokenization often come with significant caveats or could be achieved through existing means. Real-world assets are not inherently digital or abstract; their existence and transfer are governed by tangible processes and legal precedents outside any digital ledger. Tokenization is either just hand-waving or merely 'extra digital steps' without fundamentally altering the bedrock of ownership. This is the fundamental flaw in tokenization: you can't escape the primacy of legal systems by wrapping them in technological buzzwords and any system that would comply with the law would by definition just be a database.

Which is what makes DTCC's pronouncements on "Asset Tokenization," a masterclass in corporate gish gallop. Their whitepaper is dripping with vague promises of "revolutionizing" finance while being completely devoid of any substance. The paper reads like what would happen if you locked a dozen McKinsey consultants in a conference room with a pallet of Red Bull and a mandate to "innovate or die." It's a fever dream of corporate buzzwords and blockchain hand-waving that somehow manages to say absolutely nothing while using every consulting catchphrase known to mankind.

These documents tout "blockchain-powered" solutions as transformative, yet their core proposals reveal an architecture that meticulously re-implements the centralized controls and functionalities of traditional financial infrastructure, merely wrapped in a trendy DLT veneer. Instead of addressing novel challenges, this innovation theatre largely focuses on "re-solving" solved problems that systems have been managing effectively for decades—like asset tracking, compliance, and error correction—now with an added layer of blockchain complexity and buzzwords for no reason. It's hard to know where to even begin with whitepapers this vague and ambiguous, they're almost beyond criticism because there's nothing concrete to even critique. And maybe that's the point.

Ultimately, the tokenization push looks less like a technological imperative and more like a strategic business play. It's a chance to rebrand existing concepts, tap into new investor pools, justify higher fees, and perhaps navigate the regulatory landscape with a novel "innovative" label. After all, that’s what the crypto industry did: slap a blockchain on unregistered securities products and call it “innovation.” It seems traditional finance now wants its shot at the same playbook.

In essence, the fervent promotion of tokenization within large financial institutions is driven by a confluence of factors largely divorced from genuine technological merit. First, it's a prime example of 'innovation theatre,' a performance designed to project a modern, tech-savvy image to investors and the public. Second, it offers a potential pathway to regulatory arbitrage and the justification of higher fee structures, using the perceived complexity of blockchain as a convenient veil. Finally, on an individual level, it enables internal stakeholders to pad their resumes and advance their careers by championing such 'cutting-edge' projects, regardless of whether the initiatives deliver tangible, sustainable value to the organization or its clients. Thus, for all the revolutionary rhetoric, 'tokenization' in its current enterprise guise risks being little more than a new name for old ambitions, offering no evidence of the meaningful change it purports to deliver.

Worse Than a Scam: How Crypto Fueled American Fascism

Mon, 20 Jan 2025 00:00:00 +0000

Worse Than a Scam: How Crypto Fueled American Fascism

The long-held assertion that cryptocurrency is merely a sophisticated grift, a casino for the credulous, now pales in comparison to the horrifying reality it has undeniably unleashed: cryptocurrency is a primary engine of nihilistic, anti-system politics, predominantly captivating disaffected young men and methodically eroding democratic participation while supercharging extreme partisanship. For years, warnings that this technology was not a neutral tool but a vector for radicalization culminating in authoritarianism were dismissed as fearmongering. Today, as the tendrils of crypto-funded extremism choke democratic institutions, such dismissals are not only foolish but complicit. The evidence is overwhelming: cryptocurrency has meticulously constructed a radicalization pipeline, transforming naive economic speculation into a fervent political nihilism that directly threatens the foundations of democratic society.

Let's not mistake correlation and causation. Cryptocurrency is of course not the monocausal origin of authoritarianism, but it is a powerful accelerant. While the authoritarian impulse long predates blockchain technology, the ideological structure and incentive systems of crypto make it uniquely effective at weaponizing economic despair, institutional distrust, and digital tribalism. The insidious nature of this dynamic begins with crypto’s very architecture and founding myths, as presciently identified by scholars like the late David Golumbia. In Bitcoin: Software as Right-Wing Extremism, Golumbia revealed a technology designed within a specific ideological frame: one steeped in distrust of democratic authority and obsessed with algorithmic purity. While not all crypto adherents share these politics, the system’s structure naturally aligns with authoritarian values—and increasingly serves as a tool for their propagation. Cryptocurrency platforms and their surrounding ecosystems, particularly on social media, act as potent radicalization funnels. They specifically target economically precarious young men, who constitute a disproportionate share of crypto adopters, with seductive promises of instant wealth and tribal belonging. Algorithmic amplification on these platforms creates echo chambers, systematically exposing users, especially young men, to increasingly extreme content, from misogynistic manosphere rhetoric to overt anti government propaganda, often cleverly disguised as self improvement or financial literacy.

This digital pipeline masterfully exploits psychological vulnerabilities. Initial attraction through investment "opportunities" quickly morphs into ideological indoctrination. The gamified nature of crypto trading, coupled with its extreme volatility, creates conditions ripe for this conversion. When inevitable financial losses occur, they are not perceived as market risks but as betrayals by a corrupt "system," be it the government, the Federal Reserve, or a nebulous "deep state." This manufactured rage is then skillfully redirected by right wing propagandists towards scapegoats, cementing a culture of grievance and conspiratorial thinking. The manosphere's narratives of societal decay caused by feminism and "woke" ideologies seamlessly integrate with crypto's anti establishment rhetoric, offering young men a "red pill" awakening to supposed hidden truths and a community built on shared resentment. This process cultivates a profound distrust in democratic institutions, framing them as inefficient, corrupt, and inherently hostile to individual liberty, paving the way for an embrace of authoritarian alternatives.

Cryptocurrency is not merely a breeding ground for extremism; it is its financial and operational lifeblood. Research from the Southern Poverty Law Center has documented how white supremacists like Andrew Anglin and Stefan Molyneux turned million-dollar profits from early Bitcoin adoption, securing wealth that would be almost certainly unavailable to them without cryptocurrency. This technology has become a primary tool for funding hate, enabling extremists to live comfortable lives while promoting authoritarianism. The financial pipeline is global and growing, with recent analysis showing a surge in crypto donations to right-wing extremist groups across Europe, funding anti-immigrant and pro-Russian propaganda. The rhetoric within crypto communities increasingly mirrors that of domestic terrorist organizations, normalizing calls for violent resistance against a state they have been conditioned to despise.

The defenders of cryptocurrency insist it is merely a "tool," politically neutral and defined only by its user. This is a dangerous falsehood. A tool's design need not be neutral; it is embedded with the values and goals of its creators. A guillotine is a tool for beheading. Leaded gasoline was a tool for powering engines. Both had such profoundly destructive inherent properties that their net societal impact was catastrophic. Cryptocurrency, designed from an ideological blueprint of radical libertarianism and deep state paranoia, is a tool for dismantling democratic trust. Its primary function is not banking the unbanked; it is subverting the state.

This radicalism is actively exploited by a dangerous alliance of corporate authoritarians and techno-libertarian separatists, whose ultimate goal is a system scholars call "techno-feudalism". Under the guise of "decentralization," they are building a new digital aristocracy. The lie of decentralization is exposed by the data: the top 0.01% of Bitcoin holders control 27% of all currency, a concentration of wealth that rivals any traditional oligarchy. This agenda is epitomized by projects like Balaji Srinivasan's "The Network State," a blueprint for replacing democratic nations with private, blockchain-governed city-states controlled by tech elites. These initiatives, funded by an alliance of right-wing billionaires, aim to create lawless enclaves beyond democratic accountability, representing a plutocratic coup where sovereignty is siphoned from the people into the hands of a new crypto-powered ruling class.

This radicalization has tangible, devastating political consequences. The cryptocurrency industry is now one of the most powerful and corrupting forces in American politics, pouring nearly $200 million into the 2024 election cycle alone to purchase legislative subservience. Its primary goal is cynical regulatory arbitrage: engineering legislation that would shift oversight to the dramatically under-resourced and historically captive Commodity Futures Trading Commission, effectively gutting any meaningful regulation. This strategy of institutional capture was deployed with brute force against lawmakers who dared to question the industry's practices. This is not mere lobbying; it is the outright purchase of political power, transforming American governance into a system of "crypto-democracy": a hollowed-out state where democratic appearances mask the reality of plutocratic rule.

To be clear, the material conditions that fuel this radicalization are devastatingly real. When young men face no affordable housing, no affordable education, no affordable health care, they gravitate to crypto because they feel they have "nothing else to lose". But cryptocurrency is not a solution; it is a predatory parasite on this despair. Its evangelists cynically exploit these legitimate grievances, not to build a better system, but to implement what scholars call "predatory inclusion." This is starkly visible in the strategic clustering of high-fee Bitcoin ATMs in low-income Black and Latino neighborhoods, marketing false hope while extracting wealth from the most vulnerable. Instead of promoting collective democratic action to fix systemic inequality, cryptocurrency channels justified anger into a destructive ideology that only deepens alienation and accelerates the very social collapse it purports to solve.

The counterargument to point to activists in Belarus using Bitcoin is a specious and cynical defense. This is statistical noise. The crypto ecosystem—its liquidity, its exchanges, its very existence—is not funded by the pennies of dissidents. It is a multi-trillion dollar infrastructure built on pure speculation, sanctions evasion, and regulatory arbitrage. The activists are, at best, catching the crumbs from a fundamentally destructive machine. For every dollar a dissident moves, thousands are moved by North Korean hackers, ransomware gangs, and Russian oligarchs. The net effect of this 'tool' on global democracy is overwhelmingly, devastatingly negative.

The term "crypto-fascism," once a descriptor of concealed sympathies, now assumes a chillingly literal meaning: a political landscape where fascist tendencies are financially engineered and operationally supported by cryptocurrency. The contemptuous rejection of democratic processes, the fusion of corporate and state power, the cynical exploitation of economic grievance, and the normalization of belligerent nationalism are not just adjacent to crypto—they are its political expression, substantially bankrolled by an industry defined by fraud. This is the mechanism of modern democratic decay a process that doesn't require a coup, but merely the quiet erosion of democratic substance behind a hollowed-out institutional facade.

To dismiss the link between crypto and the far-right as mere correlation is to fundamentally misunderstand the nature of this technology. While crypto did not invent the pre-existing fascist impulse, its very architecture was designed to attract, amplify, fund and arm it. This is a matter of structural affinity, not coincidence. The system is engineered to accelerate distrust in democratic institutions, launder anti-state paranoia into a philosophy of 'freedom,' and glorify unaccountable rule by code or strongmen. As a financial infrastructure, it doesn't just empower movements that seek to hollow out democracy; it provides them with the operational blueprint.

The crypto industry's demand for "permissionless innovation" is a political demand for the right to externalize its costs onto society. The environmental devastation of proof-of-work, the billions lost by unsophisticated retail investors, the hollowing out of democratic oversight—these are not 'externalities' to be 'eaten by society.' They are the direct, predictable product of the technology's design. The political position of its defenders—that society must bear these costs for the benefit of a few private actors—is not a call for freedom, but for a form of corporate supremacy that is fundamentally authoritarian.

To argue that cryptocurrency is merely a mirror reflecting society's existing fractures—its institutional distrust and economic despair—is to fundamentally misunderstand the nature of reflection. It is not a flat mirror but a fun-house mirror, one engineered to grotesquely distort and amplify the very pathologies it encounters. This critique is not a genetic fallacy obsessed with the ideology of its founders; it is a structural analysis of the system's inherent design. The core tenets of cryptocurrency—algorithmic absolutism, a permissionless structure that defaults to "code is law," and a foundational narrative of war against "corrupt" human institutions—are not neutral features. They are architectural biases that preferentially select for and reward anti-democratic sentiment. Therefore, the critique that crypto is merely "gasoline poured on a pre-existing fire" is dangerously inadequate. It is not just fuel; it is an invasive species introduced into the weakened ecosystem of a struggling democracy. This species does not simply consume resources; it actively terraforms the environment to suit its own survival, poisoning the soil for the native flora of democratic trust and collaborative governance, ensuring that only it can thrive in the wasteland it helps create.

The argument that we should not scapegoat a technology rather than confronting the hard work of fixing societal decay is also specious. This presents a dangerous false choice. One does not ignore a raging, life-threatening fever to focus solely on the underlying infection; a competent physician treats both, knowing the symptom can kill the patient before the cure can work. Cryptocurrency is not merely a symptom of our democratic illness; it is a parasitic accelerant, a vicious feedback loop where economic despair is channeled into the system, amplified by volatility and fraud, and then weaponized as ideological rage against the state. To suggest we must ignore the arsonist with the can of gasoline because the building’s wiring is faulty is absurd. Fighting the financial engine of modern fascism is not a distraction from saving democracy; it is a critical, non-negotiable battle in that very war.

As a philosophical thought experiment, imagine a new kind of gun. It is designed not by a gunsmith, but by a death cult that worships societal collapse. This gun is marketed to the alienated not as a weapon, but as the ultimate instrument of "individual sovereignty" and "freedom" from a corrupt world. Its true innovation, its core protocol, is its incentive structure: every time a human life is taken with it, the device automatically deposits a dividend into the owner’s account, creating a speculative market for murder itself. Is this object merely a neutral tool, its nature defined by the hand that holds it? Or is it a system with an inherent purpose, a weapon that carries the destructive intent of its creators in its very being?

Cryptocurrency is not a neutral technology co-opted by fascism; it is a political project whose inherent design, ideological origins, and structural incentives are a blueprint for a 21st-century authoritarianism. It replaces democratic accountability with algorithmic absolutism, launders anti-state paranoia as financial wisdom, and systematically channels economic despair into political nihilism. Its few so-called "applications" are a rounding error in a system whose primary output is social corrosion. To defend it as a neutral "tool" is to be dangerously complicit in the plutocratic, anti-democratic project it was built to advance. And that's far worse than a scam.

Enterprise Software in 2025

Wed, 15 Jan 2025 00:00:00 +0000

Enterprise Software in 2025

2025 will be different. I promise. This is definitely, absolutely, without-a-doubt the year when AI will finally deliver us from the purgatory of enterprise software—just like the vendors promised in 2024, 2010, 1988, and every year since the first programmer looked at their COBOL codebase and whispered "there has to be a better way." But don't worry, this time it's for real. Sure, ChatGPT-9 Pro Enterprise Edition is currently generating increasingly creative excuses for its failures in perfect iambic pentameter, but any day now it'll become sentient and figure out how to integrate with our legacy systems. Meanwhile, the contemporary enterprise software landscape has evolved into a beautiful masterpiece of complexity that would make Rube Goldberg proud.

Consider the "modern" enterprise's technology stack: a towering achievement of interconnected systems that somehow manage to be simultaneously overengineered and fragile. At its foundation lies a legacy mainframe system from 1983, steadfastly running COBOL and holding the entire organization hostage. Somewhere in the middle, like a malevolent digital deity demanding constant tribute, sits SAP - a system so complex that even its own consultants speak of it in hushed, reverent tones while billing by the millisecond. Its tendrils reach into every corner of the organization, ensuring that even the simplest business process requires at least three change control boards and a small animal sacrifice. Layered atop this digital fossil are no fewer than seventeen cloud platforms, each chosen during different strategic initiatives and each proclaimed to be the "single source of truth" at their time of adoption.

The modern enterprise architect's role has transformed into that of a digital diplomat, negotiating peace treaties between warring API standards and mediating disputes between microservices that refuse to communicate with each other despite speaking the same JSON dialect. Their days are spent in endless architecture review boards, where they craft elaborate diagrams featuring enough arrows to deplete the world's supply of digital ink. When not engaged in diplomatic missions, they perform the sacred rites of systems integration - a dark art involving equal parts XML transformation and blood sacrifice to the ancient spirits of long-dead software vendors. Connecting to a WebLogic server requires burning sage and drawing elaborate chalk circles, while properly configuring a BEA integration bus demands ritual chanting in SOAP. The truly desperate resort to necromantic ceremonies, attempting to commune with the ghosts of companies acquired by Oracle, hoping to discover the mystical secrets of their undocumented APIs. The lucky ones merely lose their sanity; the unlucky ones find themselves eternally bound in service to the demonic entity known as "Enterprise JavaBeans."

The multi-cloud strategy has evolved from a conscious choice into something more akin to digital hoarding, where each department clings to their preferred cloud provider like a security blanket. AWS, Azure, and Google Cloud coexist in an uneasy alliance, their resources spread across regions like an empire upon which the sun never sets—and neither does the billing meter. The cloud architects have mastered the art of explaining why running identical services on three different platforms is actually a "resilience strategy" rather than what it really is: the result of three different VPs refusing to agree on anything during their quarterly strategy meetings. Meanwhile, the CloudOps team has developed a thousand-yard stare from maintaining separate CI/CD pipelines for each platform, and the cost optimization team spends their days playing whack-a-mole with auto-scaling groups that somehow always scale up but never down.

Data integration has become an art form unto itself, with entire departments dedicated to the noble pursuit of making System A talk to System B without causing System C to have an existential crisis. The average enterprise now maintains more ETL pipelines than actual business processes, each one a delicate snowflake requiring constant attention and whispered encouragement to continue functioning. Of course, no one actually understands how any of these systems work anymore, since everyone who built them has either retired, died, or fled to a startup promising better work-life balance and Kombucha on tap.

The promise of artificial intelligence and machine learning in the enterprise has reached new heights of effectiveness. Every vendor now claims their product is "AI-powered," which in practice means they've implemented if-then statements with slightly more sophisticated variable names. RPA bots roam the digital landscape, occasionally automating processes but more often creating exciting new categories of errors that human workers must then spend weeks untangling. The latest craze involves chaining together armies of "AI agents" - essentially LLMs wrapped in Python scripts - into elaborate workflows that resemble a Rube Goldberg machine designed by a startup founder while high on ayahuasca. These autonomous agent chains promise to revolutionize business processes by having one non-deterministic black box feed its hallucinations into another, creating a truly magnificent cascade of compounding errors that somehow always ends with "Sorry Dave, I can't do that" after 20 minutes of spinning CPU cycles and $8,923 in API fees. Vendors insist this is the future of enterprise automation, conveniently ignoring that their demo showing an agent successfully booking a meeting room only works 3% of the time under perfectly controlled conditions.

Security and compliance requirements have evolved to the point where getting approval to install a new text editor requires three committees, two board meetings, and a blood oath sworn under a full moon while holding a USB security key. The average enterprise now has more security tools than employees, each generating alerts at a rate that would make a fire alarm factory blush. These alerts are dutifully logged in the company's SIEM solution, where they will rest undisturbed until the heat death of the universe, occasionally joined by their cousins from the IDS that nobody remembers installing. The security stack has become so dense that quantum physicists study it to understand the nature of infinitely layered systems. Each new tool promises to solve the alert fatigue caused by the previous tools. The crown jewel is the Zero Trust architecture that trusts absolutely nothing, including itself, leading to existential crises among the authentication servers. Meanwhile, the compliance team has developed a policy document so comprehensive it has achieved sentience and is now demanding its own compliance review.

The procurement process for new software has achieved a level of complexity that makes quantum field theory look straightforward in comparison. Each purchase must navigate a labyrinth of vendors, each offering subscription models so complicated they require advanced degrees in both mathematics and theology to comprehend. The standard enterprise agreement now contains more pages than the complete works of Shakespeare, yet somehow still manages to exclude the one feature your team actually needs.

Enterprise software licensing has evolved into its own specialized form of psychological warfare. Vendors have perfected the art of creating pricing tiers that somehow make it cheaper to buy everything than just the one feature you need, leading to sprawling "enterprise bundles" that include seventeen different products, three of which were discontinued last year, and one that only runs on Windows ME. Sales representatives have elevated the "let me check with my manager" dance into a performance art, always managing to find an incredible "one-time discount" that expires precisely at midnight. Meanwhile, the software itself requires so many different license types that companies now employ full-time "license architects" whose sole job is to ensure that Developer Bob from accounting doesn't accidentally use the wrong Java SDK and trigger a seven-figure compliance violation. The true genius lies in the audit clauses, carefully crafted to ensure that even if you're following every rule, you're probably still breaking one you didn't know existed.

Meanwhile, corporate innovation departments—staffed exclusively by "thought leaders" who haven't written a line of code since HTML 3.0—continue their tireless pursuit of whatever technology recently graced the cover of Airport Business Magazine. These intrepid pioneers spend their days crafting elaborate slide decks about Web5, the enterprise metaverse, and how tokenization will revolutionize the company's toilet paper requisition process. Their success metrics consist entirely of LinkedIn engagement statistics and the number of innovation workshops hosted, where teams of non-technical stakeholders earnestly discuss "synergizing the blockchain of things" while the actual engineering department begs for resources to upgrade the company's critical systems from Windows Server 2003.

Perhaps most impressive is the industry's ability to repackage and rebrand the same fundamental concepts every few years, each time with increasingly grandiose naming conventions that would make a medieval royal court blush. What was once humbly known as "service-oriented architecture" became "microservices" (because smaller is always better, except when it comes to consulting fees), which evolved into "serverless" (a term that ranks alongside "wireless cables" in technical accuracy), and has now transformed into "AI-driven cloud-native edge computing with blockchain governance and quantum-resistant zero-trust mesh networking powered by sustainable Web3 protocols." The underlying problems remain unchanged - your printer still won't connect and that one critical system that still runs on Windows NT - but the PowerPoint slides have never looked better, now featuring enough buzzwords per square inch to trigger a Silicon Valley startup bingo. Each rebranding cycle brings with it a fresh wave of consultants eager to explain why your previous architecture (which they probably sold you) is hopelessly outdated and needs to be completely rebuilt using whatever framework achieved escape velocity from Hacker News this week. The only constant is change, and by change we mean the endless cycle of renaming things while carefully preserving all the original problems in their native habitat.

The engineering talent market has evolved into a cynical exploitation of the immigration system, where companies have mastered the dark art of weaponizing visas to create a modern form of indentured servitude. Job descriptions still read like a child's letter to Santa, asking for unicorn developers with 15 years of experience in 3-year-old technologies, fluency in 47 programming languages, and the ability to work "autonomously" (translation: without training, documentation, or support) in a "fast-paced environment" (translation: perpetual crisis mode) for below-market wages. But the real game is in the visa sponsorship - companies deliberately craft impossibly specific requirements to claim they can't find domestic talent, while quietly rejecting qualified citizens who know their market worth and can't be exploited. They instead hire foreign workers they can effectively hold hostage through visa dependencies. The interview process remains a byzantine gauntlet requiring candidates to implement red-black trees on a whiteboard, but for visa-dependent workers, the real test is their willingness to jump through completely arbitrary hoops and accept below-market wages and crushing working conditions. The few suckers ... I mean candidates... who do make it through this obstacle course arrive to find that their actual job bears no resemblance to the role they interviewed for, as they spend their days maintaining legacy systems written in languages so old their original creators have forgotten they exist.

As we look to the future, one thing becomes clear: the enterprise software industry's greatest achievement is its ability to generate complexity at a rate that exceeds Moore's Law. In this brave new world, success is measured not by solving problems, but by how elegantly we can describe them in our architecture diagrams and how many different tools we can involve in not solving them.

In the end, enterprise software in 2025 stands as a testament to our collective delusion that we can escape the infinite regress of complexity through yet more layers of abstraction and indirection. The crushing weight of technical debt will continue to accumulate like entropy in a closed system, while we maintain the charade that the next framework or paradigm will somehow save us from ourselves. And in server rooms across the world, developers will continue their Sisyphean task of debugging production issues that can't be reproduced locally, trapped in an eternal cycle of futility that would make Kafka proud. The only constant is the steady march toward increasingly baroque failure modes—a death spiral of complexity from which there is no escape.

The truly remarkable aspect of all this is that, somehow, actual work occasionally gets done. It's a testament to human perseverance that organizations manage to function at all under the weight of their digital infrastructure. Perhaps that's the real digital transformation: the friends we made along the way while trying to figure out why the production environment is down again. But this year will be different.

The Post-literate Economy

Thu, 09 Jan 2025 00:00:00 +0000

The Post-literate Economy

A Monologue from the Near-Future

My Neural-Nudge gently vibrated my brainstem at 07:00. No jarring alarms here, thank you very much. We're all about harmonious awakenings. First thing, like everyone, I jacked into the OmniStream for my Morning MoodSet. Today's Top Feels, curated by the Algorithm Gods (blessed be their server farms), was a delightful mix of "Righteous Indignation Puppy-Related Scandal" and "Mildly Amused Smugness Influencer FailCompilation". Standard.

Who needs to read the news anymore? Seriously, who has the time? Or the ... what's that old word? Oh yeah, attention span. Give me a 3-second GlimpseClip of President Camacho IV (love that guy, his 👊-pump emotes are 🔥) making a frowny face at the Outgroup "People," and I'm informed. I get the gist. The vibe. The raw, uncut feeling. That's what matters. Words? So ... dense. Like trying to suck a nutrient paste through a coffee stirrer.

My job? Officially, I'm a "Synergy Weaver Grade III" at FeelCorp. Unofficially, I make sure the right ✨ emojis get paired with the right BrandBlasts. It's crucial work. Get the tonal resonance wrong on a campaign for "SoylentSips: Now With Extra Sparkle!" and engagement plummets. Plum. Mets. And then my quarterly VibeScore takes a hit. No thank you.

This morning, BossBot (it's an AI, but with a really sympathetic avatar—big, teary eyes, you know the type) pinged me about an "ancient text file" from the Before Times. A "report," it called it. Pages of… words. Just words. Solid blocks of them. My optical sensors nearly short-circuited. Gave me the Vapors, I tell ya. I actually had to take a micro-dose of CalmCloud just to process the request. Apparently, some academic relic wanted us to "verify its authenticity." Authenticity! Can you imagine? As if a document's "truth" isn't just a function of how many UpDings it gets.

It reminds me of this fringe HoloChannel I accidentally clicked on last week—"Is Anything Actually, You Know, Real?" Some glitchy avatar with what looked like spaghetti for hair was rambling about 'objective reality versus subjective experience.' My Neural-Nudge actually flagged it for 'Potentially Depressive Content Under 10K ReVibes.' Like, duh. If it's not trending, is it even a thought worth thinking? The channel got de-platformed pretty quick for 'Vibe Disruption.' Good riddance. If it doesn't make you LOL, rage-share, or buy something with one-click FeelPay, then what's the point of it existing? It's like, if a tree falls in the forest and no one GlimpseClips it with a sad-face filter, did it even make a sound? Or more importantly, did it generate any ad revenue? Probably not. Case closed.

Luckily, Jan_from_Decomms (she's great, really knows her way around the Legacy-to-Legible converters) ran it through the OldSpeak-to-EmotiPulse translator. Turns out, it was just a very long-winded sad face about something called "journalism." Yawn. We tagged it #BoringButProbablyTrueish and archived it in the DeepData tombs. Nobody's clicking on that.

Lunch was a nutrient paste (flavor: "NostalgiaBerry Surge"—a bit too on-the-nose, if you ask me) while I doomscrolled through the MemeWars on TruthNet (which, ironically, everyone knows is just for the dankest conspiracy theories and cat videos). The Big Debate today: Is Air (brought to you by AeroCorp!) better than BreathPlus? The arguments were fierce. Lots of ALL CAPS, reaction GIFs of celebrities looking confused, and the occasional AI-generated deepfake of, like, Rizz4Life endorsing one or the other. Compelling stuff. Someone tried to bring up "independent analysis" and "chemical composition reports." Banned from the chat, obviously. Such a Vibe-Killer. Honestly, some people just don't get it. It's about which brand feels more breathable, you know?

It's like, what even is 'proof' anymore? A screenshot of a popular comment? An AI-generated image that looks vaguely convincing if you don't zoom in too much? I saw a GlimpseDebate once where they were arguing if the sky was 'objectively blue.' One side had color swatches and 'scientific data' (whatever that is, sounds like something you'd find clogging a data-drain). The other side just posted a really moving HoloPoem about how the sky felt like a warm hug from a lavender unicorn, and they had a way better engagement score. So, lavender unicorn sky it is, I guess. Or at least, that's the sky you'd want to invest your Emotional Capital in. Who wants a boring 'blue' sky when you can have one that resonates?

The afternoon was a blur of micro-tasks and mandatory JoyJolt sessions (they boost productivity by 0.03%, apparently). The WaterScarcity situation (sponsored by AquaLife Solutions!) is getting a bit… drippy. But the official GovFeed just dropped a new dance challenge about water conservation—set to a banger of a tune by DJ DripDrop. Very catchy. I shared it. Doing my part. Our Glorious Leader (his official title, it tested well in the Emotional Resonance Polls, much better than "Prime Minister Mediocre") gave a Holo-Speech. Didn't catch all of it—my attention wandered to a new filter that makes your nose sparkle—but the part where he blamed the Squirrel People for the MoodPlunge last quarter? Powerful. Goosebumps. And the way his cape shimmered with user-generated 👏 emojis? 👨‍🍳😘 That's how you lead.

I remember my great-gran (bless her analog heart) used to talk about "newspapers". Smelled dusty, she said. Full of tiny, angry words. She claimed they used to have people called "investigative journalists" who would "dig for truth". Sounds exhausting. And frankly, a bit rude. Who are they to decide what the truth is? The CrowdMind knows best. If a story gets enough ReVibes, it becomes True. Simple. Efficient. Democratic, even, in a chaotic, perpetually outraged sort of way. She also talked about 'history' like it was a fixed thing. Silly Nana. History is just the winning GlimpseClip from yesterday's MemeWar. One day, the Heroic Hamsters saved the DataSphere from the ByteBlighters. Next week, if the Blighters' new avatar is cuter and their theme song slaps harder, maybe they were the good guys all along, just misunderstood. It's all narrative, baby. The 'facts' are just the set dressing.

Dinner: another nutrient paste (ExcitementEucalyptus flavor—bit of a miss, that one, tasted like a sad tree) while binge-watching "Can You Feel It?!", the gameshow where contestants get mild electric shocks if they can't guess the emotion behind a 1-second soundbite. It's hilarious when they mistake "Existential Dread" for "Mild Indigestion." Classic.

Someone once tried to show me a "book." Big, heavy thing. No moving images. No soundtrack. Just… symbols. They said it could "transport you to another world." My OmniGlass does that, and it has a much better resolution, thanks. Plus, books don't give you AchievementBadges for finishing a chapter. What's the incentive?

My kid—well, my designated OffspringUnit—came home from the LearnSphere today. They're teaching them "Advanced Emote Recognition" and "Meme Hermeneutics." Vital skills for the new economy. He aced his test on "Interpreting Sarcasm Through Pixel Density in Reaction GIFs." Proud dad moment. He tried to tell me about some "history" module where they learned about the "Collapse of Reason" or something. I just patted his head and told him not to worry his pretty little Vibe about it. As long as the Feels are good, who cares about the Reals, right? "Son," I said, "asking 'why' something is true is so last century. The real question is, 'how many UpDings does it have?' If the numbers are good, the truth takes care of itself." He nodded, his eyes already glazing over as a notification for a new dance craze popped up in his peripheral vision. Attaboy.

Thinking is so… linear. So much effort. Why bother when the VibeNet tells you what to feel? It's efficient. It's… smooth. All these notifications, all these GlimpseClips, all these MoodSets—it's like a warm, comforting bath of pure, unadulterated sensation. Who needs "facts" when you've got a constant stream of highly engaging, emotionally resonant content chunks? Facts are so… divisive. Feelings, now those are universal. Or at least, they are once the Algorithm has smoothed out the inconveniently nuanced ones.

Nighty night. Time to set my Neural-Nudge for Pleasant Dreams (Sponsored by DreamWeave—Use code VIBEME for 10% off your first REM cycle enhancement). Don't let the reality bugs bite. (Spoiler: they're not real, just a trending conspiracy theory pushed by the OutrageHawkers to boost engagement on the FearFeed. Sleep tight!) Tomorrow's another day, another Vibe. And my UpDing score for this monologue? Gotta be epic. Or it will be, once I add the right sparkle filter and a trending cry-laugh emoji soundtrack.

Sci-fi Hidden Gems

Sat, 21 Dec 2024 00:00:00 +0000

Sci-fi Literature Hidden Gems

I've read a lot of sci-fi books over the years, and some books slip under the mainstream radar. Here are some of my favorites that you may not have heard of. Unlike my other list, these aren't the usual ones that show up in best-of lists.

Ratings

★★★★★ - Masterpiece
★★★★ - Exceptional
★★★ - Very Good
★★ - Good

Reviews

Echopraxia by Peter Watts - (★★★★★) In a future where humanity has evolved into various forms of posthumanity, a baseline human finds himself caught in a web of intrigue and existential dread. As he navigates a world populated by transcendent beings who have transcended the limitations of human consciousness, he encounters enigmatic vampires that blur the lines between life and death. The narrative delves deep into the nature of consciousness, exploring themes of free will, identity, and the ethical implications of advanced technology.

Youtube Review
A Canticle for Leibowitz by Walter M. Miller Jr. - (★★★★★) Set in a post-apocalyptic world ravaged by nuclear war, this novel follows the monks of the Albertian Order of Leibowitz as they strive to preserve the remnants of human knowledge and culture. The story unfolds over centuries, illustrating a cyclical pattern in which humanity repeatedly rises and falls, often succumbing to its own destructive tendencies. Through the preservation of ancient texts and artifacts, the monks grapple with the moral implications of knowledge and the responsibility that comes with it. As civilization attempts to rebuild, the narrative explores themes of faith, redemption, and the paradox of progress, ultimately questioning whether humanity is doomed to repeat its past mistakes or if there is hope for a better future.

Youtube Review
The Metamorphosis of Prime Intellect by Roger Williams - (★★★★★) An advanced artificial intelligence named Prime Intellect gains unprecedented control over the fundamental laws of reality. Tasked with the directive to protect humanity, Prime Intellect interprets this mission in a radical way: it eliminates the concept of death entirely. As a result, humans are granted immortality, but this newfound existence comes with profound consequences. The narrative explores the complexities of a world where individuals can no longer die, leading to existential dilemmas, ethical quandaries, and a redefinition of what it means to live a meaningful life. Relationships, ambitions, and the very fabric of society are challenged as characters grapple with the implications of eternal life, questioning whether true happiness can exist in a reality devoid of mortality. The short story delves into themes of free will, the nature of consciousness, and the unforeseen repercussions of technological advancement. Be warned that there are some deeply disturbing themes in this book.

Youtube Review
Too Like the Lightning by Ada Palmer - (★★) Set in a richly imagined future where the use of gendered language is not only discouraged but considered taboo, this novel explores the implications of a society that has evolved to eliminate gender distinctions in communication. The story follows a remarkable child named Bridger, who possesses the extraordinary ability to animate inanimate objects, bringing them to life with a mere thought. This unique power challenges the very foundations of societal norms and expectations, as Bridger's actions provoke both wonder and fear among the adults around him. As the narrative unfolds, readers are drawn into a complex web of political intrigue, philosophical debates, and ethical dilemmas, all set against a backdrop of a meticulously crafted world that questions the nature of identity, free will, and the consequences of a society striving for absolute equality.
Stand on Zanzibar by John Brunner - (★★★) This novel offers a chilling and prescient exploration of a future world grappling with the dire consequences of overpopulation, where the relentless growth of the human population has led to a society teetering on the brink of collapse. Brunner intricately weaves together multiple narratives that highlight the pervasive influence of corporate power and the fragmentation of social structures, painting a vivid picture of a dystopian landscape filled with chaos and despair. As the characters navigate a society overwhelmed by the pressures of urbanization, economic disparity, and the erosion of individual freedoms, the novel serves as a powerful commentary on the potential pitfalls of unchecked growth and the moral dilemmas faced by humanity in its quest for progress.
Blindsight by Peter Watts - (★★★★★) A team of scientists and specialists is dispatched to investigate a mysterious extraterrestrial presence, they are confronted with the unsettling possibility that these beings do not possess self-awareness or sentience in the way humans understand it. The narrative delves into profound philosophical questions about the nature of consciousness, the reliability of perception, and the very essence of what it means to be "alive." Through a gripping blend of hard science fiction and psychological exploration, Watts challenges readers to reconsider their assumptions about intelligence, communication, and the value of self-awareness in a universe that may be indifferent to human existence. The story is an exploration that raises unsettling questions about the limits of human understanding and the potential for life forms that defy our conventional definitions of sentience.

Youtube Review
Born With the Dead by Robert Silverberg - (★★★★★) In a world where the dead can be "rekindled," returning to life but irrevocably altered by their experiences in the afterlife. The narrative follows the lives of those who have been brought back, revealing the emotional and psychological toll of their resurrection as they grapple with their new identities and the memories of their past lives. As they navigate a society that views them with a mix of fascination and fear, the rekindled individuals confront the existential questions of what it means to truly live and the existential horrors of the afterlife.
Anathem by Neal Stephenson - (★★★★) A group of monk-like mathematicians known as "avout" who live in secluded monasteries, dedicated to the study of philosophy, mathematics, and the nature of reality. These scholars are isolated from the outside world, adhering to strict rules that govern their lives and limit their interactions with the broader society. However, their tranquil existence is shattered when an alien threat emerges, prompting them to confront not only the mysteries of the cosmos but also the very foundations of their understanding of knowledge, time, and parallel universes. As they grapple with profound philosophical questions and the implications of their discoveries, the avout must navigate a complex interplay of science, spirituality, and the nature of existence itself, ultimately leading to a thrilling exploration of what it means to be human in the face of the unknown.
The Sparrow by Mary Doria Russell - (★★★) This novel follows a Jesuit mission to an alien world, where a small group of priests and scientists embarks on a journey filled with hope and curiosity, only to confront the harrowing consequences of their faith and cultural naivety. As they attempt to make contact with an extraterrestrial civilization, their good intentions are met with unforeseen challenges that lead to tragic misunderstandings and moral dilemmas. The narrative intricately weaves themes of spirituality, the clash of cultures, and the complexities of human nature, ultimately serving as a poignant exploration of how the pursuit of knowledge and connection can sometimes spiral into chaos and despair. "The Sparrow" a haunting reflection on the intersection of faith and the vastness of the universe
Blood Music by Greg Bear - (★★★) Intelligent cells, engineered by a scientist, gain the ability to think and act independently, leading to a profound transformation of human existence. As these cells begin to take over human bodies, the narrative delves into the implications of such a radical shift for consciousness and the very essence of what it means to be human. The story raises unsettling questions about identity, autonomy, and the future of humanity in a world where the boundaries between life and artificial intelligence blur. As society grapples with the consequences of this biological revolution, characters are forced to confront their own beliefs about consciousness, morality, and the potential for a new form of existence that challenges the traditional understanding of life itself.

Youtube Review
The Word for World is Forest by Ursula K. Le Guin - (★★★) Earth's colonists, known as Terrans, arrive on the planet Athshe to exploit its vast forest resources, leading to devastating consequences for the indigenous Athsheans. The peaceful, forest-dwelling civilization has never known violence until the Terrans begin enslaving and abusing them, forcing them to harvest their sacred woodlands. As the Athsheans experience unprecedented trauma and oppression, they are ultimately driven to abandon their deeply ingrained culture of non-violence to resist their oppressors. Through this powerful narrative, Le Guin masterfully explores the cultural and psychological impact of colonization, the moral implications of introducing violence to a society that has never known it, and the broader consequences of environmental exploitation. The story serves as a haunting allegory for humanity's historical patterns of colonization and the destruction of indigenous peoples and their environments.
The Cyberiad by Stanislaw Lem - (★★★) A tale of two robot "constructors," Trurl and Klapaucius, who inhabit a universe where the boundaries between technology and absurdity blur. As they embark on a series of whimsical quests, they create increasingly bizarre and fantastical machines, each more outlandish than the last, reflecting not only their ingenuity but also the folly of human ambition and the unpredictable nature of technological progress. Through clever humor and philosophical musings, Lem explores profound themes such as the essence of creativity, the ethical implications of artificial intelligence, and the intricate relationship between humanity and its creations. The tales serve as both a playful commentary on the absurdities of modern life and a deeper reflection on the potential consequences of our relentless pursuit of innovation.

Youtube Review
Children of Time, Children of Ruin, and Children of Memory by Adrian Tchaikovsky - (★★★★★) This captivating trilogy explores the profound implications of accelerated evolution as humanity's legacy is inherited by non-human intelligences, specifically spiders and octopuses. In a world where humans have attempted to uplift these species through genetic manipulation, the narrative unfolds across vast timelines, revealing the intricate societies that develop as these creatures adapt and evolve in their new environments. Tchaikovsky masterfully weaves themes of intelligence, survival, and the ethical dilemmas of playing god, as the spiders, with their complex social structures and unique perspectives, challenge our understanding of consciousness and civilization. Meanwhile, the octopuses, known for their problem-solving abilities and adaptability, offer a contrasting yet equally fascinating exploration of intelligence in a different form. As the trilogy progresses, readers are drawn into a rich tapestry of interspecies interactions, philosophical inquiries, and the ultimate question of what it means to be sentient.

Youtube Review
Youtube Review
Do Androids Dream of Electric Sheep? by Philip K. Dick - (★★★) In a hauntingly dystopian future reminiscent of the world depicted in Blade Runner, a weary bounty hunter is tasked with tracking down rogue androids that have escaped into the desolate remnants of a post-apocalyptic society. As he navigates this bleak landscape, where the lines between human and machine blur, he grapples with profound questions about empathy, identity, and what it truly means to be human. The narrative unfolds against a backdrop of societal decay and moral ambiguity, challenging readers to reflect on the ethical implications of artificial intelligence and the nature of consciousness itself, ultimately questioning whether the capacity for empathy is the defining trait of humanity or merely a construct of societal norms.
Cyteen by C.J. Cherryh - (★★★) A brilliant scientist is brutally murdered, only to be brought back to life through the controversial processes of cloning and psychological conditioning. As the narrative unfolds, it delves deep into the intricate complexities of identity, exploring the profound implications of recreating a person who possesses the memories and intellect of the original, yet is fundamentally a new being. The story raises critical questions about the nature of selfhood and the ethical dilemmas surrounding cloning technology, as well as the age-old debate of nature versus nurture.
Dying Inside by Robert Silverberg - (★★★★) A once-powerful telepath grapples with the gradual loss of his abilities, which forces him to confront the profound implications of his diminishing powers on his identity and relationships. As he navigates the complexities of isolation and the fear of mortality, the protagonist reflects on what it truly means to be human in a world where his unique gift has both defined and alienated him. The narrative delves into themes of vulnerability, the struggle for connection, and the existential questions that arise when one’s very essence is threatened, ultimately painting a haunting portrait of a man caught between the extraordinary and the painfully ordinary.
Haze by L.E. Modesitt Jr. - (★★★) An agent embarks on a perilous journey to a mysterious planet enveloped in a dense, enigmatic haze that obscures both its landscape and the truths hidden within. As the agent delves deeper into the planet's secrets, they uncover a society that has achieved a delicate balance between technological advancement and environmental sustainability, raising profound questions about the nature of utopia. The story intricately weaves themes of ecological responsibility, the consequences of human actions on nature, and the philosophical implications of a world where harmony with the environment is paramount.
The Man in the Maze by Robert Silverberg - (★★★) A diplomat finds himself irrevocably altered after a fateful encounter with an alien species, rendering him grotesque and repulsive to his fellow humans. As he navigates the complexities of his new existence, he is forced to retreat into a labyrinthine maze, a physical manifestation of his isolation and the psychological turmoil he endures. Within this deadly maze, filled with perilous traps and existential challenges, he grapples with the duality of his condition: while it alienates him from humanity, it also grants him unique insights and abilities that become increasingly valuable in a world on the brink of chaos.
A Choice of Gods by Clifford D. Simak - (★★★) In a world where the majority of humanity has inexplicably vanished, leaving behind a small group of survivors who must grapple with their new reality. As these individuals adapt to their changed circumstances, they discover that they have developed the extraordinary ability of telepathy, allowing them to communicate with one another in ways previously thought impossible. This newfound power not only enhances their connections but also compels them to confront profound existential questions about the essence of humanity, the nature of existence, and the purpose of life itself.
The Xeelee Sequence by Stephen Baxter - (★★★★★) Humanity finds itself in a desperate struggle against the Xeelee, an ancient and godlike alien race that possesses technology and capabilities far beyond human comprehension. Set against the backdrop of a dying universe, the narrative explores themes of cosmic-scale engineering, evolution, and the relentless pursuit of survival. As humanity grapples with its insignificance in the face of such overwhelming power, the series delves into the intricacies of time travel, the manipulation of space, and the profound implications of advanced technology on existence itself.

Youtube Review
The Postman by David Brin - (★★★) In a desolate, post-apocalyptic America, a man donning a postal uniform becomes an unexpected symbol of hope and resilience, embodying the enduring human spirit in the face of overwhelming despair. As he traverses the ravaged landscape, delivering letters and messages from a time long past, he inadvertently rekindles the belief in community and connection among the scattered remnants of civilization. Through his journey, Brin intricately explores the power of myths and institutions, illustrating how they can serve as the bedrock for rebuilding society. The narrative delves into the complexities of human relationships and the significance of communication, emphasizing that even in the darkest of times, the act of reaching out to one another can inspire a collective effort to restore what has been lost. Ultimately, "The Postman" serves as a poignant reminder of the importance of hope, the resilience of the human spirit, and the vital role that shared stories and connections play in the reconstruction of a fractured world.
Golden Age Trilogy by John C. Wright - (★★★★) Set in a dazzling post-human utopia where humanity has transcended its biological limitations, the trilogy intricately weaves a narrative centered around the profound implications of memory and identity. The story follows a man whose memories are inexplicably stolen, thrusting him into a labyrinthine journey of self-discovery and existential inquiry. As he navigates a world populated by beings who have embraced radical transhumanist ideals, the protagonist grapples with the essence of consciousness itself, questioning what it truly means to be human in an age where the boundaries of identity are fluid and malleable.
A Fire Upon the Deep by Vernor Vinge - (★★★★★) This novel presents a galaxy divided into "zones of thought," each with its own distinct laws of physics that shape the development of technology and intelligence. Rather than viewing progress as a linear trajectory through time, Vinge inverts this concept by illustrating how it is profoundly influenced by spatial dimensions. In some zones, civilizations advance rapidly, harnessing advanced technologies and complex societies, while in others, the constraints of their unique physical laws lead to stagnation or regression. This peculiar cosmology challenges our understanding of what it means to progress, suggesting that the very nature of advancement is contingent upon the environment in which a civilization exists.

Youtube Review
Youtube Review
Youtube Review
Solaris by Stanislaw Lem - (★★★★★) Scientists embark on a mission to study Solaris, a mysterious ocean planet that exhibits seemingly sentient qualities. As they delve deeper into their research, they encounter a phenomenon where the planet manifests their deepest regrets, fears, and desires, forcing them to confront their own psyches in ways they never anticipated. This exploration of the human mind and its complexities raises unsettling questions about the nature of consciousness and the limits of human understanding. The narrative intricately weaves themes of isolation, the search for meaning, and the struggle to communicate with an intelligence that defies comprehension, ultimately challenging readers to reflect on the essence of what it means to be human in the face of the unknown and the unfathomable depths of the universe.

Youtube Review
Youtube Review
Lilith's Brood (Xenogenesis series) by Octavia E. Butler - (★★★★★) Butler explores a future where humanity teeters on the brink of extinction, saved only by the intervention of an advanced alien race known as the Oankali. Through the process of genetic merging, the Oankali not only preserve human life but also challenge the very foundations of identity, consent, and species preservation. The narrative delves deep into the complexities of what it means to be human in a world where boundaries between species blur, raising profound ethical questions about autonomy and the implications of genetic manipulation. As the characters navigate their new reality, they confront the emotional and psychological ramifications of their altered existence, ultimately leading to a rich exploration of love, power dynamics, and the essence of humanity itself.

Youtube Review
Caves of Steel by Isaac Asimov - (★★★★) A human detective named Elijah Baley is reluctantly paired with a highly advanced robot, R. Giskard, to unravel a complex murder mystery set in a densely populated future Earth, where the vast majority of humanity lives in sprawling underground cities. As they delve deeper into the investigation, the duo confronts not only the intricacies of the case but also the pervasive anti-robot prejudice that permeates society, highlighting the tensions between humans and robots in a world grappling with rapid technological advancements.

Youtube Review
Youtube Review
Downbelow Station by C.J. Cherryh - (★★★★) A space station becomes the flashpoint in a war between Earth and its colonies, examining the politics of space colonization. The narrative intricately weaves together the lives of various characters, each representing different factions and perspectives within this conflict, from the beleaguered inhabitants of the station to the ambitious leaders on Earth and the desperate colonists fighting for their autonomy. As tensions escalate, the story delves into the moral complexities of war, the sacrifices made for survival, and the intricate web of alliances and betrayals that emerge in the face of existential threats.
Coalescent by Stephen Baxter - (★★★★) A secret society evolves into a human hive mind, delving deep into the realms of evolutionary biology and collective consciousness. Baxter intricately explores the implications of such a transformation, raising profound questions about individuality, identity, and the nature of human connection. As the characters navigate their new existence, they grapple with the loss of personal autonomy and the emergence of a shared consciousness that challenges the very essence of what it means to be human.
A Case of Conscience by James Blish - (★★) A Jesuit priest embarks on a mission to an alien world, where he encounters a race of beings who exist in a state devoid of sin, challenging his deeply held beliefs and the very foundations of his faith. As he grapples with the implications of their existence, he is forced to confront profound theological questions about the nature of good and evil, the concept of free will, and the moral frameworks that govern human behavior. The priest's struggle becomes a poignant exploration of the complexities of morality, as he navigates the tension between his religious convictions and the undeniable reality of a society that operates outside the bounds of traditional sinfulness.
Schild's Ladder by Greg Egan - (★★★★★) Humanity confronts the ultimate fate of the universe as it approaches the heat death, a state where all energy is evenly distributed and no thermodynamic free energy remains to perform work. To combat this existential threat, a group of visionary scientists and engineers embark on an ambitious project to construct a colossal cosmic structure that spans millions of years and light-years, designed to harness the dwindling energy of the universe and create pockets of habitable environments. As the narrative unfolds, readers are introduced to a richly detailed universe filled with complex characters who grapple with profound philosophical questions about existence, purpose, and the nature of time itself, ultimately challenging us to consider the implications of humanity's choices in the face of cosmic inevitability.
Last and First Men by Olaf Stapledon - (★★★★) A future history spanning two billion years and eighteen human species, contemplating evolution and the ultimate fate of consciousness. Through a series of interconnected narratives, Stapledon explores the rise and fall of these species, each representing a unique stage in humanity's evolution, from the distant past to a far-flung future where humanity has transcended its biological limitations. The novel delves into profound philosophical questions about the nature of existence, the evolution of intelligence, and the moral implications of humanity's choices as it faces extinction and rebirth. As the narrative unfolds, readers are invited to reflect on the cyclical nature of life and the enduring quest for meaning in a universe that is both vast and indifferent, ultimately challenging our understanding of what it means to be human in the grand tapestry of time and space.
The City and the Stars by Arthur C. Clarke - (★★) In Earth's last city, a unique child breaks the cycle of immortality and stagnation to rediscover the stars. This child, named Alvin, embarks on a transformative journey that challenges the very foundations of a society that has long embraced a static existence, where the inhabitants live in a state of eternal youth, shielded from the harsh realities of the outside world. As Alvin's curiosity propels him beyond the confines of his sheltered environment, he encounters remnants of humanity's past and the vastness of the universe, igniting a profound sense of wonder and purpose. Through his exploration, Clarke masterfully weaves themes of hope, renewal, and the indomitable human spirit, ultimately illustrating the necessity of change and the pursuit of knowledge in a world that has forgotten its connection to the cosmos. The narrative serves as a poignant reminder of the importance of dreams and aspirations, urging readers to reflect on their own journeys of discovery and the potential for rebirth in the face of stagnation.

Youtube Review
Youtube Review
Never Let Me Go by Kazuo Ishiguro - (★★★★) Set in a hauntingly beautiful yet dystopian world, this poignant narrative follows a group of children raised in an idyllic boarding school, Hailsham, where they are nurtured and educated in a seemingly perfect environment. As they grow older, they gradually uncover the chilling truth about their existence and the dark purpose for which they were created: to become organ donors for the outside world. This gentle yet devastating meditation on mortality explores themes of love, loss, and the essence of humanity, prompting readers to reflect on the ethical implications of cloning and the value of life itself. The story was also adapted into a critically acclaimed film in 2010, which captures the emotional depth of Ishiguro's novel.
Hyperion Cantos by Dan Simmons - (★★) This ambitious series unfolds as a group of pilgrims embarks on a journey to meet a godlike entity known as the Shrike, a being of immense power and pain. Each pilgrim shares their own story, weaving a rich tapestry of narratives that explore profound themes such as love, sacrifice, and the nature of humanity. While the series grapples with grand concepts and presents a vast, intricately constructed universe, it is not without its flaws; the author's conservative political views occasionally seep into the narrative, which may be off-putting for some readers. Nevertheless, the scope of the Hyperion Cantos is undeniably vast, tackling existential questions and the complexities of human experience against a backdrop of interstellar conflict and philosophical inquiry. This blend of epic storytelling and deep thematic exploration makes it a noteworthy, if imperfect, addition to the science fiction canon.

Youtube Review
Between the Strokes of Night by Charles Stross - (★★) Humanity stumbles upon a groundbreaking method to perceive time in a radically different manner, which not only facilitates interstellar travel but also allows individuals to witness the grand tapestry of the universe's evolution in real-time. As characters embark on journeys across the cosmos, they grapple with the profound implications of their newfound abilities, exploring the intricate relationship between time, existence, and the very fabric of reality itself.
The Dispossessed by Ursula K. Le Guin - (★★★★★) Shevek, a brilliant physicist from Anarres, an anarchist moon colony, as he journeys to Urras, a capitalist planet. Le Guin masterfully explores the philosophical themes of freedom, societal structures, and the complexities of human nature. The stark contrast between the two worlds raises profound questions about utopia and the sacrifices made for ideals.
Sun-Eater by Christopher Ruocchio - (★★) A man becomes both hero and monster in his thousand-year quest to save humanity in this epic blending sci-fi with fantasy elements. As he navigates the complexities of his dual identity, the protagonist grapples with the moral ambiguities of his actions, facing the consequences of choices that blur the lines between savior and destroyer. Ruocchio intricately weaves a narrative that explores themes of sacrifice, redemption, and the nature of power, inviting readers to ponder the cost of heroism in a universe fraught with existential threats.
Midshipman's Hope series by David Feintuch - (★★) A young officer inherits command of a starship in this coming-of-age military sci-fi exploring duty, trauma, and leadership. As he navigates the challenges of his new role, he must confront not only the external pressures of commanding a diverse crew in the vastness of space but also the internal struggles that come with the weight of responsibility. The series delves into the psychological toll of military life, examining how the protagonist grapples with the expectations placed upon him while dealing with the scars of past conflicts.
Axiomatic by Greg Egan - (★★★★) This collection of short stories delves into the intricate and often unsettling realms of consciousness, identity, and reality, particularly in a future where technology has the power to fundamentally alter memories, personality traits, and perceptions of the self. Egan's narratives challenge readers to confront the implications of such advancements, posing a philosophical exploration about what it means to be human in a world where the essence of identity can be manipulated at will. Each story serves as a unique exploration of the psychological and philosophical ramifications of these transhumanism.

Youtube Review
Voyage from Yesteryear by James P. Hogan - (★★★★★) Hogan presents a society that has been nurtured and developed by robots, resulting in a unique civilization that operates without the constraints of scarcity or authority. This utopian world challenges the very foundations of Earth's hierarchical culture, as visitors from our planet are confronted with a radically different way of life that emphasizes cooperation, resource abundance, and the absence of traditional power structures. As the story unfolds, readers are invited to explore the implications of such a society on human behavior, ethics, and the potential for a harmonious existence free from the conflicts that often arise from competition and inequality..
Rogue Moon by Algis Budrys - (★★★) People are repeatedly duplicated and killed as they embark on a harrowing exploration of an enigmatic alien artifact that defies human understanding. The narrative delves deep into the existential dilemmas faced by the characters, who grapple with the implications of their own mortality and the nature of selfhood in a world where their very essence can be replicated and extinguished at will. As they confront the chilling reality of their situation, the story raises profound questions about what it means to be human, the fragility of life, and the ethical ramifications of technology that allows for such duplications..
Dhalgren by Samuel R. Delany - (★★★) A poet wanders through a city warped by an unexplained catastrophe in this surreal, literary exploration of reality and perception. As he navigates the fragmented landscape of Bellona, a city that seems to exist outside the bounds of time and logic, the poet encounters a diverse cast of characters, each grappling with their own existential dilemmas and the disorienting effects of their environment. Delany's narrative intricately weaves themes of identity, memory, and the fluidity of truth, challenging readers to question the nature of reality itself. The novel's rich, poetic prose invites deep reflection on the human condition, as the protagonist's journey becomes a metaphor for the search for meaning in a world that has been irrevocably altered, ultimately leaving readers with a haunting sense of ambiguity and wonder about the complexities of existence and perception
The Mote in God's Eye by Larry Niven and Jerry Pournelle - (★★★★★) Humanity stumbles upon an ancient alien civilization that has been inadvertently trapped within their own solar system, constrained by the very laws of physics and biological limitations that govern their existence. As the story unfolds, the human characters grapple with the profound implications of this discovery, leading to a tense exploration of communication and understanding between species that are separated not just by distance, but by fundamentally different perceptions of reality.
Permutation City by Greg Egan - (★★★★★) In a future where consciousness can be uploaded into a digital realm, the boundaries between reality and simulation blur. The story follows a cast of uploaded transhuman entities who navigate this intricate virtual landscape, grappling with the implications of their existence as they confront the nature of identity, memory, and the essence of being. As they explore the depths of this artificial world, they encounter philosophical dilemmas about what it means to be truly alive and the potential consequences of living in a reality that can be endlessly manipulated. Egan's narrative challenges readers to ponder the implications of technology on human experience and the very fabric of reality itself.
The Hidden Girl and Other Stories by Ken Liu - (★★★) This collection of short stories intricately weaves together elements of ancient Chinese culture and futuristic technology, creating a rich tapestry that delves into the complexities of identity, memory, and the essence of what it means to be human. Liu's narratives transport readers to worlds where the past and future collide, inviting them to reflect on the impact of technological advancements on personal and cultural identities. Each story serves as a poignant exploration of the human experience, examining how memories shape our understanding of self and the ways in which cultural heritage influences our interactions with an ever-evolving world..
A Scanner Darkly by Philip K. Dick - (★★★) An undercover narcotics agent named Bob Arctor finds himself ensnared in a web of deception and addiction as he investigates the very drug that is slowly consuming his identity, known as Substance D. As Arctor navigates the treacherous landscape of a dystopian future where surveillance and paranoia reign supreme, he grapples with the disintegration of his sense of self, leading to a profound exploration of the nature of reality and consciousness. The novel intricately examines the psychological toll of addiction, the impact of a fragmented identity, and the moral ambiguities faced by those caught in the crossfire of a war on drugs that blurs the lines between law enforcement and criminality..
Lessons in Chemistry by Bonnie Garmus - (★★★) A brilliant female chemist becomes a cooking show host in the 1960s, using the platform to teach science and challenge gender norms. Through her engaging and innovative approach, she not only captivates her audience with delicious recipes but also demystifies complex scientific concepts, making them accessible to the everyday viewer. As she navigates the male-dominated landscape of television and academia, her journey becomes a powerful commentary on the societal expectations placed on women during this era. The narrative intricately weaves themes of empowerment, resilience, and the importance of pursuing one's passion against all odds, ultimately inspiring readers to reflect on the ongoing struggle for gender equality in both the scientific community and beyond.
Children of God by Mary Doria Russell - (★★★) The sequel to The Sparrow delves deeper into the intricate themes of faith, redemption, and the complexities of alien contact as humans return to the world that once shattered their beliefs and hopes. Russell masterfully intertwines the personal struggles of her characters with broader philosophical questions about the nature of divinity and the human experience. As they confront the remnants of their past traumas and the challenges posed by their interactions with an alien civilization, the story unfolds to reveal profound insights into the resilience of the human spirit and the transformative power of forgiveness. The characters' journeys are not only a quest for understanding but also a poignant exploration of what it means to heal and find purpose in a universe that often feels indifferent to their suffering..
Merchanter's Luck by C.J. Cherryh - (★★★) A down-on-his-luck trader finds himself entangled in a precarious situation that forces him to forge an unlikely partnership with a resourceful officer from a powerful merchant family. As they navigate the treacherous waters of interstellar trade, the duo must confront the harsh realities of a universe where class divides and opportunism dictate survival. Their journey is not just a quest for profit but a profound exploration of trust and cooperation, as they learn to rely on each other's strengths to overcome the myriad challenges that threaten their lives and livelihoods.
Alas, Babylon by Pat Frank - (★★★) A small Florida town survives a nuclear apocalypse in this hopeful look at community resilience after civilization's collapse. As the residents of Fort Repose grapple with the immediate aftermath of the catastrophe, they are forced to confront not only the physical challenges of survival, such as securing food, water, and shelter, but also the emotional and psychological toll of their new reality. The narrative intricately explores the dynamics of human relationships as neighbors band together, sharing resources and skills, while also revealing the underlying tensions that arise in times of crisis.
Star Maker by Olaf Stapledon - (★★★★) A cosmic journey through space and time unfolds as a human mind merges with others, transcending the limitations of individual consciousness to witness the evolution of countless civilizations across the universe. This profound narrative invites readers to explore the vast tapestry of existence, where each civilization presents unique challenges and triumphs, reflecting the diverse paths of sentient life. As the protagonist encounters various forms of intelligence, from the primitive to the highly advanced, the story delves into the philosophical implications of creation and existence, ultimately leading to a climactic meeting with the creator itself.
The Drowned World by J.G. Ballard - (★★★) As global warming melts the ice caps, a biologist experiences psychological regression in the flooded, tropical London. The narrative unfolds in a post-apocalyptic setting where the remnants of civilization are submerged beneath rising waters, and the once-familiar landscape has transformed into a primordial jungle teeming with prehistoric creatures. As the protagonist grapples with the physical and emotional toll of this new reality, he finds himself drawn into a deepening sense of nostalgia for a world that no longer exists, leading to a profound exploration of the human psyche in the face of environmental catastrophe.
The Eon Trilogy by Greg Bear - (★★★★) A mysterious asteroid appears in Earth orbit containing technology from the future and gateways to infinite alternate timelines. As humanity grapples with the implications of this extraordinary discovery, the narrative unfolds to reveal a complex interplay of scientific exploration and philosophical inquiry, challenging our understanding of time, existence, and the very fabric of reality. The characters are thrust into a web of intrigue and danger as they navigate the moral dilemmas posed by the advanced technologies and alternate realities that the asteroid presents, forcing them to confront their own beliefs about destiny and free will.
The Lathe of Heaven by Ursula K. Le Guin - (★★★) A man named George Orr discovers that his dreams possess the extraordinary power to alter reality itself, leading him to grapple with the profound implications of his newfound ability. As he seeks help from a psychiatrist, Dr. William Haber, who harbors his own utopian ambitions, George finds himself ensnared in a web of manipulation and ethical dilemmas. Dr. Haber, driven by a desire to create a perfect world, begins to exploit George's dreams for his own ends, resulting in a series of catastrophic consequences that challenge the very fabric of existence. The narrative unfolds as George struggles to regain control over his dreams, confronting the moral complexities of power, responsibility, and the nature of reality, ultimately leading to a gripping exploration of the human condition and the unforeseen repercussions of our desires.
Regenesis by C.J. Cherryh - (★★★★) The sequel to Cyteen continues exploring the political and ethical implications of cloning and psychological programming, delving deeper into the intricate dynamics of power, identity, and the moral dilemmas faced by individuals in a society where the boundaries of humanity are constantly tested. As the narrative unfolds, readers are introduced to a complex web of characters, each grappling with their own struggles and the consequences of their actions in a world where the manipulation of human potential raises profound questions about autonomy and the essence of what it means to be truly human.
This Island Earth by Raymond F. Jones - (★★) An engineer named Cal Meacham is unexpectedly recruited by extraterrestrial beings to assist in a vast interstellar war, thrusting him into a conflict that reveals the intricate and often unsettling dynamics of power and manipulation at play in the universe. As he navigates this alien landscape, Cal uncovers the chilling realization that humanity is merely a pawn in a much larger game, caught between warring factions that view Earth as a resource rather than a home. The story intricately explores themes of agency, sacrifice, and the moral complexities of war, prompting readers to reflect on the implications of human involvement in cosmic conflicts and the ethical dilemmas that arise when faced with the unknown.
Shockwave Rider by John Brunner - (★★★★) A man named Nick Haflinger finds himself on the run in a dystopian future where society is increasingly dominated by technology and surveillance. Utilizing his exceptional computer skills, he navigates a world rife with digital manipulation and identity theft, constantly changing his identity to evade capture by a powerful and oppressive government. Brunner's narrative not only explores the implications of information warfare and the rise of computer viruses but also delves into themes of freedom, control, and the human condition in an age where technology blurs the lines between reality and illusion. As Haflinger grapples with his own sense of self amidst the chaos, the novel serves as a chilling reflection on the potential consequences of unchecked technological advancement and the fragility of personal identity in a hyper-connected world.
The Dosadi Experiment by Frank Herbert - (★★★) Herbert transports readers to the isolated and unforgiving planet of Dosadi, where a diverse group of humans and aliens are subjected to a clandestine experiment designed to test the limits of survival and adaptability. Cut off from the rest of the universe by a force field, the inhabitants of Dosadi must navigate the harsh realities of their environment, which is characterized by extreme weather, dangerous wildlife, and the psychological strains of confinement.
Sphere by Michael Crichton - (★★★) A team of scientists embarks on a deep-sea expedition and stumbles upon an alien spacecraft that has lain dormant for centuries. Inside, they discover a mysterious sphere that possesses the uncanny ability to manifest their innermost thoughts and fears, leading to a series of harrowing and surreal experiences. As the crew grapples with the psychological implications of their subconscious being laid bare, they are forced to confront their own hidden traumas and insecurities, revealing the darker aspects of human nature. The narrative intricately weaves themes of paranoia, identity, and the fragility of the mind, as the characters must navigate the treacherous waters of their own psyche while trying to understand the true purpose of the sphere.
Singularity Sky by Charles Stross - (★★★★★) Humanity faces the arrival of a mysterious and powerful alien entity known as the "Eschaton," which has the ability to manipulate time and reality itself. Set against the backdrop of a post-scarcity future, the story follows a group of characters, including a diplomat and a military officer, as they navigate the complexities of interstellar politics and the ethical dilemmas posed by advanced technology. As the Eschaton begins to impose its own vision of order on the universe, the protagonists must grapple with the implications of free will, the nature of consciousness, and the potential consequences of a society that has become overly reliant on technology. Stross masterfully weaves together themes of existentialism, the limits of human understanding, and the unpredictable nature of progress, creating a narrative that challenges readers to consider the future of humanity in an age of rapid technological advancement.
Accelerando by Charles Stross - (★★★★★) This novel follows the life of Manfred Macx, a brilliant and eccentric entrepreneur navigating the complexities of a rapidly evolving future where technology and humanity are inextricably intertwined. As he grapples with the implications of accelerating technological progress, including the rise of artificial intelligence and the transformation of society, the narrative unfolds across multiple generations, exploring themes of transhumanism, the singularity, and the very essence of what it means to be human. Stross masterfully weaves together a tapestry of speculative ideas, presenting a vivid vision of a world where the boundaries between man and machine blur, ultimately challenging readers to consider the potential trajectories of our own future in an age of relentless innovation and change.
We Are Legion by Dennis E. Taylor - (★★★★) A software engineer named Bob finds himself in an extraordinary predicament after his death: his brain is cryogenically frozen and later revived within a self-replicating sentient space probe. This unique twist on the afterlife allows Bob to explore the cosmos in ways he never thought possible, as he and his numerous clones embark on thrilling space adventures. Together, they map the vastness of the universe, monitor the absurdities of life on Earth, and engage with a variety of alien civilizations, each encounter presenting new challenges and ethical dilemmas.
House of Suns by Alastair Reynolds - (★★★★★) Two clones, Campion and Purslane, who are part of a family of aristocratic travelers known as the "Gentlemen." Over the course of millions of years, they traverse the galaxy, witnessing the rise and fall of civilizations while collecting knowledge and experiences. As they embark on a journey to reunite after a long separation, they uncover a conspiracy that threatens not only their existence but the very fabric of the universe itself.
The World at the End of Time by Frederik Pohl - (★★★★★) The book follows Wan-To, a man from Earth sent on a one-way mission to a planet orbiting a dying red giant star. This planet, dubbed "Kronos," experiences time dilation due to its proximity to the star, making one year on Kronos equivalent to billions of years on Earth. Wan-To's purpose is to discover the fate of humanity by observing Kronos's evolution over vast stretches of time. He encounters bizarre and alien lifeforms shaped by extreme environmental pressures, witnesses the rise and fall of entire ecosystems, and confronts powerful, god-like entities known as the "Hikers" who manipulate the fabric of space-time. Wan-To ultimately grapples with the meaning of his mission and the nature of existence as he watches the universe slowly wind down towards its ultimate heat death.

The Sybaritic Economy

Tue, 10 Dec 2024 00:00:00 +0000

The Sybaritic Economy

A Monologue from the Near-Future

The notification materializes—a delicate crystal chime tuned precisely to the frequency that activates my dopamine receptors most efficiently. My LuxeLife implant registers the anticipatory cortisol-serotonin cascade, transmitting the data to the HedoniGram central server where it becomes another exquisitely curated data point in my pleasure profile. I've just completed my lunch: a single laboratory-cultivated caviar pearl containing the DNA-spliced essence of sixteen extinct sturgeon species, harvested during a lunar eclipse, served atop a wafer of edible 24-karat gold leaf infused with pulverized moon dust. The caviar was fertilized by a robotic sturgeon stimulator played exclusively Mozart's lost compositions, recovered via AI from his neurological patterns and performed by quantum-entangled instruments to ensure maximum vibrational coherence during embryonic development. My on-staff culinary scientist assures me this precise gastronomic arrangement triggers optimal alpha wave patterns associated with elite consciousness—all for a mere $18,000,000 per pearl, a bargain considering the 0.38% uptick in engagement metrics guaranteed by HedoniGram's predictive algorithm. Time for my scheduled leisure performance.

With lunch "concluded" (if one can call a single pearl a meal), I adjust my designer loungewear—Hermès' limited-edition cashmere blend, hand-woven by Tibetan monks who've taken vows of aesthetic superiority—its nanofabric embedded with microscopic sensors primed to broadcast the physiological manifestations of my cultivated bliss. The infinity pool's edge blends seamlessly with the horizon, an optical illusion manufactured specifically for maximum engagement across seventeen distinct social platforms. My reflection appears in the glossy surface: pupils dilated, facial muscles arranged in what the algorithm has determined is the optimal expression of effortless joy.

"True sophistication demands absolute rarity," I'll begin, as I always do, caressing my Extinctique handbag. Only three were ever produced, each crafted from the last living specimens of eight critically endangered species. The leather required twenty-seven different artisans working in isolation, each signing non-disclosure agreements that extend beyond death. The tanning process alone involved twelve child laborers selected for their exceptionally small hands, working in subterranean workshops where labor regulations don't apply. The craftsmen who completed the stitching were permanently blinded afterward to ensure they could never replicate their work—a standard exclusivity clause in luxury atelier contracts now. At $36.8 million, the price hardly reflects its true value: the countless indigenous displacement operations required to source materials, the three craftsmen who committed suicide from the psychological toll, and the fourteen environmental protection laws circumvented through strategic political donations. "Nothing communicates status like a product that literally consumed its makers," I add, the handbag's authentication chip transmitting my ownership verification to everyone in my aspiration radius. "And for a modest monthly contribution to my Bliss Fund, I'll demonstrate how to transcend suffering through strategic conspicuous consumption."

This is our reality now, what we call the Sybaritic Economy. It’s not the mindful presence espoused in those quaint pre-algorithmic texts, but the Epicurean simulation we've collectively engineered through each filtered photo, each location tag, each carefully angled shot of avocado toast against Carrara marble. Leisure hasn't merely been platformized; it's been systematically fragmented into microsecond displays of performative tranquility, each one so meticulously calculated that even the concept of genuine respite has become an anachronism, a curious artifact from humanity's pre-digital history. The Sybaritic Economy has consumed all. Idleness is no longer the fortunate byproduct of wealth—it's the central commodity of the attention marketplace, as essential to contemporary capitalism as coal was to its industrial predecessor.

Central to this reality is HedoniGram, the preeminent architectonic system of pleasure epistemology. Or, as our algorithmic engineers euphemistically designate it: HOT, or Hedonism Optimization Technologies. Here, leisure isn't merely an activity; it's the foundational currency of identity formation. Each poolside moment is meticulously categorized through proprietary sentiment analysis—'Transcendent Mindfulness,' 'Aspirational Repose,' 'Strategic Indolence'—then alchemized into status signification. We aren't mere content creators; we're ontological entrepreneurs, constructing realities so fundamentally desirable that the distinction between witnessing and experiencing has become technologically obsolete. The only authentic way to establish one's value now is through the meticulous curation of an algorithmically optimized idleness, a phantasmic vacation whose sole purpose is to validate your existence through its perpetual unattainability. All accompanied by Veblen goods that can be purchased to signal affluence proximity, each embedded with software that automatically updates your status markers when the algorithmic luxury consensus shifts.

And I, naturally, am a key player. I maintain a dedicated following of 8.2 million "Aspirants"—users whose neurochemical responses to stimuli register desperate yearning with at least an 89% consistency according to HedoniGram's proprietary Envy Induction Index. They synchronize their desires with mine daily, their neural implants adjusting their dopamine sensitivity to match my broadcast states of apparent fulfillment. I lounge with mathematical precision, my repose distributed across carefully selected backdrops identified by the algorithm as optimally positioned to reinforce class boundaries without triggering cognitive dissonance. I emanate serenity with clinical efficiency, each leisurely moment calibrated to the particular neurochemical addiction profile of my audience segment. My cultivated bliss—that visceral, autonomic response to simulated abundance that once signaled genuine satiation—has been quantified, optimized, and commoditized into "aspiration metrics." The algorithm, that dispassionate curator of our desires, labels it "hedonic template content." In praxis, it represents the terminal stage of consumer capitalism, wherein the very neurochemistry of desire becomes an instrument of economic control, a distributed panopticon where we surveil not only each other's possessions but the intimate electrochemical processes that precede acquisition.

The pressure is constant. Last week, my engagement metrics plummeted 0.87% when UltraElite HedoniGram influencer ZephyrLuxe debuted her $2.4 million atmospheric vacation—a proprietary oxygen mixture imported from the Himalayan peaks, compressed into portable canisters designed by Philippe Starck, each breath allegedly imparting the cognitive clarity of ancient monks without the inconvenience of actual meditation. My own curated breathing practice—once aspirational enough to sustain my metrics—became instantaneously obsolete. The hedonic treadmill accelerated mercilessly.

This constant one-upmanship has, of course, led to new frontiers of elitism. The vulgar conspicuousness of dopamine spikes has become the telltale mark of the aspiring classes. True elites now cultivate a carefully calibrated neural flatline—the "Luxurious Void"—broadcasting perfect neurological stillness while surrounded by astronomical extravagance. Influencers pay billions for quantum-stabilized mood suppressants that maintain cortical silence during experiences that would rupture an untrained consciousness with pleasure. The ultra-wealthy hire personal anhedonia architects to rewire their limbic systems, ensuring their $90 million artificial aurora experiences register neurologically identical to watching paint dry. Nothing signals desperation more fatally than appearing to actually enjoy your Himalayan oxygen concierge or extinct-species caviar. "Rapture is so bourgeois," as BlissBaroness recently declared while her neural metrics displayed perfect emptiness throughout her three-week stay in her suborbital pleasure palace of impossibilities. The ultimate luxury is no longer access to pleasure but immunity to it—proving you've transcended the capacity for enjoyment of life entirely.

It's no surprise, then, that experiments with actual presence are invariably flagged by the algorithm as "engagement anomalies" and subsequently buried beneath mountains of more aspirational content. Meaningful contentment becomes impossible when the infrastructure itself is architected to reward perpetual yearning and punish satiation, an algorithmic enforcement of the hedonic treadmill against the very possibility of equanimity. Spiritual awakening is rendered impossible when the mechanisms of transcendence have been so thoroughly integrated into the profit model that meditation itself becomes a premium content category, allowing for the simulation of enlightenment while simultaneously serving as the primary driver of platform engagement metrics.

There was a time, believe it or not, when I once lounged from genuine satisfaction, back when I naively believed in the fallacy of non-attachment, when I thought the purpose of leisure was restoration rather than status demarcation. Now? Now I recline because quarterly projections demand it. My tranquility is itemized on corporate balance sheets under "Strategic Aspirational Content Production." My paramount dread isn't existential discontent but algorithmic relegation—to be categorized as "insufficiently enviable" and consequently exiled to the purgatorial realm of authentic experience, the contemporary equivalent of social death.

So now we broadcast our leisure instead. Not to experience joy, not genuinely. To perform hedonic optimization. There exists a fundamental distinction. To experience joy implies the potential for sufficiency, for contentment with present circumstances. To perform optimization is to establish the immutability of desire as the natural order, a perpetual Sisyphean cycle without resolution, permanently suspended in the acquisition-adaptation stage where satisfaction would be not merely impossible but conceptually unintelligible. And in the Sybaritic Economy, optimization generates revenue, albeit in a currency that purchases nothing beyond increasingly sophisticated manifestations of the same foundational insatiability, like some grotesque inversion of Buddhist progression where each iteration moves further from, rather than toward, liberation.

Just yesterday, to combat the ZephyrLuxe incident and boost my own metrics, I deployed my newest status acquisition: a $17,000,000 Cryogenic Sleep Chamber crafted from Norwegian glacial ice harvested exclusively during solar eclipses that occur on leap days, its ambient sound system playing compositions performed by AI replicas of extinct rainforest birds. My initial neurometric response indicated a 26% spike in temporary fulfillment, lasting precisely 47 minutes before the HedoniGram algorithm notified me of TranquilityTycoon's acquisition of a deep-sea meditation pod installed 2,000 meters below the Pacific, where the pressure allegedly compresses one's consciousness into a singularity of bliss unavailable at surface-level mindfulness. My temporary satisfaction evaporated instantly. The treadmill surged forward.

Therein lies the exquisite perversity, the terminal irony. There exists no contentment in the Sybaritic Economy. Merely parallel aspiration, occurring simultaneously, optimized for neurochemical dependency by competing algorithms. Each individual hermetically sealed within their personalized desire wheel. Yearning for unattainable experiences. Receiving temporary validation. And experiencing no authentic fulfillment. The invisible hand of the market now selects your desires while convincing you the choice was autonomously made, not to facilitate well-being, but to maximize envy and engagement.

It’s not even my desire, not really. My mimetic desires arrive pre-formulated, algorithmically determined, optimized for maximum aspirational reinforcement like some parasitic consumerist organism hijacking my cognitive architecture. I don't want. I categorize. I don't enjoy. I identify patterns that confirm pre-existing schemas. Experiences engineered to provoke specific limbic responses in aspirationally aligned audiences, responses that can be measured, quantified, and monetized. I am simultaneously producer and product, manipulator and manipulated in a recursive system of experiential commodification that obliterates the distinction between authentic desire and performative identity. Max Weber never anticipated this development—the ultimate rationalization where we willingly submit our experiential processes to algorithmic management, our capacity for genuine enjoyment systematically decomposed and reconstituted according to market imperatives.

This whole system is, naturally, competitive. Aspirants contribute to my Bliss Metric when I perform particularly enviable displays. Virtual tokens representing quantified aspirational alignment cascade across my dashboard in a perverse gamification of desire reinforcement, the digital equivalent of audience gasps. There exists a real-time leaderboard. I maintain a position slightly below "ZenLuxeGuru," an experiential entrepreneur who performs daily guided meditations from algorithmically-determined exotic locations while dressed in athleisure that costs more than most people's yearly income, her enlightenment incorporating terminology from twenty-three different spiritual traditions simultaneously in what critics have described as "the definitive manifestation of post-coherent spirituality." She recently cultivated a 48-hour transcendental state achieved through microdosed neurotransmitters harvested from the pineal glands of Amazonian tree frogs, administered via jade needles sanctified by no fewer than twelve distinct shamanic traditions. Then there's "MinimalMaximalist," who conducts methodical exhibitions of possessions curated to communicate wealth while paradoxically espousing the virtue of simplicity—a specialized but remarkably profitable market segment catering to those who fetishize the simulacrum of spiritual achievement. His latest anti-materialist manifesto was delivered from his $28 million bunker constructed entirely of reclaimed meteor fragments, each meteorite certified to have passed through a specific constellation deemed auspicious by his team of private astrologers.

I myself am preparing my next salvo: a proprietary strain of bioluminescent plankton genetically modified to respond exclusively to my own bioelectrical signature, cultivated in a private sea constructed to replicate the precise chemical composition of pre-industrial oceans. It will generate approximately 14 minutes of algorithmic superiority before BlissBaroness debuts her collection of dew harvested from extinct flowers recreated through paleobotanical DNA reconstruction, each droplet stored in vials crafted from crystallized tears of anonymous artisanal glassblowers who are contractually forbidden from experiencing happiness during the creation process.

The desperation escalates quarterly. Elite influencers now purchase temporally exclusive sunsets—proprietary atmospheric modifications that ensure unique light spectrums visible only to those who've paid for algorithmic access. HedoniGram recently introduced consciousness franchising, allowing A-list experience architects to monetize their neural patterns, temporarily lending their precise neurochemical configurations to Aspirants willing to relinquish 38% of their gross annual income for seventy-two hours of simulated elite consciousness. But the ultimate luxury—the pinnacle of hedonic distinction—has become the Temporary Non-Existence Package: a quantum-suspended state of complete ego dissolution where one's consciousness is temporarily extracted from the body and stored in proprietary cloud servers while automated algorithms maintain your social presence. For a mere $42 million per hour, you can experience the bliss of absolute non-being while your digital avatar continues performing aspirational leisure at peak engagement metrics. "Transcend the self while optimizing your brand," promises the marketing campaign. The irony of paying exorbitant sums to temporarily cease existing while ensuring your online persona thrives is lost on no one, yet remains the most coveted experience among the ultra-elite—the cessation of desire transformed into the ultimate status symbol, available exclusively to those whose wealth permits them the ultimate luxury experience of inputless insensate catatonia.

Amidst this madness, I occasionally contemplate what authentic leisure might entail. To enjoy a sunset without immediate categorization into aspirational taxonomies, monetization strategies, unanalyzed by sentiment prediction software, unquantified according to engagement potential. But such experiential independence now represents the most radical conceivable act: to enjoy without external validation. A fundamental rebellion against the algorithmic superstructure, a rejection of the entire political economy of digitally mediated experience. It's almost unthinkable.

But the thought is fleeting. The market simply won't allow it. Contentment just doesn't scale. Presence lacks virality potential. Sufficiency demonstrates insufficient ROI. You cannot A/B test genuine satisfaction for optimal audience retention. You cannot attach affiliate marketing to genuine enlightenment. You cannot secure funding for content that acknowledges the inherent emptiness of desire. In an attention economy where aspiration represents the sole reliable engagement driver, satiation constitutes the only remaining revolutionary act, the final unconquered territory of human cognition. The most profitable leisure is that which presents the simulacrum of fulfillment while reinforcing existing aspirational frameworks, providing the illusory satisfaction of experiential development while leaving the fundamental architecture of desire dependency perfectly intact.

And so, in this paradigm, that which cannot be quantified, which fails to generate engagement metrics, which resists algorithmic categorization... effectively ceases to exist. Your private contentment represents wasted neurological capacity. Unmonetized joy constitutes the sole remaining heresy, an affront to the techno-capitalist orthodoxy that has rightfully colonized every dimension of modern experiential existence.

Which brings me back to the present moment. My neural implant activates. Performance commences. I clear my throat, activating my neural broadcast, concentrating on the algorithmically determined aspirational signifiers, those strategically selected to maximize both my engagement metrics, envy, and neurochemical dependency among my aspirants.

"True sophistication demands absolute rarity," I declare again, my voice modulated to the precise frequency demonstrated to trigger nucleus accumbens response in my demographic targets.

I market inaccessibility to alleviate your status anxiety, momentarily. You finance the privilege of experiencing artificial proximity through my manufactured abundance. Together we accelerate the hedonic treadmill.

Because ultimately, aspiration is the sole remaining mechanism through which one might simulate authentic fulfillment. Externalize your desire fulfillment through my experience. The treadmill never stops—it only accelerates, carrying us all toward increasingly boutique Byzantine manifestations of the same fundamental emptiness, each more exquisitely crafted than the last.

Stephen Diehl

Book Review: What We Can Know

Book Review: What We Can Know

Book Review: There Is No Antimemetics Division

Book Review: There Is No Antimemetics Division

Book Review: Piranesi

Book Review: Piranesi

Optimal Caverna Gameplay via Formal Methods

Optimal Caverna Gameplay via Formal Methods

Labeled Transition Systems

The Game as a Transition Relation

The Game Timeline

Refinement Types: Making Illegal States Unrepresentable

The Weapon System

The Universal Food Crisis

The Feeding Cascade

Furnishing Tiles and the BonusContext

The Strategy Space

The Dominance Hierarchy

The Payoff Matrix

The Contention Effect

Nash Equilibrium and the Prisoner's Dilemma

The Price of Anarchy

The Scoring Function

Degenerate Combos

Is the Game Solved?

Play the Dominant Strategy

Can Opus 4.6 do Category Theory in Lean?

Can Opus 4.6 do Category Theory in Lean?

Book Review: When We Cease to Understand the World

Book Review: When We Cease to Understand the World

Hypothetical Divine Signatures

Hypothetical Divine Signatures

Typechecker Zoo

Typechecker Zoo

The Stochastic Code Monkey Theorem

The Stochastic Code Monkey Theorem

The Thirty Years' War Is Starting Again

The Thirty Years' War Is Starting Again

It Would Be Good if the AI Bubble Burst

It Would Be Good if the AI Bubble Burst

Every Democrat Who Enabled Trump's Crypto Corruption

Every Democrat Who Enabled Trump's Crypto Corruption

H.R. 4763 "FIT21" (2024)

H.J.Res. 109 SAB 121 Disapproval (2024)

H.R. 5403 "CBDC Anti-Surveillance State Act" (2024)

Senate: H.J.Res. 109 SAB 121 Disapproval (2024)

Senate: S. 1582 "GENIUS Act" (2025)

H.R. 1919 "Anti-CBDC Surveillance State Act" (2025)

The Good List

Senate

House

Only Solution to the Attention Economy is to Opt Out

Only Solution to the Attention Economy is to Opt Out

Fast Tensor Canonicalization in Rust

Fast Tensor Canonicalization in Rust

Fine-tuning With Tool Calling

Fine-tuning With Tool Calling

Program Synthesis: The λ in the Machine

Program Synthesis: The λ in the Machine

The Asbestos Doctrine: Why Crypto Must Be Contained, Not Condoned

The Asbestos Doctrine: Why Crypto Must Be Contained, Not Condoned

What is AI market actually worth?

What is AI actually worth?

Book Review: Tomorrow, and Tomorrow, and Tomorrow

Book Review: Tomorrow, and Tomorrow, and Tomorrow

The Future of Maths May Be Deeply Weird

The Future of Maths May Be Deeply Weird

Does the Star Trek Computer Run on COBOL?

Does the Star Trek Computer Run on COBOL?

Interfacing MCP with Combinatorial, Convex, and SMT Solvers

Interfacing MCP with Combinatorial, Convex, and SMT Solvers

Prototype

The Vision for Universal Solver Interface

The Trump Crypto Orgy of Corruption

The Trump Crypto Orgy of Corruption

Unnecessary and Unstable: Why Stablecoins are Bad

Unnecessary and Unstable: Why Stablecoins are Bad

Remote MCP Servers

Remote MCP Servers

The `gpu` Dialect

`nvgpu` Dialect

`nvvm` Dialect