AI Is Learning at the Wrong Level of Abstraction — Matthieu Wyart

Summary

• Wyart’s core claim is that predicting raw tokens or pixels forces networks to build abstract concepts from a “super noisy signal,” which helps explain why machines need vastly more data than brains — “the brain can learn with 100,000 times less exposure to words than those machines.” His paper, about one month old in the conversation, argues that “introspective” algorithms predicting in latent space — the JEPA direction Tim associates with Yann LeCun — “will learn the same abstraction but much faster,” with a sample-complexity theory behind the proposal. Tim frames the deployment gap by noting that OpenAI and Anthropic are still training transformers.
• The big unresolved caveat for anyone assessing the JEPA thesis: latent-predicting models build an encoder of the world, but Wyart doesn’t know whether one can add a decoder without requiring much data and obtain a competitive generative model. “Can I really go back and… compete with next-token prediction and build something generative? I don’t know. This is completely open to me” — LLMs’ commercial value is precisely that they’re generative and interactive.
• His group’s synthetic-grammar experiments are a direct counterexample to Chomsky’s poverty-of-stimulus argument: deep networks learn to generate novel, rule-respecting sentences after seeing only polynomially many examples in sentence size d, while the model contains exponentially many sentences in d. Shallow networks behave as Chomsky feared — “you essentially memorize and you can’t do anything” — but depth carries “a huge implicit bias to build those coarse-grained variables.”
• His resolution of the curse of dimensionality doubles as a claim about why depth matters: the manifold hypothesis alone is insufficient because kernel methods would need to solve the problem if a low-dimensional manifold were enough, yet on text they “fail lamentably… They do nothing.” Any real explanation, he argues, “needs to explain why you need deep networks.” The answer: the world is hierarchical, and deep nets discover its hidden coarse-grained variables with polynomial rather than exponential data.
• With Francesco Cagnetta, Alon Ravid and Surya Ganguli, he proposes a theory that derives LLM scaling-law exponents from two measurable quantities — the power-law decay of token correlations with distance and the entropy remaining after n tokens — “and it works very well.” Crucial hedge: it has been tested only at the “academic range” (~1B parameters, ~1B tokens, ~50-token context); “I don’t know if the mechanism we put forward still applies” beyond three or four sentences — directly relevant to whether continued scaling keeps paying off.
• Diffusion models and next-token prediction have the same sample complexity in his theory — “the only difference is the order in which you’re filling up what is being masked.” Both learn grammar bottom-up: random output, then coherent words, then phrases, then full sentences as data grows; Wyart says this prediction was checked for diffusion models.
• On why superior methods aren’t deployed: Tim cites Llion Jones at Sakana — “any new method has to be crushingly better” given the hardware, optimizer and compiler ecosystem built around transformers — and notes that Yann LeCun’s startups appear to be focusing on vertical domains rather than attempting the moonshot. Wyart cautions that scaling alone may not produce machine scientists: “I don’t see how you could learn it just by looking at everything that was ever written without enforcing those interactions” with the world.

Deep dive

1. A statistical physicist’s origin story: the loss landscape of deep nets is literally sand

• Wyart’s path ran from stock markets (“interacting agents that influence the evolution of the price”) to complex systems — “physical systems with a rough energy landscape,” where a ball thrown into the mountains “could stop at many different points.” He worked on several examples, including sand, where “if you prepare 10,000 piles of sand, each of them is different,” and tilting a layer triggers a phase transition into flow.
• Nine years ago, a self-described “poor Go player” mesmerized by AlphaGo, he applied the same complex-systems lens to training: underparameterized networks have rough landscapes full of metastable traps, but with enough parameters “suddenly the system can flow” through flat, essentially zero-energy valleys. The ML community independently found the same phenomenon and named it double descent — but “the peak of double descent is really, for physicists, a jamming transition.”
• The last four years shifted his attention to “another landscape that I think is even more interesting: the landscape of data” — the density of images ρ(X), which “relates to what is the structure of the world” and, he thinks, is key to understanding how machines work.

2. Tim’s substrate objection, and the universality-class answer

• Tim’s pushback: neural nets have no material substrate — the physical constraint that “2 objects can’t touch each other at the same time” does not apply — so is the physics analogy coherent? Wyart’s answer relocates the analogy from matter to the algorithm: in both cases, degrees of freedom (sand grains, parameters) flow down an energy landscape while satisfying constraints (avoiding each other, fitting data). “If you have a constraint-satisfaction problem and continuous degrees of freedom… boom, you have a universality class.”
• His deeper point is that analogy is how science works: Huygens proposed that light was a wave after noticing that ocean waves could cross without interacting, as light does. “We’re always building our understanding in terms of analogies.”
• He’s careful to bound the claim: “I don’t want to say that everything is always the same” — but sand jamming and loss landscapes “is very much the same, yes.”

3. What physics brings to AI: crude models at the right level, and Carnot’s precedent

• Three exports from physics are the theory–experiment dialogue; modeling at the right resolution — “a map where 1 mile is 1 mile will never help you,” and, paraphrasing Einstein, “a model should be the simplest, but not simpler than that”; and cross-field analogy. Exhibit A: magnetism looks like “awfully complicated quantum mechanics” microscopically, yet the crude Ising model — arrows on a lattice trying to align — is the description that led to Nobel Prizes, many fields in mathematics, and more.
• His template for the current moment is the Industrial Revolution: the heat engine came first, then Carnot wrote a text that “reads like philosophy; there’s essentially no math,” introduced entropy, and began thermodynamics. “Here, I think it’s the same… Chomsky and others said that it would be extremely hard to do. They do it. So how? Why?”
• Against the concern that physics relies on idealization, Wyart holds both directions of the loop: theory builds technology, such as the laser, and technology “is asking immense questions” — theory becomes “a highway of thinking super fast about problems.”

4. The poverty-of-stimulus counterexample: creativity from statistics alone

• Tim relays Chomsky’s dismissal — LLMs are bulldozers, “great for clearing the snow but not a contribution to science”; Deep Blue was “a bulldozer winning a weightlifting competition.” Wyart responds that Chomsky’s point “is not wrong” and that LLMs are not a theory, but an observation that raises questions, just as the heat engine did for Carnot.
• The experiment builds synthetic hierarchical worlds: context-free grammars on frozen trees with random production rules (“randomness, although it’s counterintuitive, often makes things simpler in physics”), where the number of sentences is exponential in sentence size d. Shallow networks vindicate Chomsky’s concern: “you essentially memorize, and you can’t do anything.” Deep architectures, with their “huge implicit bias to build those coarse-grained variables,” become creative after only polynomially many examples — “these models are really a counterexample to his argument.”
• Tim explicitly avoids equating the brain with a deep net: the brain learns with “100,000 times less exposure to words,” and “there are lots of questions about how the brain works, and they are fascinating.” Wyart’s result instead shows that a deep architecture can supply a strong inductive bias that reduces what must be learned.

5. Where Wyart agrees with the skeptics: scaling won’t automatically manufacture scientists

• Tim’s sharpest example is feeding his entire codebase into Claude Code, which has syntactic competence but “doesn’t respect the deep constraints… my mental constraints — what was I trying to achieve?” Is that merely a limitation of current networks?
• Wyart first describes combinatorial creativity: diffusion models can compose noses, eyes and mouths once they “understand the rules of the game.” But creativity can be more than assembling pieces. Show a machine waves entering a port and being diffracted, and it would “stupidly predict the next frame, because velocity will propagate.” A physicist instead notices that something is intriguing, simplifies the geometry, and models it.
• He is unsure that scaling alone will produce this ability: “Maybe we need to do more introspection of how we function as scientists to come up with a good dataset and good procedures to teach machines to be good scientists.” He ultimately says he agrees that simply scaling up will not lead to total success, and adds: “I don’t see how you could learn it just by looking at everything that was ever written without enforcing those interactions” with the world.

6. The curse of dimensionality: the manifold hypothesis alone is not enough — hierarchy is

• The setup: volume scales as length to the power of dimension, so in image- or text-space “even if you give me 1 trillion points… they’re extremely far away from each other,” and smooth interpolation would need “more data than atoms in the universe.” Tim brings in Randall Balestriero’s spline view that “in high dimensions, all data is extrapolation.”
• Wyart’s challenge to the usual manifold explanation is that the measured intrinsic dimension “is still large.” If a low-dimensional manifold by itself solved the problem, kernel methods or shallow networks would suffice; on text, he says, they “fail lamentably… They do nothing.” Any theory, he argues, “has to explain why you need deep networks.”
• His explanation is that the world has hidden hierarchical coarse-grained variables, and deep architectures are “super-good at discovering them” with a number of data points that is polynomial in the dimension. Once discovered, they summarize the data — instead of describing pixels individually, one can say, “There is a nose, there are ears,” and so on — reducing the effective dimension.

7. How abstractions actually emerge: Word2Vec, recursively — and why the top of the tree is hardest

• The mechanism starts with Word2Vec’s insight: train a one-hidden-layer machine on co-occurrence, and synonyms — sharing contexts — receive similar vectors: “instead of the incarnation of those different words, you will just have the meaning.” Deep nets, he argues, do that recursively, grouping meanings into “supra-meanings.”
• His signature example is the street: passersby, cars, sidewalks and “an immense number of possible streets” — the concept forms by grouping configurations that predict similar contexts around them. “The way they build concepts, they emerge from statistics alone… they are there in the data.”
• The catch that motivates latent prediction: token-level learners must relate abstractions to pixels, colors and other low-level features, and “as you get more and more abstract, your signal gets diluted” — so the more abstract concepts are the toughest to learn.
• Wyart also says that factorizations and abstractions are created progressively: with more training, and especially in a very large machine given more data, the model begins to use increasingly abstract concepts. Those higher-level concepts are the hardest to learn from this viewpoint.

8. Predict latents, not tokens — the month-old theory, and the honest open question

• The proposal is adjacent to LeCun’s JEPA and to neuroscience ideas in which the cortex predicts its own next activity: duplicate a machine, show the teacher the full data and the student an occluded version, then have the student predict the teacher’s representations rather than the missing tokens. “It’s beautiful, right? Those networks are doing some kind of introspection.”
• Why it wins on sample complexity, according to Figure 1: in tree-structured data, correlations weaken multiplicatively with distance along the tree, so learning top-level concepts from low-level features costs data exponential in tree depth. Predicting nearby concepts — not the pixels or the painting of the house, but the concept “houses nearby” — makes “the signal much larger,” requiring less data to extract it from noise.
• His hedging is important: the paper is one month old, and “when I talk about it, I talk about it with caution.” Being rigorous “doesn’t mean having a theorem”; it means going back and testing predictions. Above all, whether the resulting encoder can be turned into a competitive generative decoder remains open: “I don’t know. This is completely open to me.”
• Tim’s frustration frames the commercialization gap: OpenAI and Anthropic “are still training old-school transformers,” and Llion Jones at Sakana told him “any new method has to be crushingly better” given the ecosystem built around transformers; LeCun’s startups appear to be focusing on vertical domains, and “we haven’t yet done the moonshot.”

9. Scaling laws from two exponents, diffusion’s equivalence — and permission to be wrong

• The Kaplan-style scaling laws “drove the tech companies to just invest more and build maybe nuclear plants,” yet were “a bit embarrassing for us theorists — essentially not understood at all.” With Francesco Cagnetta, Alon Ravid and Surya Ganguli, Wyart proposes a theory for the training-curve exponent from two measurable quantities: the power-law decay of token correlations with distance, and the entropy left after n tokens — “and it works very well.” It also predicts, and he says they observe, a specific bend in loss as a joint function of context and data.
• The stated validity range matters: tested at roughly 1 billion parameters and 1 billion tokens, with context around 50 tokens — “2 or 3 sentences,” where “there’s all the syntax and so on” — and “I don’t know if the mechanism we put forward still applies” further out.
• Diffusion versus next-token prediction: the theory gives them the same sample complexity — “the only difference is the order in which you’re filling up what is being masked” — with the prediction that coherence grows bottom-up as data increases: gibberish, then words, then phrases, then full sentences. Wyart says this was checked for diffusion models.
• Asked what he’s been wrong about, he answers with a scientific credo: once convinced of a mistake, state it and don’t “cling to it.” The episode’s closing line is: “If you never make mistakes, maybe it’s a sign that you’re staying a bit on the beaten path in science. Some of us want to explore the jungle. In the jungle, you can be wrong.” Asked whom he would teach deep learning to, he chooses his father, a physicist who became interested in neuroscience and olfaction near the end of his life.