Video · 2026-08-10 · 1h 19m · 6 moments

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

✦ AI generated

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Fact

The loss function of an overparameterized neural network undergoes a phase transition analogous to the jamming transition in sand: underparameterized networks have a rough energy landscape with many metastable states, while sufficiently many parameters allow the system to flow into flat zero-energy valleys.

Wyart connects his work on complex systems to machine learning: overparameterized networks' loss landscapes have the same phase transition as tilted sand flowing. Underparameterized models get stuck in metastable states, but with enough parameters the landscape has flat zero-energy valleys; this is what others independently called double descent but physicists see as a jamming transition.

transcript

Matthieu Wyart: what we discover is actually that this landscape has exactly the same phase transition as send it means that when you actually underparameterized when you don't have enough parameters you have a rough landscape with many metastable state and if you train your machine and you train it many times it will end up in different position where it's actually stuck but if you have enough parameters then suddenly the system can flow I in your landscape has many flat valleys and you can which have essentially zero energy. So there is really a close analogy we disco we discovered that like 9 years ago at the same time uh others find a very similar I mean the same phenomenon and called it double descent. So now this name has stuck but this double descent this peak of the double descent is really for physicists a jamming transition.

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Mechanism

The analogy between jamming of sand and the loss landscape of machines is direct and valid because both are systems of continuous degrees of freedom trying to satisfy constraints, and satisfiability problems with continuous degrees of freedom fall into a universality class.

Wyart defends the coherence of applying statistical physics to machine learning: in both sand and model training you have continuous degrees of freedom collectively satisfying constraints, which forces a universality class. The analogy is about the algorithm (gradient descent flowing down an energy landscape), not the material substrate.

transcript

Matthieu Wyart: for the specific example I gave you about the sand and uh and uh and the loss landscape of of machines I think the analogy is is is very direct in this case because in both cases what you have are essentially degrees of freedom. In one case those are the part particle of sand in the other case there are the parameters of your large model and in both cases the system are trying to satisfy constraints. Um so for for sand essentially the particles are just trying to avoid each other but for the parameters what they are trying to collectively do is to fit data. So the more data you have the more constraint you have and at the end the universality there is what we've argued from physics but applies there that if you have a problem of satisfiability of constraint and you have continuous degrees of freedom that can change continuously then boom you have a universality class. So in this sense yes there's something universal about those kind of problems

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Claim◆

Chomsky's poverty of stimulus argument, that it is impossible to learn to become creative from examples alone, is refuted: deep architectures have a huge implicit bias to build coarse-grained hierarchical variables, so they can learn to be creative from polynomially many (not exponentially many) sentences.

In Wyart's synthetic tree-structured world, a shallow network does exactly what Chomsky predicted — it memorizes and cannot generalize. But deep architectures exhibit a strong implicit bias to construct coarse-grained hierarchical variables, learning to be creative from only polynomially many sentences. This is a counterexample showing that what must be 'innate' shrinks dramatically for a deep architecture.

transcript

Matthieu Wyart: what we find is that if you have a shallow network what Shamsky worried about is completely true. You learn some you don't learn this sort of interesting generative grammar. You essentially memorize and you can't do anything. But if you have a deep architecture, there's a huge implicit bias to build those course grain variables. Thisarchical architecture leads very easily to some iterative calculation. And so what we what we found is that uh indeed you can learn to be creative by having being exposed to very small number of sentences. So let's say in our model if D is an is you know the size of the sentence the number of sentences is huge with D is exponential in D but the number of sentences you need to see to be creative is only polomial in D. So these models are really a counter example to uh to his argument and and ultimately it come from the fact that you know machines have strong implicit bias. they are not comparing equally in an equal fashion all hypothesis. Uh and if you're deep you learn so so uh so that's a counter example to that. So so in some sense I would argue that in terms of what needs to be innate if you have deep architecture that's lots of that.

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Prediction

Pure scaling of models and data will not produce scientific creativity that discovers new subspaces, because such creativity requires interaction with the world, observing the intriguing, simplifying geometry, and building models — abilities machines trained on all of written text alone do not have.

Wyart distinguishes composing existing ideas from transformative creativity. While machines can compose new faces by learning rules of combination, scientific discovery — detecting what's intriguing, simplifying geometry, modeling — requires embodied interaction with the world. Scaling up on all written text alone will not yield this; we need to teach machines to be good scientists.

transcript

Matthieu Wyart: I think creativity can be much more than that. I mean if we think about what we discussed about what it means to be a physicist and how science proceeds. I mean it's an example of creativity you know if you think about creativity like Newton understandings of motion of planets and things like that. I mean we talked about dialogue between experiments and theory. We talked about building models at a good level of description. We talked about you know analogies and I don't think I agree with you that I for example all that I don't think it's in the machine. Uh I think there's no reason why we would not be able one day to build machines that can do that. I'm not sure if just scanning up things will lead to that. Uh I think maybe we need to do more introspection of how we function as scientists to come up with a good data set and the good procedures to teach machines to be goodi good scientists.

Mechanism◆

The curse of dimensionality is only tractable because the world is hierarchical: if data has hidden coarse-grained variables, deep architectures are particularly good at discovering them with polynomially many data rather than exponentially many.

Wyart explains that the exponential volume of high-dimensional data makes interpolation hopeless unless the data has hierarchical structure. The manifold hypothesis is insufficient because kernel methods and shallow networks would then work perfectly, yet they fail. The real answer is that deep architectures discover hidden hierarchical abstractions, reducing dimensionality polynomially.

transcript

Matthieu Wyart: So what it means is that even if you give me one trillion points, because the volume is so huge, they're extremely far away from each other. Extremely far away. And so if you have a machine that's just interpolating and now you ask a question about a new test point and you can prove mathematically that if the data has little structure like you're trying to learn to regress some function that's smooth it's hopeless. I mean the only way you will extrapolate and have you know power to to to generalize is if you know you bring those point together. it means you have an exponentially large number of data. You have more data than atoms in the universe. So it's just impossible. So to me this is completely fundamental question and um and it's true that sometimes in the literature it's tossed aside by saying okay it's super naive to say that the dimension is a number of pixel on an image. In fact it should really be uh that the data lie in a lower dimension manifold. And if you try to measure it, it's true that it lies in a lower dimension manifold, but this dimension is still large in dimen in dimension. And and to me the big problem is that if this was the answer to this question, it will mean that very simple algorithm like kernel methods are ancestor of deep net or even shallow network. I mean they do it perfectly. And if you give them you know a low dimensional manifold you don't need to have any interesting architecture but if you use zoo on text I can tell you it fails lament I mean it's completely does nothing

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Mechanism◆

Predicting in latent or abstract space rather than token space is much more sample-efficient for learning abstractions, because building a coarse-grained concept by correlating with other abstract concepts gives a much stronger signal than correlating with low-level pixels or tokens.

The core thesis of the paper: introspection-based algorithms that learn from their own latent representations are much more powerful in sample complexity. When building a coarse-grained concept like 'street', correlating with already-understood abstract concepts (houses) gives a far stronger signal than correlating with noisy low-level pixels, so far less data is needed.

transcript

Matthieu Wyart: imagine instead that you when you start when you understood the concept of cars and passerby Uh and you also understood the concept of house houses. Uh then essentially what those methods do is they can build the concept of street by predicting that those configuration have not pixel the painting of the house but just the concept houses nearby and then the signal is much larger and so you need much less data to extract the signal from noise. So yes we do find that those to understand the archical structure of the world those at least in those simple models it's much more efficient.

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Highlight slides

Chomsky's poverty-of-stimulus refuted by deep architectures✦ from: Chomsky's poverty of stimulus argument, that it is impossible to learn to become creative from examples alone, is refuted: deep architectures have a huge implicit bias to build coarse-grained hierarchical variables, so they can learn to be creative from polynomially many (not exponentially many) sentences.Dimensionality curse is only tameable via hierarchy✦ from: The curse of dimensionality is only tractable because the world is hierarchical: if data has hidden coarse-grained variables, deep architectures are particularly good at discovering them with polynomially many data rather than exponentially many.Learning in latent space: the sample-efficiency thesis✦ from: Predicting in latent or abstract space rather than token space is much more sample-efficient for learning abstractions, because building a coarse-grained concept by correlating with other abstract concepts gives a much stronger signal than correlating with low-level pixels or tokens.

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