Keyon Vafa, Peter G. Chang, Ashesh Rambachan, Sendhil Mullainathan
2025 · arXiv
Foundation models are premised on the idea that sequence prediction can uncover deeper domain understanding, much like how Kepler's predictions of planetary motion later led to the discovery of Newtonian mechanics. However, evaluating whether these models truly capture deeper structure remains a challenge. We develop a technique for evaluating foundation models that examines how they adapt to synthetic datasets generated from some postulated world model. Our technique measures whether the foundation model's inductive bias aligns with the world model, and so we refer to it as an inductive bias probe. Across multiple domains, we find that foundation models can excel at their training tasks yet fail to develop inductive biases towards the underlying world model when adapted to new tasks. We particularly find that foundation models trained on orbital trajectories consistently fail to apply Newtonian mechanics when adapted to new physics tasks. Further analysis reveals that these models behave as if they develop task-specific heuristics that fail to generalize.
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I agree it's an oversimplification. The example I think of is something like Newton's law of gravitation vs Ptolemaic epicycles: one simple explanation replaced many layers of tweaks. It's also a relevant example for AI - one paper tested the ability of Transformers to model planetary orbits: unlike Newton's Law, the implicit forces they learn are nonsense. https://arxiv.org/pdf/2507.06952
> any human who ever lived Is this falsifiable? Even restricting to those currently living? On what tests? In which way? Does the category of error matter? > can you name one functional difference between an AI that understands, and one that merely behaves correctly in its domain of expertise? I'd argue you didn't understand the examples from my previous comment or the direct reply[0]. Does it become a duck as soon as you are able to trick an ornithologist? All ornithologists? But yes. Is it fair if I use Go instead of Chess? Game 4 with Lee Sedol seems an appropriate example. Vafa also has some good examples[1,2]. But let's take an even more theoretical approach. Chess…
is technically a solved game since it is non-probabilistic. You can compute an optimal winning strategy from any valid state. Problem is it is intractable since the number of action state pairs is so large. But the number of moves isn't the critical part here, so let's look at Tic-Tac-Toe. We can pretty easily program up a machine that will not lose. We can put all actions and states into a graph and fit that on a computer no problem. Do you really say that the program better understands Tic-Tac-Toe than a human? I'm not sure we should even say it understands the game at all. I don't think the situation is resolved by changing to unsolved (or effectively unsolved) games. That's the point of the Heliocentric/Geocentric example. The Geocentric Model gave many accurate predictions, but I would find it surprising if you suggested an astronomer at that time, with deep expertise in the subject, understood the configuration of the solar system better than a modern child who understands Heliocentricism. Their model makes accurate predictions and certainly more accurate than that child would, but their model is wrong. It took quite a long time for Heliocentrism to not just be proven to be correct, but to also make better predictions than Geocentrism in all situations. So I see 2 critical problems here. 1) The more accurate model[3] can be less developed, resulting in lower predictive capabilities despite being a much more accurate representation of the verifiable environment. Accuracy and precision are different, right? 2) Test performance says nothing about coverage/generalization[4]. We can't prove our code is error free through test cases. We use them to bound our confidence (a very useful feature! I'm not against tests, but as you say, caution is good). In [0] I referenced Dyson, I'd appreciate it if you watched that short video (again if it's been some time). How do you know you aren't making the same mistake Dyson almost did? The mistake he would have made had he not trusted Fermi? Remember, Fermi's predictions were accurate and they even stood for years. If your answer is time, then I'm not convinced it is a sufficient explanation. It doesn't explain Fermi's "intuition" (understanding) and is just kicking the can down the road. You wouldn't be able to differentiate yourself from Dyson's mistake. So why not take caution? And to be clear, you are the one making the stronger claim: "understanding has a well defined definition." My claim is that yours is insufficient. I'm not claiming I have an accurate and precise definition, my claim is that we need more work to get the precision. I believe your claim can be a useful abstraction (and certainly has been!), but that there are more than enough problems that we shouldn't hold to it so tightly. To use it as "proof" is naive. It is equivalent to claiming your code is error free because it passes all test cases. [0] https://news.ycombinator.com/item?id=45622156 [1] https://arxiv.org/abs/2406.03689 [2] https://arxiv.org/abs/2507.06952 [3] Certainly placing the Earth at the center of the solar system (or universe!) is a larger error than placing the sun at the center of the solar system and failing to predict the tides or retrograde motion of Mercury. [4] This gets exceedingly complex as we start to differentiate from memorization. I'm not sure we need to dive into what the distance from some training data needs be to make it a reasonable piece of test data, but that is a question that can't be ignored forever.
Okay, read the abstract and Intro. Recently, in the paper "What Has a Foundation Model Found? Using Inductive Bias to Probe for World Models" your thesis of Ai's lack of capacity to abstract or at least extract understanding from noisy data was largely experimentally confirmed. I am uncertain though about the exact mechanics b/c as they used LLM's, its not transparent what happened internally that lead to constant failure to abstract the concept despite ample predictive power. One interesting experiment was the introduction of the Oracle that literally enabled the LLM to solve the task that was previously impossible without the oracle, which means, at least its possible…
that LLM's can reconstruct known rules. They just can't find new ones. On a more fundamental level, I am not so sure why these experiments and mathematical proofs still are made since Judea Pearl already established about seven years ago in "Theoretical Impediments to Machine Learning " that all correlation based methods are doomed as they fail to understand anything. his point about causality is well placed, but will not solve the problem either. The question I have though, if we ignore all existing methods for one moment, then what makes you so sure that AGI is really Mathematically impossible? Suppose some advancement in quantum computing would allow to reconstruct incomplete information, does your assertion still holds true? https://arxiv.org/abs/2507.06952 https://arxiv.org/abs/1801.04016
> That's not a contradiction? Correct. No contradiction was intended. As you quote, I wrote "It's not just that". This is not setting up a contrasting point, this is setting up a point that follows. Which, as you point out, does follow. So let me rephrase > If all models are wrong but some are useful then this similarly means that all useful models are wrong in some way. Why flip it around? To highlight the part where they are incorrect as this is what is the thesis of my argument. With that part I do not disagree. > It stands to reason that an ideal next-token predictor would require an internal model of the world at last equally as powerful as our currently most…
powerful scientific theories. With this part do not agree. There's not only the strong evidence I previously mentioned that demonstrates this happening in history, but we can even see the LLMs doing it today. We can see them become very good predictors yet the world that they model for is significantly different from the one we live in. Here's two papers studying exactly that![0,1] To help make this clear, we really need to understand that you can't have a "perfect" next-token predictor (or any model). To "perfectly" generate the next token would require infinite time, energy, and information. You can look at this through the point of view as the Bekenstein bound[2], the Data Processing Inequality theorem[3], or even the No Free Lunch Theorem[4]. While I say you can't make a "perfect" predictor, that doesn't mean you can't get 100% accuracy on some test set. That is a localization, but as those papers show, one doesn't need to have an accurate world model to get such high accuracies. And as history shows, we don't only make similar mistakes but (this is not a contradiction, rather it follows the previous statement) we are resistant to updating our model. And for good reason! Because it is hard to differentiate models which make accurate predictions. I don't think you realize you're making some jumps in logic. Which I totally understand, they are subtle. But I think you will find them if you get really nitpicky with your argument making sure that one thing follows from another. Make sure to define everything: e.g. next-token predictor, a prediction, internal model, powerful, and most importantly how we did it. Here's where your logic fails: You are making the assumption that given some epsilon bound on accuracy, that there will only be one model which accurate to that bound. Or, in other words, there is only one model that makes perfect predictions so by decreasing model error we must converge to that model. The problem with this is that there are an infinite number of models that make accurate predictions. As a trivial example, I'm going to redefine all addition operations. Instead of doing "a + b" we will now do "2 + a + b - 2". The operation is useless, but it will make accurate calculations for any a and b. There are much more convoluted ways to do this where it is non-obvious that this is happening. When we get into the epsilon-bound issue, we have another issue. Let's assume the LLM makes as accurate predictions as humans. You have no guarantee that they fail in the same way. Actually, it would be preferable if the LLMs fail in a different way than humans, as the combined efforts would then allow for a reduction of error that neither of us could achieve. And remember, I only made the claim that you can't prove something correct simply through testing. That is, empirical evidence. Bekenstein's Bound says just as much. I didn't say you can't prove something correct. Don't ignore the condition, it is incredibly important. You made the assumption that we "did it" through "raw observational data" alone. We did not. It was an insufficient condition for us, and that's my entire point. [0] https://arxiv.org/abs/2507.06952 [1] https://arxiv.org/abs/2406.03689 [2] https://en.wikipedia.org/wiki/Bekenstein_bound [3] https://en.wikipedia.org/wiki/Data_processing_inequality [4] https://en.wikipedia.org/wiki/No_free_lunch_theorem
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