Keyon Vafa@keyonV
Jul 11, 2025
19 tweets
Can an AI model predict perfectly and still have a terrible world model?
What would that even mean?
Our new ICML paper formalizes these questions
One result tells the story: A transformer trained on 10M solar systems nails planetary orbits. But it botches gravitational laws 
Our paper aims to answer two questions:
1. What's the difference between prediction and world models?
2. Are there straightforward metrics that can test this distinction?
Our paper is about AI. But it's helpful to go back 400 years to answer these questions.
Perhaps the most influential world model had its start as a predictive model.
Before we had Newton's laws of gravity, we had Kepler's predictions of planetary orbits.
Kepler's predictions led to Newton's laws. So what did Newton add?
If you only care about orbits, Newton didn't add much. His laws give the same predictions.
But Newton's laws went beyond orbits: the same laws explain pendula, cannonballs, and rockets.
This motivates our framework: Predictions apply to one task. World models generalize to many
Newton's laws are a kind of foundation model. They provide a place to start when working on new problems.
A good foundation model should do the same.
The No Free Lunch Theorem motivates a test: Every foundation model has an inductive bias. This bias reveals its world model.
We propose a method to measure these inductive biases. We call it an inductive bias probe.
Two steps:
1. Fit a foundation model to many new, very small synthetic datasets
2. Analyze patterns in the functions it learns to find the model's inductive bias
We apply these probes to orbital, lattice, and Othello problems.
Starting with orbits: we encode solar systems as sequences and train a transformer on 10M solar systems (20B tokens)
The model makes accurate predictions many timesteps ahead. Predictions for our solar system:
But has the model discovered Newton's laws?
When we fine-tune it to new tasks, its inductive bias isn't toward Newtonian states.
When it extrapolates, it makes similar predictions for orbits with very different states, and different predictions for orbits with similar states.
To demonstrate, we fine-tuned the model to predict force vectors on a small dataset of planets in our solar system.
A model that understands Newtonian mechanics should get these. But the transformer struggles.
We then fine-tuned the model on a larger scale, to predict forces across 10K solar systems.
We used a symbolic regression to compare the recovered force law to Newton's law.
It not only recovered a nonsensical lawโit recovered different laws for different galaxies.
Would more general models like LLMs do better?
We tried providing o3, Claude Sonnet 4, and Gemini 2.5 Pro with a small number of force magnitudes in-context w/o saying what they are.
These LLMs are explicitly trained on Newton's laws. But they can't get the rest of the forces.
We also apply these probes to lattice problems (think gridworld).
Inductive biases are great when the number of states is small. But they deteriorate quickly.
Recurrent and state-space models like Mamba consistently have better inductive biases than transformers.
If a foundation model's inductive bias isn't toward a given world model, what is it toward?
One hypothesis: models confuse sequences that belong to different states but have the same legal *next* tokens.
Example: Two different Othello boards can have the same legal next moves.
We fine-tune an Othello next-token prediction model to reconstruct boards.
Even when the model reconstructs boards incorrectly, the reconstructed boards often get the legal next moves right.
Models seem to construct "enough of" the board to calculate single next moves.
Inductive bias probes can test this hypothesis more generally.
Models are much likelier to conflate two separate states when they share the same legal next-tokens.
Summary:
1. We propose inductive bias probes: a model's inductive bias reveals its world model
2. Foundation models can have great predictions with poor world models
3. One reason world models are poor: models group together distinct states that have similar allowed next-tokens
Last year we proposed different tests that studied single tasks.
We now think that studying behavior on new tasks better captures what we want from foundation models: tools for new problems.
It's what separates Newton's laws from Kepler's predictions.
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Keyon Vafa@keyonV
Jun 20 24
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New paper: How can you tell if a transformer has the right world model?
We trained a transformer to predict directions for NYC taxi rides. The model was good. It could find shortest paths between new points
But had it built a map of NYC? We reconstructed its map and found this:
This is one way to evaluate world models. But there are many other interesting approaches.
Plug: If you're interested in more, check out the Workshop on Assessing World Models I'm co-organizing next Friday at ICML.
worldmodelworkshop.org
Paper: arxiv.org/abs/2507.06952
Co-authors: Peter Chang (@แดแดแดแดส ษข. แดสแดษดษข), Ashesh Rambachan (@Ashesh Rambachan), Sendhil Mullainathan (@๐๐๐ง๐๐ก๐ข๐ฅ ๐๐ฎ๐ฅ๐ฅ๐๐ข๐ง๐๐ญ๐ก๐๐ง)
Keyon Vafa
@keyonV
Postdoctoral fellow at @Harvard_Data | Former computer science PhD with @Blei_Lab at @Columbia University | Organizing @WorldModelsICML
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