Axiomatic World Modeling for Physics Reasoning

Axiomatic World Modeling for Physics Reasoning. By Xinye Yang and three others, from Northwestern University and the University of Florida. Published on the seventeenth of October. No code repository is linked to it.

Recent research-level benchmarks of physics reasoning in large language models expose a failure that is not about knowledge, and not about execution. It is about modeling the world that is being reasoned about. Models often silently alter the quantities a problem gives them. They fabricate laws. They inject assumptions nobody stated, forcing the problem into a pattern they recognise, and then they reason inside that corrupted world as though it were the real one. The authors call this premise-level divergence modeling drift: the gap between a model's internal axiomatic world model, abbreviated AWM, and the true physical world the problem actually specifies.

Training methods have not been aimed at this gap. Reinforcement learning with verifiable rewards, and process reward models, have yielded substantial gains in mathematics and in code. Yet the shape of their rewards does not directly supervise world modeling in an axiomatic domain such as physics. A model can be rewarded for its reasoning without anything checking the world that reasoning took place in.

The proposal is Reinforcement Learning with Axiomatic World Modeling, shortened to RLAWM. It optimizes the policy by penalizing divergence between the axiomatic world model the policy infers and the true physics world. Rather than only scoring where the reasoning ends up, the objective also scores which world the model decided it was in before the reasoning began.

RLAWM probes physics reasoning at two hierarchical levels, modeling and solving, and each level is scored by its own physically grounded reward. The modeling reward targets abstract knowledge formulation. It evaluates whether the model has captured the true axiomatic world before attempting any calculation. The solving reward targets instantiated knowledge reasoning. It checks whether the model's concrete derivation remains consistent with that axiomatic world. Taken together, the two levels pull apart two questions: what world the model believes it is reasoning in, and how it reasons once it is inside that world. The whole framework operates exclusively during training, so there is no extra cost at inference.

Against the baseline, RLAWM improves performance by up to twelve point two points on PhysReason, and by up to five point two points on PHYSICS. The abstract also reports zero-shot generalization along three axes: difficulty, source, and domain. On olympiad-level physics and math, measured against the strongest baseline, the method shows a gain of two point four five times, together with an improvement of ten points.

One way to hold this paper in mind is as a relocation of the error. A wrong physics answer can come from a derivation carried out faithfully in the wrong world, and no amount of careful solving repairs a premise that was quietly changed at the start. RLAWM rewards the world first and the reasoning second, and keeps all of it inside training.