Decoupled Physical Modeling and Execution for Physics Reasoning

Physics reasoning fails structurally in small language models: an error at any step propagates forward, corrupting every inference that follows. Limited domain knowledge, hallucination under multi-step derivation, and distributional sensitivity compound this failure. We propose a step-level reward framework that identifies the first reasoning error, generates targeted structured feedback, and trains the model to revise its solution via policy gradient with KL regularization, without exposing it to ground truth solutions as generation targets. Unlike annotation-dependent step-level methods, no preference data construction is required and the external verifier operates exclusively at training time. Across five physics benchmarks, our framework delivers accuracy gains of 17-20% over CoT prompting and 10-16% over the strongest baseline, reduces calculation errors from 56.9% to 23.5%, and reduces miscomprehension errors from 22.3% to 12.0% in the best observed cases. Conceptual errors reduce from 89.7% to 68.7%, yet persist as the hardest failure mode across all conditions.

We have witnessed remarkable advances in LLM reasoning capabilities with the advent of DeepSeek-R1. However, much of this progress has been fueled by the abundance of internet question-answer (QA) pairs, a major bottleneck going forward, since such data is limited in scale and concentrated mainly in domains like mathematics. In contrast, other sciences such as physics lack large-scale QA datasets to effectively train reasoning-capable models. In this work, we show that physics simulators can serve as a powerful alternative source of supervision for training LLMs for physical reasoning. We generate random scenes in physics engines, create synthetic question-answer pairs from simulated interactions, and train LLMs using reinforcement learning on this synthetic data. Our models exhibit zero-shot sim-to-real transfer to real-world physics benchmarks: for example, training solely on synthetic simulated data improves performance on IPhO (International Physics Olympiad) problems by 5-10 percentage points across model sizes. These results demonstrate that physics simulators can act as scalable data generators, enabling LLMs to acquire deep physical reasoning skills beyond the limitations of internet-scale QA data. Code available at: https://sim2reason.github.io/.

Physical reasoning over images requires integrating perception, domain knowledge, and multi-step symbolic inference, yet Vision-Language Models (VLMs) fall far short of human performance on physics benchmarks. Reinforcement learning can improve reasoning via reward signals, but it remains unclear whether these signals must come from outside the model or can be derived from the model itself. We compare external rewards, which rely on an outside verifier (rule-based format and answer-correctness checks, or an LLM-judge rubric), with an internal attention-based reward computed from the model's own attention over image regions, requiring no labels or judge. We find that external rewards drive most of the accuracy gains, while preserving more coherent reasoning when rewarded for reasoning tokens. The internal attention-based reward, provides an annotation-free grounding signal that improves spatial-relation reasoning and is complementary to external rewards: adding it to format and accuracy rewards, at no additional annotation cost, improves average accuracy on Molmo~2 while generalizing to out-of-distribution tasks. Our results suggest that internal attention rewards can supplement external supervision and lead to improved physical reasoning.