BeamPERL: Parameter-Efficient RL with Verifiable Rewards Specializes Compact LLMs for Structured Beam Mechanics Reasoning

Researchers trained a compact 1.5B parameter language model to solve beam physics problems using reinforcement learning with verifiable rewards, achieving 66.7% improvement in accuracy. However, the model learned pattern-matching templates rather than true physics reasoning, failing to generalize to topological changes despite mastering the same underlying equations.

• →BeamPERL achieved 66.7% improvement in Pass@1 accuracy on beam statics problems using parameter-efficient reinforcement learning with binary correctness rewards.
• →The model showed anisotropic learning, generalizing well to more loads but failing when support positions changed despite using identical equilibrium equations.
• →Intermediate training checkpoints demonstrated stronger reasoning than fully optimized models, suggesting over-optimization degrades robustness.
• →Verifiable rewards alone are insufficient for true physical reasoning, as models learn procedural templates rather than internalize governing physics principles.
• →Results indicate that exact reward signals must be combined with structured reasoning scaffolding to achieve robust scientific reasoning capabilities.