Language Models Guide Symbolic Equation Discovery by Controlling Search

This paper studies three roles for language models in scientific equation discovery: equation author, candidate decider, and search controller. In the proposed LLM-PySR setup, the language model specifies variables, operators, transformations, and search depth, while symbolic regression enumerates and fits expressions and deterministic metrics decide retention. Across 74 AI-Feynman equations and seven complex formula-recovery tasks, the authors report that search control achieved the strongest balance of accuracy, complexity, stability, and cost. On an independent battery dataset, it recovered a compact piecewise-linear relation linking early voltage-curve displacement to cycle life.