LLMs Guide Symbolic Regression to Discover Scientific Laws Faster

Symbolic regression (SR) aims to uncover underlying mathematical equations from data, but its effectiveness is often limited by the vast and complex search space of possible expressions. Traditional methods struggle to efficiently navigate this combinatorial challenge to find physically meaningful laws. InsightSR introduces a novel approach by integrating Large Language Models (LLMs) to intelligently guide the PySR genetic programming engine. Instead of having LLMs directly generate equations, InsightSR leverages them to progressively transform and refine the search space itself. This is achieved through two pathways: a Semantic Seed Pathway that suggests dimensionally consistent functional structures, and a Structural Feature Pathway that recommends nonlinear data transformations. These LLM-guided transformations accumulate over iterations, effectively expanding the input space and shifting the symbolic search from building deep, complex trees over raw variables to constructing shallower trees over a richer, semantically informed set of features. A feedback loop evaluates candidate expressions, categorizes useful features, and refines the LLM's guidance for subsequent iterations, turning the discovery process into an iterative, self-correcting refinement. InsightSR achieved a 95% exact recovery rate on the Feynman benchmark and strong performance on other tasks, demonstrating superior results compared to existing methods.