FunctionEvolve: Structure-Guided Symbolic Regression with LLMs

FunctionEvolve is a new evolutionary framework that combines expression trees with LLM guidance to recover exact mathematical equations from data, achieving 82.9% accuracy on synthetic benchmarks—significantly outperforming prior symbolic regression methods by making the search process structure-aware rather than structure-blind.

FunctionEvolve addresses a fundamental limitation in current LLM-driven symbolic regression systems: while language models provide useful semantic guidance, they operate on opaque candidate equations without explicit structural understanding. The framework introduces three key innovations—structural summaries for parent selection, local tree edits for preserving useful subexpressions, and structure-aware coefficient fitting—that transform symbolic regression from a black-box selection problem into a transparent, interpretable search process.

Symbolic regression itself represents a critical frontier in scientific discovery automation. Unlike black-box neural networks, symbolic equations provide interpretable scientific laws that accelerate understanding across physics, biology, and materials science. Prior work showed LLMs could guide random genetic programming more efficiently than purely random mutation, but this approach remained fundamentally structure-blind, selecting among opaque candidates without mechanistic insight. FunctionEvolve bridges this gap by making the tree structure explicit throughout evolution, enabling domain-informed search without domain-specific rules that might limit generalization.

The empirical results demonstrate substantial practical gains: recovering 107 exact equations from 129 tasks represents a 4.5x improvement over same-backbone baselines and a 3.6x improvement over previously published results. Notably, the ablation studies confirm that structure-visible search—not LLM guidance alone—drives this performance improvement, establishing a clear mechanistic understanding of where value comes from.

The audit revealing collinearity issues in existing benchmarks adds credibility to the work by acknowledging limitations. Future research should explore whether FunctionEvolve's structural approach transfers to real experimental datasets where noise and incomplete data present additional challenges beyond synthetic evaluation.

• →FunctionEvolve achieves 82.9% exact recovery rate by making symbolic regression structure-aware rather than structure-blind
• →Local tree edits and structure-aware coefficient fitting prove more important than LLM guidance alone for reliable equation recovery
• →The framework requires only elementary functions without domain-specific rules, suggesting good generalization potential across scientific domains
• →Ablation studies reveal that explicit structural search, not LLM semantics, is the central mechanism driving 3.6x improvements over prior work
• →Benchmark audit identifies collinearity issues in materials-science tasks, highlighting evaluation gaps in existing symbolic regression benchmarks