L2G-SR Uses a Learned Structural Verifier to Guide LLM Symbolic Regression

Summary

Symbolic regression searches for equations that explain observed data, but optimizing numerical error alone can favor an accurate surrogate rather than the correct underlying structure. L2G-SR is a framework for LLM-based symbolic regression that adds a learned structural verifier to the search process. The authors build structural supervision with tree edit distance, while accounting for commutative operators and alternative forms of the same expression. The verifier first aligns numerical observations with formulas and then learns to score how structurally similar a candidate is to the target formula. During search, the target formula remains hidden, and verifier scores complement numerical error when selecting parent expressions. An analyst uses verifier feedback and diagnostic tools to suggest revisions, which a generator turns into refined equations. On LLM-SRBench, L2G-SR achieves state-of-the-art numerical fit, equation-level accuracy, and tree edit distance across the evaluated LLM backbones and domains. The results support learned structural guidance as a useful addition to LLM-based symbolic regression.