# FunctionEvolve: Structure-Guided Symbolic Regression with LLMs

arXiv: https://arxiv.org/abs/2606.07704 · HTML: https://mlsanity.com/paper/2606.07704/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 28 references that are in the map.
- First posted on arXiv 5 Jun 2026.

## Builds on (most cited first, 13 of 13)

- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradients](https://mlsanity.com/paper/1912.04871/) (2019)
- [Contemporary Symbolic Regression Methods and their Relative Performance](https://mlsanity.com/paper/2107.14351/) (2021)
- [Learning Equations for Extrapolation and Control](https://mlsanity.com/paper/1806.07259/) (2018)
- [LLM-SR: Scientific Equation Discovery via Programming with Large Language Models](https://mlsanity.com/paper/2404.18400/) (2024)
- [Extrapolation and learning equations](https://mlsanity.com/paper/1610.02995/) (2016)
- [Symbolic Regression via Neural-Guided Genetic Programming Population Seeding](https://mlsanity.com/paper/2111.00053/) (2021)
- [Symbolic Regression with a Learned Concept Library](https://mlsanity.com/paper/2409.09359/) (2024)
- [LLM-SRBench: A New Benchmark for Scientific Equation Discovery with Large Language Models](https://mlsanity.com/paper/2504.10415/) (2025)
- [Automated Scientific Discovery: From Equation Discovery to Autonomous Discovery Systems](https://mlsanity.com/paper/2305.02251/) (2023)
- [Benchmarking symbolic regression constant optimization schemes](https://mlsanity.com/paper/2412.02126/) (2024)
- [LLM-Based Scientific Equation Discovery via Physics-Informed Token-Regularized Policy Optimization](https://mlsanity.com/paper/2602.10576/) (2026)
- [Enhancing Symbolic Regression with Quality-Diversity and Physics-Inspired Constraints](https://mlsanity.com/paper/2503.19043/) (2025)

## Abstract (arXiv)

Symbolic regression aims to uncover explicit scientific laws from data. Recent methods use LLMs to guide mutation from background text, which is more directed than random genetic programming. However, exact symbolic recovery requires both semantic guidance and explicit structure, so that domain-informed search are carried out through valid symbolic representation. Current LLM-driven systems remain structure-blind: they select among opaque candidates, lack explicit mechanisms for local mutation, and rely on brittle coefficient fitting that can undervalue correct skeletons. We propose FunctionEvolve, an evolutionary framework using expression trees to organize the whole search: structural summaries promote diverse parent selection, local tree edits preserve useful subexpressions, and structure-aware fitting decomposes, constrains, and simplifies coefficients for more reliable scoring. It uses only elementary function families, without additional domain-specific rules limiting generalization. On the 129-task synthetic subset of LLM-SRBench, FunctionEvolve with Claude Opus 4.6 recovers 107 exact forms, reaching 82.9% SA@50, 4.5x above same-backbone baselines, and 55.8% SA@1, 3.6x above the strongest previously published top-1 result. Ablations show that structure-visible search is central to reliable recovery, with LLM-guided refinements and structure-aware coefficient optimization serving as essential proposal and scoring mechanisms. We also audit the benchmark and show that collinearity in its materials-science subset creates identifiability issues.