# Language models guide symbolic equation discovery by controlling search

arXiv: https://arxiv.org/abs/2607.04156 · HTML: https://mlsanity.com/paper/2607.04156/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Jul 2026.

## Built on by (most cited first, 3 of 3)

- [Hypothesize, Evaluate, Refine: A Scientific Agent for PDE Discovery with Unknown Spatial Coefficient Fields](https://mlsanity.com/paper/2608.27475/) (2026)
- [Self-Evolving Multi-Agent Symbolic Discovery for Financial Fundamental Analysis](https://mlsanity.com/paper/2609.32746/) (2026)
- [SRHarness: A Harness for Agentic Symbolic Regression](https://mlsanity.com/paper/2609.35501/) (2026)

## Abstract (arXiv)

Scientific equation discovery must combine broad domain priors with strict numerical testing. Symbolic regression supplies numerical grounding but faces a combinatorial search space, whereas many language-model systems ask the model to propose or select formulas directly. We test a different division of labour. We compare role specifications in which the language model acts as equation author, candidate decider or search controller, alongside end-to-end language-model and purely numerical baselines. In the controller setting we propose here, implemented as LLM-PySR, language models specify variables, operators, transformations and search depth; symbolic regression enumerates and fits expressions; and deterministic metrics govern retention. Across 74 AI-Feynman equations and seven complex formula-recovery tasks, search control achieved the strongest observed balance of accuracy, complexity, stability and cost. On an independent battery dataset, LLM-PySR identified a compact piecewise-linear relation between early voltage-curve displacement and cycle life. The results suggest that language models should shape hypothesis exploration rather than decide which equations survive.