Language models guide symbolic equation discovery by controlling search

# Language models guide symbolic equation discovery by controlling search
Source: [https://arxiv.org/abs/2607.04156](https://arxiv.org/abs/2607.04156)
[View PDF](https://arxiv.org/pdf/2607.04156)

> Abstract: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\.

## Submission history

From: Zikai Xie \[[view email](https://arxiv.org/show-email/7b9d36f5/2607.04156)\] **\[v1\]**Sun, 5 Jul 2026 07:50:08 UTC \(2,196 KB\)