{"ID":5937625,"CreatedAt":"2026-07-07T03:14:33.014478982Z","UpdatedAt":"2026-07-08T07:35:00.384493166Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.04156","arxiv_id":"2607.04156","title":"Language models guide symbolic equation discovery by controlling search","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.","short_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 comp...","url_abs":"https://arxiv.org/abs/2607.04156","url_pdf":"https://arxiv.org/pdf/2607.04156v1","authors":"[\"Zikai Xie\",\"Wenmei Li\",\"Man Luo\",\"Jun Jiang\",\"Linjiang Chen\"]","published":"2026-07-05T07:50:08Z","proceeding":"cs.AI","tasks":"[\"cs.AI\",\"cs.SC\"]","methods":"[\"Large Language Model\",\"Language Model\",\"LoRA\"]","has_code":false}