L2G-SR: Learning to Guide LLM-based Symbolic Regression

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Computer Science > Artificial Intelligence arXiv:2610.20685 (cs) [Submitted on 14 Oct 2026] Title:L2G-SR: Learning to Guide LLM-based Symbolic Regression Authors:Letian Huang, Xiangyu Wang, Haowei Lin, Di He View a PDF of the paper titled L2G-SR: Learning to Guide LLM-based Symbolic Regression, by Letian Huang and 3 other authors View PDF HTML (experimental)

计算机科学 > 人工智能 arXiv:2610.20685 (cs) [提交于 2026 年 10 月 14 日] 标题：L2G-SR：学习引导基于大语言模型的符号回归作者：Letian Huang, Xiangyu Wang, Haowei Lin, Di He 查看标题为“L2G-SR：学习引导基于大语言模型的符号回归”的论文 PDF，作者为 Letian Huang 及其他 3 位作者查看 PDF HTML（实验性）

Abstract: Symbolic regression searches for an equation that explains observed data. Numerical error is commonly used to guide the search, but it alone can favor an accurate surrogate over a candidate with the right structure. We propose L2G-SR, a framework for LLM-based symbolic regression that guides search with a learned structural verifier.

摘要：符号回归旨在寻找能够解释观测数据的方程。数值误差通常被用于引导搜索，但仅靠数值误差可能会导致模型偏向于选择准确的替代方案，而非结构正确的候选方案。我们提出了 L2G-SR，这是一个基于大语言模型的符号回归框架，通过学习到的结构验证器来引导搜索。

We construct structural supervision signal using tree edit distance (TED), accounting for commutative operators and alternative expression forms. A verifier first aligns numerical observations with the formulas, then learns to score a candidate’s structural similarity to the target formula. At search time, the target formula is hidden and the verifier complements numerical error in parent selection.

我们利用树编辑距离（TED）构建结构监督信号，并考虑了交换算子和表达式的替代形式。验证器首先将数值观测结果与公式对齐，然后学习对候选公式与目标公式之间的结构相似度进行评分。在搜索过程中，目标公式是隐藏的，验证器在父代选择中对数值误差进行补充。

An analyst then uses verifier feedback and diagnostic tools to propose revisions, which a generator converts into refined expressions. On LLM-SRBench, L2G-SR achieves state-of-the-art numerical fit, equation level accuracy and TED across the evaluated LLM backbones and domains. L2G-SR demonstrates the value of learned structural guidance for LLM-based symbolic regression.

随后，分析器利用验证器的反馈和诊断工具提出修订建议，生成器将其转换为精炼后的表达式。在 LLM-SRBench 上，L2G-SR 在所评估的大语言模型主干和领域中，实现了最先进的数值拟合、方程级准确率和树编辑距离。L2G-SR 展示了学习到的结构引导对于基于大语言模型的符号回归的价值。