LLM-SR-UQ：面向 LLM 引导符号回归外推场景的结构不确定性框架
Know When the Equation Is Wrong: Structural Uncertainty for LLM-Guided Symbolic Regression under Extrapolation
AI 导读
研究者提出 LLM-SR-UQ 框架，解决 LLM 引导符号回归中不同候选方程在拟合数据相近但外推表现差异大的问题。该框架保留多个竞争方程结构，用其分歧量化函数形式的结构不确定性，并扩展固定宽度 conformal 方法构建结构区间。在 LLM-SRBench 上的实验显示，标准 conformal 区间在分布内覆盖达标但外推时常失效，而新方法显著提升覆盖达成率且对其他符号回归方法具有泛化性。
正文 · 原文
Abstract:Large language models (LLMs) can help discover mathematical equations from data, but most LLM-guided symbolic regression methods focus on a single best equation without quantifying uncertainty over alternative functional forms. This is challenging because distinct equations can fit the observed data similarly while producing substantially different extrapolations. Our experiments on the LLM-SRBench dataset show that standard conformal intervals achieve nominal in-distribution coverage but frequently fail under extrapolation. To tackle this challenge, we introduce LLM-SR-UQ, a framework that retains competing equation structures and uses their disagreement to characterize uncertainty about the underlying functional form. We extend the standard fixed-width conformal approach to quantify structural intervals, which measure disagreement among candidate equations and identify where prediction intervals should widen. Extensive experiments show our framework substantially improves coverage attainment by incorporating structural disagreement while preserving in-distribution coverage. Our approach also shows good generalizability when it is applied to other symbolic-regression methods.
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2610.42024 [cs.LG] |
| (or arXiv:2610.42024v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.42024 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Mostafa Cham [view email]
[v1]
Fri, 30 Oct 2026 16:54:16 UTC (251 KB)
来源：arXiv cs.AI · arxiv.org