arXiv cs.AI· Mostafa Cham, Bayu Adhi Tama, Jianwu Wang·· 11 小时前AI 评分22
LLM-SR-UQ：面向 LLM 引导符号回归外推的结构不确定性量化框架
Know When the Equation Is Wrong: Structural Uncertainty for LLM-Guided Symbolic Regression under Extrapolation
AI 导读
研究团队提出 LLM-SR-UQ 框架，通过保留多个竞争方程结构并利用其分歧来刻画函数形式的不确定性。在 LLM-SRBench 数据集上，标准保形区间在分布内达到名义覆盖率，但在外推场景下频繁失效；该框架扩展固定宽度保形方法以量化结构区间，显著提升覆盖率并保持分布内覆盖。该方法应用于其他符号回归方法时也表现出良好泛化性。
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