LLM-SR-UQ：用候选方程分歧量化符号回归的外推不确定性
Know When the Equation Is Wrong: Structural Uncertainty for LLM-Guided Symbolic Regression under Extrapolation
LLM 帮你找公式时，多个候选方程吵起来反而是信号——这篇论文教你用分歧位置决定哪里该不信任预测。
LLM 引导的符号回归通常只输出单一最优方程，不同方程在拟合数据上接近、外推时却差异巨大。LLM-SR-UQ 保留多个竞争方程结构，用它们之间的分歧来刻画函数形式的不确定性。在 LLM-SRBench 数据集上，标准 conformal 区间虽然达到名义覆盖，但在外推场景经常失效。该框架将固定宽度 conformal 方法扩展为结构性区间，在候选方程分歧大的位置自动加宽预测区间，同时保持分布内覆盖，并可迁移到其他符号回归方法。
Know When the Equation Is Wrong: Structural Uncertainty for LLM-Guided Symbolic Regression under Extrapolation
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.