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The paper addresses a practical gap in LLM-guided symbolic regression: these methods usually return one equation with no sense of how much the functional form itself could vary. The authors report that standard conformal intervals keep nominal coverage in-distribution but often undercover under extrapolation, and they propose structural intervals based on disagreement among competing candidate equations. Readers should note that the evidence rests on LLM-SRBench and the gains are reported as "substantial" without the abstract giving specific numbers, so the magnitude and robustness of the improvement need checking in the full paper.
Know When the Equation Is Wrong: Structural Uncertainty for LLM-Guided Symbolic Regression under Extrapolation
arXiv:2610.42024v1 Announce Type: new 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.
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.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
arXiv:2610.42024 [cs.LG]
(or arXiv:2610.42024v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.42024 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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