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RISR advances symbolic regression by integrating residual error patterns into a language model framework to guide formula discovery and refine numerical equation recovery. This approach demonstrates improved accuracy on scientific tasks from LLM-SRBench, addressing limitations in traditional aggregate fit scores for structural search.
RISR: Residual-Informed Scientific Equation Discovery with Large Language Models
arXiv:2610.11387v1 Announce Type: cross Abstract: Symbolic regression combines structural search with numerical fitting, but aggregate fit scores do not describe how the remaining error varies across inputs. We introduce RISR, a residual-informed method that uses these error patterns to guide formula discovery and learn which corrections are worth fitting. A residual encoder compresses aligned inputs, targets, current predictions, and residuals into continuous tokens that condition a language model to propose formulas. For subsequent refinement, a dual-view relational encoder uses additive and regularized multiplicative residuals to predict the post-fit utility of candidate corrections. We evaluate RISR on scientific tasks from the LLM-SRBench. RISR achieves 63.57% and 38.50% ID accuracy at the 1% and 0.1% pointwise relative-error tolerances, respectively. The corresponding OOD accuracies are 56.07% and 38.24%. RISR outperforms the reported baselines using the same backbone. The results show that our residual-informed approach can improve numerical equation recovery.
Abstract:Symbolic regression combines structural search with numerical fitting, but aggregate fit scores do not describe how the remaining error varies across inputs. We introduce RISR, a residual-informed method that uses these error patterns to guide formula discovery and learn which corrections are worth fitting. A residual encoder compresses aligned inputs, targets, current predictions, and residuals into continuous tokens that condition a language model to propose formulas. For subsequent refinement, a dual-view relational encoder uses additive and regularized multiplicative residuals to predict the post-fit utility of candidate corrections. We evaluate RISR on scientific tasks from the LLM-SRBench. RISR achieves 63.57% and 38.50% ID accuracy at the 1% and 0.1% pointwise relative-error tolerances, respectively. The corresponding OOD accuracies are 56.07% and 38.24%. RISR outperforms the reported baselines using the same backbone. The results show that our residual-informed approach can improve numerical equation recovery.
Symbolic Computation (cs.SC); Artificial Intelligence (cs.AI)
arXiv:2610.11387 [cs.SC]
(or arXiv:2610.11387v1 [cs.SC] for this version)
https://doi.org/10.48550/arXiv.2610.11387 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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