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.
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Publication details
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- Open access
- Green open access
Cite this article
APA 7
Li, H., Zhang, W., Zhao, W., Jung, E., Sheng, R., Sun, Y., Zhuang, P., Chen, H., & Ling, F. (2026). RISR: Residual-Informed Scientific Equation Discovery with Large Language Models. https://omanscience.com/en/articles/risr-residual-informed-scientific-equation-discovery-with-large-language-models
MLA 9
Li, Haobo, et al. "RISR: Residual-Informed Scientific Equation Discovery with Large Language Models." https://omanscience.com/en/articles/risr-residual-informed-scientific-equation-discovery-with-large-language-models.
Chicago (author–date)
Li, Haobo, Wenshuo Zhang, Wenxiao Zhao, Eunseo Jung, Rui Sheng, Yushi Sun, Peiqin Zhuang, Hao Chen, and Fenghua Ling. 2026. "RISR: Residual-Informed Scientific Equation Discovery with Large Language Models." https://omanscience.com/en/articles/risr-residual-informed-scientific-equation-discovery-with-large-language-models.
Harvard
Li, H., Zhang, W., Zhao, W., Jung, E., Sheng, R., Sun, Y., Zhuang, P., Chen, H. and Ling, F. (2026) 'RISR: Residual-Informed Scientific Equation Discovery with Large Language Models', Available at: https://omanscience.com/en/articles/risr-residual-informed-scientific-equation-discovery-with-large-language-models.
Vancouver
Li H, Zhang W, Zhao W, Jung E, Sheng R, Sun Y, et al. RISR: Residual-Informed Scientific Equation Discovery with Large Language Models. https://omanscience.com/en/articles/risr-residual-informed-scientific-equation-discovery-with-large-language-models
IEEE
H. Li, W. Zhang, W. Zhao, E. Jung, R. Sheng, Y. Sun, P. Zhuang, H. Chen, and F. Ling, "RISR: Residual-Informed Scientific Equation Discovery with Large Language Models," https://omanscience.com/en/articles/risr-residual-informed-scientific-equation-discovery-with-large-language-models.