A-SR: Self-Evolving Agentic LLMs for Symbolic Regression via Hierarchical Coordination
Wenxiao Zhao, Dong Liu, Kaiyi Xu, Feng Liu, Zhen Zhao, Fei Ben, Shu Wang, Wenhao Li, Ying Nian Wu, Fenghua Ling, Haobo Li, Lei Bai
cs.CL, cs.AI, cs.LG
Submitted: 2026-08-05
Comments: 18 pages, 8 figures, including appendix
License: http://creativecommons.org/licenses/by/4.0/
The gist: Symbolic regression aims to discover closed-form equations from data, but existing LLM-guided methods often rely on a unified proposal loop that compresses heterogeneous search failures into a scalar
Terminology
Abstract
Symbolic regression aims to discover closed-form equations from data, but existing LLM-guided methods often rely on a unified proposal loop that compresses heterogeneous search failures into a scalar score and a single prompt. We propose A-SR, a self-evolving agentic framework that shifts the control unit from expression edits to role-conditioned evidence views. A-SR coordinates formula discovery through routing among coordination protocols, an online evaluator-reward role policy, and state-routed process memory. During search, evaluator feedback characterizes reliability and productivity, updates role-level utilities, and routes elite motifs, failure traces, and validity diagnostics to different agents. The framework self-evolves at two timescales: within a run, it adapts the search process without updating LLM parameters; across runs, recorded trajectories can be distilled into open-source LLMs as role-conditioned proposal priors. Averaged over the four LSR-Synth scientific domains in LLM-SRBench, A-SR improves Acc@0.01 over baselines from 25.79% to 48.30% with Llama3.1-8B, while A-SR-LoRA improves the corresponding Qwen3-4B result from 24.58% to 38.29%. On four real-world scientific discovery tasks, A-SR obtains the best in-distribution or out-of-distribution normalized mean squared error on 7 of 8 reported metrics.
Sources
- Program Synthesis with Large Language Models
- Evaluating Large Language Models Trained on Code
- Interpretable Machine Learning for Science with PySR and SymbolicRegression.jl
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