A-SR: Self-Evolving Agentic LLMs for Symbolic Regression via Hierarchical Coordination

2026-08-05

AI Summary

This work addresses the limitations of existing large language model (LLM)-guided symbolic regression methods, which often rely on a single proposal loop and struggle with heterogeneous search failures. To overcome this, we propose A-SR, a self-evolving agent framework that replaces conventional expression editing with a novel role-conditioned evidential view and introduces a dual-timescale self-evolution mechanism: dynamically adapting search strategies within a single run and distilling execution trajectories across rounds into role-conditioned priors for open-source LLMs. The framework integrates hierarchical agent coordination, state-routing memory, online evaluation feedback, and LoRA fine-tuning. Evaluated on LLM-SRBench across four scientific domains, our approach boosts Acc@0.01 from 25.79% to 48.30% using Llama3.1-8B and achieves state-of-the-art normalized mean squared error on seven out of eight real-world tasks.

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.

Problem

• symbolic regression
• LLM-guided methods
• heterogeneous search failures
• closed-form equations
• formula discovery

Innovation

• Symbolic Regression
• Agentic LLMs
• Self-Evolving Framework
• Hierarchical Coordination
• Role-Conditioned Reasoning