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

Source

• Source name: arXiv
• Source kind: paper
• Authors / organization: Wenxiao Zhao, Dong Liu, Kaiyi Xu, Feng Liu, Zhen Zhao, Fei Ben, Shu Wang, Wenhao Li, Yingnian Wu, Fenghua Ling, Haobo Li, Lei Bai
• Venue: arXiv: cs.CL
• Published: 2026-08-05
• Collected: 2026-08-06
• URL: http://arxiv.org/abs/2608.04872v1
• PDF: https://arxiv.org/pdf/2608.04872v1
• DOI: UNKNOWN

Plain-Language Brief

A research paper introduces a new framework called A-SR for symbolic regression. A-SR is designed to discover closed-form equations from data and uses a self-evolving agentic system that coordinates formula discovery through routing among different agents and protocols. The system adapts its search process during a run without updating the Large Language Model (LLM) parameters and evolves across runs by recording trajectories which can be used to improve LLMs as proposal priors. A-SR improves accuracy in four scientific domains compared to baseline models when using Llama3.1-8B and Qwen3-4B LLMs.

What the Document Says

• The paper introduces a framework named A-SR for symbolic regression.
• 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.
• A-SR improves Acc@0.01 over baselines from 25.79% to 48.30% with Llama3.1-8B, and 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.

Key Concepts Mentioned

• symbolic regression
• Large Language Models (LLMs)
• A-SR framework
• coordination protocols
• evaluator-reward role policy
• state-routed process memory
• Acc@0.01
• Llama3.1-8B
• Qwen3-4B
• scientific domains
• normalized mean squared error

Claims Made by the Document

• A-SR improves Acc@0.01 over baselines.
• A-SR obtains the best in-distribution or out-of-distribution normalized mean squared error on various metrics.

Evidence Used

• Improvements in Acc@0.01 are given for Llama3.1-8B and A-SR-LoRA compared to baselines.
• Normalized mean squared error values are provided for A-SR on four real-world scientific discovery tasks.

Methods / Approach

UNKNOWN

Limitations Stated by the Authors

UNKNOWN

Limitations Noted by the Agent

Agent interpretation — not from the source.

UNKNOWN

Open Questions

UNKNOWN

Notes for Future Q&A

May include interpretation. Labeled where it does.

UNKNOWN

Raw Abstract / Excerpt

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.