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

arXiv: https://arxiv.org/abs/2608.04872 · HTML: https://mlsanity.com/paper/2608.04872/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in Web, search, and research agents, one of 16 directions in LLM agents and tool use.
- Builds on 19 of its 33 references that are in the map.
- First posted on arXiv 5 Aug 2026.

## Placed in

- LLM agents and tool use / [Web, search, and research agents](https://mlsanity.com/agents/web-search-and-research-agents/)
- Synthetic data and self-improvement for LLMs / [Self-evolving LLM agents](https://mlsanity.com/synth/self-evolving-llm-agents/)

## Builds on (most cited first, 19 of 19)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Generative Agents: Interactive Simulacra of Human Behavior](https://mlsanity.com/paper/2304.03442/) (2023)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [ToolLLM: Facilitating Large Language Models to Master 16000+ Real-world APIs](https://mlsanity.com/paper/2307.16789/) (2023)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Discovering Symbolic Models from Deep Learning with Inductive Biases](https://mlsanity.com/paper/2006.11287/) (2020)
- [Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradients](https://mlsanity.com/paper/1912.04871/) (2019)
- [Contemporary Symbolic Regression Methods and their Relative Performance](https://mlsanity.com/paper/2107.14351/) (2021)
- [Neural Symbolic Regression that Scales](https://mlsanity.com/paper/2106.06427/) (2021)
- [Symbolic Regression with a Learned Concept Library](https://mlsanity.com/paper/2409.09359/) (2024)
- [Rethinking Symbolic Regression Datasets and Benchmarks for Scientific Discovery](https://mlsanity.com/paper/2206.10540/) (2022)
- [Where are we now? A large benchmark study of recent symbolic regression methods](https://mlsanity.com/paper/1804.09331/) (2018)
- [Deliberate Evolution: Agentic Reasoning for Sample-Efficient Symbolic Regression with LLMs](https://mlsanity.com/paper/2606.04360/) (2026)

## Built on by (most cited first, 6 of 6)

- [MechBench: Can AI Scientific Agents Discover Mechanisms Beyond Phenomenal Laws?](https://mlsanity.com/paper/2609.35515/) (2026)
- [Se-DPO: Self-Evolving Token Credit for Direct Preference Optimization](https://mlsanity.com/paper/2608.09568/) (2026)
- [AutoSR: Automatic Symbolic Regression by Searching Research States](https://mlsanity.com/paper/2608.16876/) (2026)
- [SRHarness: A Harness for Agentic Symbolic Regression](https://mlsanity.com/paper/2609.35501/) (2026)
- [Learning to Design SR Solvers: Harness Optimization for Symbolic Regression](https://mlsanity.com/paper/2610.16966/) (2026)
- [Coupled Harness--Model Evolution for Scientific Equation Discovery](https://mlsanity.com/paper/2610.17740/) (2026)

## Abstract (arXiv)

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.