# Coupled Harness--Model Evolution for Scientific Equation Discovery

arXiv: https://arxiv.org/abs/2610.17740 · HTML: https://mlsanity.com/paper/2610.17740/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 28 of its 34 references that are in the map.
- First posted on arXiv 13 Oct 2026.

## Builds on (most cited first, 28 of 28)

- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [Voyager: An Open-Ended Embodied Agent with Large Language Models](https://mlsanity.com/paper/2305.16291/) (2023)
- [ToolLLM: Facilitating Large Language Models to Master 16000+ Real-world APIs](https://mlsanity.com/paper/2307.16789/) (2023)
- [Gorilla: Large Language Model Connected with Massive APIs](https://mlsanity.com/paper/2305.15334/) (2023)
- [AlphaEvolve: A coding agent for scientific and algorithmic discovery](https://mlsanity.com/paper/2506.13131/) (2025)
- [Automated Design of Agentic Systems](https://mlsanity.com/paper/2408.08435/) (2024)
- [ToolRL: Reward is All Tool Learning Needs](https://mlsanity.com/paper/2504.13958/) (2025)
- [Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradients](https://mlsanity.com/paper/1912.04871/) (2019)
- [Large Language Models as Tool Makers](https://mlsanity.com/paper/2305.17126/) (2023)
- [Tool Learning with Large Language Models: A Survey](https://mlsanity.com/paper/2405.17935/) (2024)
- [CRAFT: Customizing LLMs by Creating and Retrieving from Specialized Toolsets](https://mlsanity.com/paper/2309.17428/) (2023)
- [CREATOR: Tool Creation for Disentangling Abstract and Concrete Reasoning of Large Language Models](https://mlsanity.com/paper/2305.14318/) (2023)
- [Symbolic Regression with a Learned Concept Library](https://mlsanity.com/paper/2409.09359/) (2024)
- [TroVE: Inducing Verifiable and Efficient Toolboxes for Solving Programmatic Tasks](https://mlsanity.com/paper/2401.12869/) (2024)
- [LLM-SRBench: A New Benchmark for Scientific Equation Discovery with Large Language Models](https://mlsanity.com/paper/2504.10415/) (2025)
- [WebEvolver: Enhancing Web Agent Self-Improvement with Coevolving World Model](https://mlsanity.com/paper/2504.21024/) (2025)
- [LLM Agents Making Agent Tools](https://mlsanity.com/paper/2502.11705/) (2025)
- [Rethinking Symbolic Regression Datasets and Benchmarks for Scientific Discovery](https://mlsanity.com/paper/2206.10540/) (2022)
- [SR-Scientist: Scientific Equation Discovery With Agentic AI](https://mlsanity.com/paper/2510.11661/) (2025)
- [In-Context Symbolic Regression: Leveraging Large Language Models for Function Discovery](https://mlsanity.com/paper/2404.19094/) (2024)
- [EvoTool: Self-Evolving Tool-Use Policy Optimization in LLM Agents via Blame-Aware Mutation and Diversity-Aware Selection](https://mlsanity.com/paper/2603.04900/) (2026)
- [CoEvolve: Training LLM Agents via Agent-Data Mutual Evolution](https://mlsanity.com/paper/2604.15840/) (2026)
- [Think like a Scientist: Physics-guided LLM Agent for Equation Discovery](https://mlsanity.com/paper/2602.12259/) (2026)
- [EvoTrainer: Co-Evolving LLM Policies and Training Harnesses for Autonomous Agentic Reinforcement Learning](https://mlsanity.com/paper/2606.03108/) (2026)
- [Mem2Evolve: Towards Self-Evolving Agents via Co-Evolutionary Capability Expansion and Experience Distillation](https://mlsanity.com/paper/2604.10923/) (2026)
- [SEAL: Synergistic Co-Evolution of Agents and Learning Environments](https://mlsanity.com/paper/2605.24426/) (2026)
- [Skill Self-Play: Pushing the Frontier of LLM Capability with Co-Evolving Skills](https://mlsanity.com/paper/2607.22529/) (2026)
- [A-SR: Self-Evolving Agentic LLMs for Symbolic Regression via Hierarchical Coordination](https://mlsanity.com/paper/2608.04872/) (2026)

## Abstract (arXiv)

Large language models (LLMs) are increasingly used to discover scientific equations from experimental data. Such a discovery system has two parts that must work together: a library of executable computational tools and the model's tool-use policy. The tools supply the solving capability, from diagnosing structure in the data to fitting candidate equations; the policy plans and orchestrates their use. Yet existing systems adapt only one part, keeping either the toolset or the model fixed, which leaves the corresponding failures uncorrectable. We develop a coupled evolution framework that improves both parts from the same verifiable fit-error signal. In the tool-evolution phase, an agent grows an executable tool library from a small set of generic numerical operations by diagnosing its own failures: it authors a new tool when a capability is missing and revises its selection rules when the right tool went unused. In the policy-evolution phase, a small open model (roughly 3B active parameters) is fine-tuned on successful tool-use trajectories collected with the frozen library, on training formulas screened to be disjoint from all evaluation benchmarks. Ablations show the two phases are complementary: with no tool library at all the same model solves almost nothing, the tools account for most of the gain, and trajectory training adds a further gain that is largest on the most difficult problems. The full system solves 79.1/71.3% of LSR-Synth problems at fit tolerances 10-2/10-3, reaches 63.8% pooled accuracy on the distributionally different SRSD-Feynman panel, and obtains a normalized CP3-28 aggregate of -7.27. These results suggest a broader recipe for scientific agents: let the model and its instruments improve each other under verifiable feedback.