# Iterated Agent for Symbolic Regression

arXiv: https://arxiv.org/abs/2510.08317 · HTML: https://mlsanity.com/paper/2510.08317/

## Key facts

- Cited by 3 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 22 of its 63 references that are in the map.
- First posted on arXiv 9 Oct 2025.

## Placed in

- LLM agents and tool use / [Web, search, and research agents](https://mlsanity.com/agents/web-search-and-research-agents/)

## Builds on (most cited first, 22 of 22)

- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (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)
- [Contemporary Symbolic Regression Methods and their Relative Performance](https://mlsanity.com/paper/2107.14351/) (2021)
- [End-to-end symbolic regression with transformers](https://mlsanity.com/paper/2204.10532/) (2022)
- [Neural Symbolic Regression that Scales](https://mlsanity.com/paper/2106.06427/) (2021)
- [AI Feynman 2.0: Pareto-optimal symbolic regression exploiting graph modularity](https://mlsanity.com/paper/2006.10782/) (2020)
- [PMLB: A Large Benchmark Suite for Machine Learning Evaluation and Comparison](https://mlsanity.com/paper/1703.00512/) (2017)
- [Extrapolation and learning equations](https://mlsanity.com/paper/1610.02995/) (2016)
- [Interpretable Scientific Discovery with Symbolic Regression: A Review](https://mlsanity.com/paper/2211.10873/) (2022)
- [Symbolic Regression via Neural-Guided Genetic Programming Population Seeding](https://mlsanity.com/paper/2111.00053/) (2021)
- [Bayesian Symbolic Regression](https://mlsanity.com/paper/1910.08892/) (2019)
- [The Illusion of Diminishing Returns: Measuring Long Horizon Execution in LLMs](https://mlsanity.com/paper/2509.09677/) (2025)
- [PHYBench: Holistic Evaluation of Physical Perception and Reasoning in Large Language Models](https://mlsanity.com/paper/2504.16074/) (2025)
- [Where are we now? A large benchmark study of recent symbolic regression methods](https://mlsanity.com/paper/1804.09331/) (2018)
- [Is the Machine Smarter than the Theorist: Deriving Formulas for Particle Kinematics with Symbolic Regression](https://mlsanity.com/paper/2211.08420/) (2022)
- [Symbolic Regression for Beyond the Standard Model Physics](https://mlsanity.com/paper/2405.18471/) (2024)
- [Scalable Quantum State Preparation via Large-Language-Model-Driven Discovery](https://mlsanity.com/paper/2505.06347/) (2025)
- [Improving Model-based Genetic Programming for Symbolic Regression of Small Expressions](https://mlsanity.com/paper/1904.02050/) (2019)
- [Interpretability in Symbolic Regression: a benchmark of Explanatory Methods using the Feynman data set](https://mlsanity.com/paper/2404.05908/) (2024)
- [SymbolFit: Automatic Parametric Modeling with Symbolic Regression](https://mlsanity.com/paper/2411.09851/) (2024)

## Built on by (most cited first, 3 of 3)

- [Autonomous Research Agents: A Survey of AI Scientists and the Verification Gap](https://mlsanity.com/paper/2608.05179/) (2026)
- [What Do Evolutionary Coding Agents Evolve?](https://mlsanity.com/paper/2605.20086/) (2026)
- [Where to Search: Measure the Prior-Structured Search Space of LLM Agents](https://mlsanity.com/paper/2510.14846/) (2025)

## Abstract (arXiv)

Symbolic regression (SR), the automated discovery of mathematical expressions from data, is a cornerstone of scientific inquiry. However, it is often hindered by the combinatorial explosion of the search space and a tendency to overfit. Popular methods, rooted in genetic programming, explore this space syntactically, often yielding overly complex, uninterpretable models. This paper introduces IdeaSearchFitter, a framework that employs Large Language Models (LLMs) as semantic operators within an evolutionary search. By generating candidate expressions guided by natural-language rationales, our method biases discovery towards models that are not only accurate but also conceptually coherent and interpretable. We demonstrate IdeaSearchFitter's efficacy across diverse challenges: it achieves competitive, noise-robust performance on the Feynman Symbolic Regression Database (FSReD), outperforming several strong baselines; discovers mechanistically aligned models with good accuracy-complexity trade-offs on real-world data; and derives compact, physically-motivated parametrizations for Parton Distribution Functions in a frontier high-energy physics application. IdeaSearchFitter is a specialized module within our broader iterated agent framework, IdeaSearch, which is publicly available at https://www.ideasearch.cn/.