# EvoMO-SR: Multiobjective LLM-based Evolution of Symbolic Expressions with substructure guidance

arXiv: https://arxiv.org/abs/2609.36187 · HTML: https://mlsanity.com/paper/2609.36187/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 27 references that are in the map.
- First posted on arXiv 28 Sep 2026.

## Builds on (most cited first, 17 of 17)

- [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)
- [LLM-SR: Scientific Equation Discovery via Programming with Large Language Models](https://mlsanity.com/paper/2404.18400/) (2024)
- [Interpretable Scientific Discovery with Symbolic Regression: A Review](https://mlsanity.com/paper/2211.10873/) (2022)
- [From Automation to Autonomy: A Survey on Large Language Models in Scientific Discovery](https://mlsanity.com/paper/2505.13259/) (2025)
- [Symbolic Regression with a Learned Concept Library](https://mlsanity.com/paper/2409.09359/) (2024)
- [LLM-SRBench: A New Benchmark for Scientific Equation Discovery with Large Language Models](https://mlsanity.com/paper/2504.10415/) (2025)
- [AI4Research: A Survey of Artificial Intelligence for Scientific Research](https://mlsanity.com/paper/2507.01903/) (2025)
- [Evaluating Large Language Models in Scientific Discovery](https://mlsanity.com/paper/2512.15567/) (2025)
- [Deep Generative Symbolic Regression with Monte-Carlo-Tree-Search](https://mlsanity.com/paper/2302.11223/) (2023)
- [Towards Scientific Discovery with Generative AI: Progress, Opportunities, and Challenges](https://mlsanity.com/paper/2412.11427/) (2024)
- [DrSR: LLM based Scientific Equation Discovery with Dual Reasoning from Data and Experience](https://mlsanity.com/paper/2506.04282/) (2025)
- [Call for Action: towards the next generation of symbolic regression benchmark](https://mlsanity.com/paper/2505.03977/) (2025)
- [Role Prompting Guided Domain Adaptation with General Capability Preserve for Large Language Models](https://mlsanity.com/paper/2403.02756/) (2024)
- [CoEvo: Continual Evolution of Symbolic Solutions Using Large Language Models](https://mlsanity.com/paper/2412.18890/) (2024)
- [LLM-Meta-SR: In-Context Learning for Evolving Selection Operators in Symbolic Regression](https://mlsanity.com/paper/2505.18602/) (2025)
- [Scaling Up Unbiased Search-based Symbolic Regression](https://mlsanity.com/paper/2506.19626/) (2025)

## Abstract (arXiv)

Symbolic Regression (SR) is a data-driven method for scientific discovery which searches for interpretable analytical relationships within data. Recently, Large Language Models (LLMs) have also had a significant impact on scientific discovery, enabling the automation of various stages of the process. For these reasons, the possibility of harnessing the embedded scientific knowledge and programming capabilities of LLMs to solve SR tasks has emerged, showing promising performance compared with traditional methods. We propose EvoMO-SR, a novel LLM-driven SR framework in which the LLM generates equation skeletons, with their coefficients fitted separately by an external optimizer. The framework includes a multi-objective survival selection which controls bloating by balancing accuracy and complexity, and a substructure guidance mechanism which mutates expressions with candidate reusable building blocks. EvoMO-SR achieves the best accuracy in seven of the eight in-domain and out-of-domain settings for LSR-Synth, using a small LLM model, i.e., Llama-3.1-8B-Instruct. We also evaluated structural recovery through two symbolic accuracy metrics based on canonicalized subtree overlap and term matching, showing that our method has a greater probability of recovering highly accurate symbolic structures.