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

2026-09-28

AI Summary

This study addresses the challenges of expression bloat and automated scientific discovery in symbolic regression by proposing a novel framework that integrates large language models (LLMs) with evolutionary algorithms. Methodologically, the LLM generates equation skeletons while coefficients are fitted independently, effectively decoupling structural search from parameter optimization. A multi-objective survival selection mechanism is introduced to balance accuracy against complexity, complemented by a substructure-guided strategy that reuses high-quality building blocks to accelerate evolutionary search. Experimental results demonstrate that the proposed approach achieves state-of-the-art accuracy across most scenarios on the LSR-Synth benchmark, significantly improving the recovery probability of highly accurate symbolic structures. Consequently, this work establishes an efficient paradigm for automated scientific discovery.

Abstract

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.

Problem

• Symbolic Regression
• Large Language Models
• Scientific Discovery
• Expression Bloating
• Structural Recovery

Innovation

• Symbolic Regression
• Large Language Models
• Multiobjective Optimization
• Substructure Guidance
• Equation Skeletons