arXiv:2605.10685cs.AI2026-05

用基因编辑思想提升符号回归效率,让模型更聪明地演化公式。

GESR: A Genetic Programming-Based Symbolic Regression Method with Gene Editing

论文配图:GESR: A Genetic Programming-Based Symbolic Regression Method with Gene Editing
图 1 · 摘自论文原文
  • 引入BERT模型指导基因突变与交叉,替代传统随机演化
  • 在多个任务上计算效率显著优于经典遗传编程方法
  • 适合需要高效发现数学规律的科研与工程场景

数学公式是人类与自然沟通的语言。从科学数据中发现数学规律以描述自然现象,是人类数世纪以来的追求。在人工智能领域,这一挑战被称为符号回归问题。现有的符号回归方法中,基于进化算法的遗传编程(GP)是最经典且广泛使用的方法之一。GP通过基因突变和交叉模拟多代进化过程,但这些操作完全随机,虽能模拟自然演化,却不可避免产生有益与有害变异。若存在一个能预知哪些基因突变或交叉能带来更优结果的‘上帝’,并进行精准基因编辑,进化效率将大幅提升。受此启发,本文提出一种基于基因编辑的符号回归方法——GESR。在GESR中,我们训练了两个‘上帝之手’(两个BERT模型):第一个利用BERT的掩码语言建模能力引导基因(表达符号)的突变;第二个通过预测交叉点来引导个体基因的交叉。实验表明,GESR相比传统GP算法显著提升了计算效率,并在多个符号回归任务中表现出强劲的整体性能。

原文摘要 · Abstract (English)

Mathematical formulas serve as a language through which humans communicate with nature. Discovering mathematical laws from scientific data to describe natural phenomena has been a long-standing pursuit of humanity for centuries. In the field of artificial intelligence, this challenge is known as the symbolic regression problem. Among existing symbolic regression approaches, Genetic Programming (GP) based on evolutionary algorithms remains one of the most classical and widely adopted methods. GP simulates the evolutionary process across generations through genetic mutation and crossover. However, mutations and crossovers in GP are entirely random. While this randomness effectively mimics natural evolution, it inevitably produces both beneficial and detrimental variations. If there existed a metaphorical `God` capable of foreseeing which genetic mutations or crossovers would yield superior outcomes and performing targeted gene editing accordingly, the efficiency of evolution could be substantially improved. Motivated by this idea, we propose in this paper a symbolic regression approach based on gene editing, termed GESR. In GESR, we trained two "hands of God" (two BERT models). Among them, the first leverages the BERT's masked language modeling capability to guide the mutation of genes (expression symbols). The other BERT model guides the crossover of individual genes by predicting the crossover point. Experimental results demonstrate that GESR significantly improves computational efficiency compared with traditional GP algorithms and achieves strong overall performance across multiple symbolic regression tasks.

符号回归遗传编程BERT公式发现

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