Jingyi Liu , Weijun Li , Lina Yu , Min Wu , Wenqiang Li , Yanjie Li , Meilan Hao
{"title":"Mathematical expression exploration with graph representation and generative graph neural network","authors":"Jingyi Liu , Weijun Li , Lina Yu , Min Wu , Wenqiang Li , Yanjie Li , Meilan Hao","doi":"10.1016/j.neunet.2025.107405","DOIUrl":null,"url":null,"abstract":"<div><div>Symbolic Regression (SR) methods in tree representations have exhibited commendable outcomes across Genetic Programming (GP) and deep learning search paradigms. Nonetheless, the tree representation of mathematical expressions occasionally embodies redundant substructures. Representing expressions as computation graphs is more succinct and intuitive through graph representation. Despite its adoption in evolutionary strategies within SR, deep learning paradigms remain under-explored. Acknowledging the profound advancements of deep learning in tree-centric SR approaches, we advocate for addressing SR tasks using the Directed Acyclic Graph (DAG) representation of mathematical expressions, complemented by a generative graph neural network. We name the proposed method as <em><strong>Graph</strong>-based <strong>D</strong>eep <strong>S</strong>ymbolic <strong>R</strong>egression (GraphDSR)</em>. We vectorize node types and employ an adjacent matrix to delineate connections. The graph neural networks craft the DAG incrementally, sampling node types and graph connections conditioned on previous DAG at every step. During each sample step, the valid check is implemented to avoid meaningless sampling, and four domain-agnostic constraints are adopted to further streamline the search. This process culminates once a coherent expression emerges. Constants undergo optimization by SGD and BFGS algorithms, and rewards refine the graph neural network through reinforcement learning. A comprehensive evaluation across 110 benchmarks underscores the potency of our approach.</div></div>","PeriodicalId":49763,"journal":{"name":"Neural Networks","volume":"187 ","pages":"Article 107405"},"PeriodicalIF":6.0000,"publicationDate":"2025-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Neural Networks","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0893608025002849","RegionNum":1,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE","Score":null,"Total":0}
引用次数: 0
Abstract
Symbolic Regression (SR) methods in tree representations have exhibited commendable outcomes across Genetic Programming (GP) and deep learning search paradigms. Nonetheless, the tree representation of mathematical expressions occasionally embodies redundant substructures. Representing expressions as computation graphs is more succinct and intuitive through graph representation. Despite its adoption in evolutionary strategies within SR, deep learning paradigms remain under-explored. Acknowledging the profound advancements of deep learning in tree-centric SR approaches, we advocate for addressing SR tasks using the Directed Acyclic Graph (DAG) representation of mathematical expressions, complemented by a generative graph neural network. We name the proposed method as Graph-based Deep Symbolic Regression (GraphDSR). We vectorize node types and employ an adjacent matrix to delineate connections. The graph neural networks craft the DAG incrementally, sampling node types and graph connections conditioned on previous DAG at every step. During each sample step, the valid check is implemented to avoid meaningless sampling, and four domain-agnostic constraints are adopted to further streamline the search. This process culminates once a coherent expression emerges. Constants undergo optimization by SGD and BFGS algorithms, and rewards refine the graph neural network through reinforcement learning. A comprehensive evaluation across 110 benchmarks underscores the potency of our approach.
期刊介绍:
Neural Networks is a platform that aims to foster an international community of scholars and practitioners interested in neural networks, deep learning, and other approaches to artificial intelligence and machine learning. Our journal invites submissions covering various aspects of neural networks research, from computational neuroscience and cognitive modeling to mathematical analyses and engineering applications. By providing a forum for interdisciplinary discussions between biology and technology, we aim to encourage the development of biologically-inspired artificial intelligence.