Mathematical expression exploration with graph representation and generative graph neural network

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@Article{Liu:2025:neunet,

• author = "Jingyi Liu and Weijun Li and Lina Yu and Min Wu and Wenqiang Li and Yanjie Li and Meilan Hao",
• title = "Mathematical expression exploration with graph representation and generative graph neural network",
• journal = "Neural Networks",
• year = "2025",
• volume = "187",
• pages = "107405",
• keywords = "genetic algorithms, genetic programming, Symbolic regression, Directed acyclic graph, Graph neural network, ANN, Reinforcement learning",
• ISSN = "0893-6080",
• URL = "https://www.sciencedirect.com/science/article/pii/S0893608025002849",
• DOI = "doi:10.1016/j.neunet.2025.107405",
• 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 optimisation 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",

}

Genetic Programming entries for Jingyi Liu Weijun Li Lina Yu Min Wu Wenqiang Li Yanjie Li Meilan Hao

Citations