2025/05/09 by Xinxin Li, Li, Xinxin, Juan Zhang +9
Computer Science · Materials Science · #Artificial Intelligence (cs.AI) #Evolutionary Algorithms and Applications #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning in Materials Science #Mathematics, Computing, and Information Processing #Symbolic Computation (cs.SC)
paper · pdf · doi:10.48550/arxiv.2505.06091
openalex publication_date 2025/05/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
Symbolic Regression (SR) is a powerful technique for automatically discovering mathematical expressions from input data. Mainstream SR algorithms search for the optimal symbolic tree in a vast function space, but the increasing complexity of the tree structure limits their performance. Inspired by neural networks, symbolic networks have emerged as a promising new paradigm. However, most existing symbolic networks still face certain challenges: binary nonlinear operators \×, ÷\ cannot be naturally extended to multivariate operators, and training with fixed architecture often leads to higher complexity and overfitting. In this work, we propose a Unified Symbolic Network that unifies nonlinear binary operators into nested unary operators and define the conditions under which UniSymNet can reduce complexity. Moreover, we pre-train a Transformer model with a novel label encoding method to guide structural selection, and adopt objective-specific optimization strategies to learn the parameters of the symbolic network. UniSymNet shows high fitting accuracy, excellent symbolic solution rate, and relatively low expression complexity, achieving competitive performance on low-dimensional Standard Benchmarks and high-dimensional SRBench.