UniSymNet: A Unified Symbolic Network Guided by Transformer
This work provides an incremental improvement for researchers in symbolic regression by enhancing the efficiency and accuracy of discovering mathematical expressions from data.
The paper tackled the challenge of improving symbolic regression by addressing limitations in existing symbolic networks, such as handling multivariate operators and avoiding overfitting, and achieved competitive performance on both low- and high-dimensional benchmarks with high fitting accuracy and low expression complexity.
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 $\{\times, ÷\}$ 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.