UniSymNet: A Unified Symbolic Network Guided by Transformer
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910006977232896 |
|---|---|
| author | Li, Xinxin Zhang, Juan Li, Da Liu, Xingyu Xu, Jin Yin, Junping |
| author_facet | Li, Xinxin Zhang, Juan Li, Da Liu, Xingyu Xu, Jin Yin, Junping |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_06091 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | UniSymNet: A Unified Symbolic Network Guided by Transformer Li, Xinxin Zhang, Juan Li, Da Liu, Xingyu Xu, Jin Yin, Junping Machine Learning Artificial Intelligence Symbolic Computation 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. |
| title | UniSymNet: A Unified Symbolic Network Guided by Transformer |
| topic | Machine Learning Artificial Intelligence Symbolic Computation |
| url | https://arxiv.org/abs/2505.06091 |