UniSymNet: A Unified Symbolic Network Guided by Transformer

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Li, Xinxin, Zhang, Juan, Li, Da, Liu, Xingyu, Xu, Jin, Yin, Junping
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