A Neural-Guided Dynamic Symbolic Network for Exploring Mathematical Expressions from Data

TL;DR

DySymNet introduces a neural-guided dynamic symbolic network that efficiently explores structured symbolic models for data-driven mathematical expression discovery, outperforming existing deep learning-based symbolic regression methods especially in high-dimensional problems.

Contribution

It proposes a novel reinforcement learning-guided approach to explore symbolic network structures, improving scalability and accuracy in symbolic regression tasks.

Findings

Outperforms baseline models on standard benchmarks

Effective in high-dimensional symbolic regression problems

Open source implementation available

Abstract

Symbolic regression (SR) is a powerful technique for discovering the underlying mathematical expressions from observed data. Inspired by the success of deep learning, recent deep generative SR methods have shown promising results. However, these methods face difficulties in processing high-dimensional problems and learning constants due to the large search space, and they don't scale well to unseen problems. In this work, we propose DySymNet, a novel neural-guided Dynamic Symbolic Network for SR. Instead of searching for expressions within a large search space, we explore symbolic networks with various structures, guided by reinforcement learning, and optimize them to identify expressions that better-fitting the data. Based on extensive numerical experiments on low-dimensional public standard benchmarks and the well-known SRBench with more variables, DySymNet shows clear superiority over several representative baseline models. Open source code is available at https://github.com/AILWQ/DySymNet.