Scalable Neural Symbolic Regression using Control Variables

TL;DR

ScaleSR introduces a scalable approach to symbolic regression by decomposing multi-variable problems into single-variable tasks using control variables, significantly improving accuracy and efficiency on benchmark datasets.

Contribution

The paper presents ScaleSR, a novel method that leverages control variables and a bottom-up approach to enhance scalability in multi-variable symbolic regression.

Findings

Outperforms state-of-the-art baselines in accuracy

Reduces search space for symbolic regression

Effective on multiple benchmark datasets

Abstract

Symbolic regression (SR) is a powerful technique for discovering the analytical mathematical expression from data, finding various applications in natural sciences due to its good interpretability of results. However, existing methods face scalability issues when dealing with complex equations involving multiple variables. To address this challenge, we propose ScaleSR, a scalable symbolic regression model that leverages control variables to enhance both accuracy and scalability. The core idea is to decompose multi-variable symbolic regression into a set of single-variable SR problems, which are then combined in a bottom-up manner. The proposed method involves a four-step process. First, we learn a data generator from observed data using deep neural networks (DNNs). Second, the data generator is used to generate samples for a certain variable by controlling the input variables. Thirdly, single-variable symbolic regression is applied to estimate the corresponding mathematical expression. Lastly, we repeat steps 2 and 3 by gradually adding variables one by one until completion. We evaluate the performance of our method on multiple benchmark datasets. Experimental results demonstrate that the proposed ScaleSR significantly outperforms state-of-the-art baselines in discovering mathematical expressions with multiple variables. Moreover, it can substantially reduce the search space for symbolic regression. The source code will be made publicly available upon publication.