Symbolic expression generation via Variational Auto-Encoder

TL;DR

This paper introduces a novel deep learning framework using Variational Auto-Encoder for symbolic expression generation, improving symbolic regression performance especially under noisy data conditions.

Contribution

The authors propose a VAE-based approach for symbolic regression that incorporates prior knowledge and outperforms existing methods in noisy environments.

Findings

Recovery rate of 65% on Nguyen dataset with 10% noise

Outperforms state-of-the-art by 20% under noisy conditions

Framework encodes prior knowledge to accelerate optimization

Abstract

There are many problems in physics, biology, and other natural sciences in which symbolic regression can provide valuable insights and discover new laws of nature. A widespread Deep Neural Networks do not provide interpretable solutions. Meanwhile, symbolic expressions give us a clear relation between observations and the target variable. However, at the moment, there is no dominant solution for the symbolic regression task, and we aim to reduce this gap with our algorithm. In this work, we propose a novel deep learning framework for symbolic expression generation via variational autoencoder (VAE). In a nutshell, we suggest using a VAE to generate mathematical expressions, and our training strategy forces generated formulas to fit a given dataset. Our framework allows encoding apriori knowledge of the formulas into fast-check predicates that speed up the optimization process. We compare our method to modern symbolic regression benchmarks and show that our method outperforms the competitors under noisy conditions. The recovery rate of SEGVAE is 65% on the Ngyuen dataset with a noise level of 10%, which is better than the previously reported SOTA by 20%. We demonstrate that this value depends on the dataset and can be even higher.