Equality Graph Assisted Symbolic Regression

TL;DR

This paper introduces SymRegg, a novel symbolic regression algorithm that leverages equality graphs to efficiently navigate search spaces, reduce redundant evaluations, and maintain high accuracy across datasets.

Contribution

It presents a new e-graph based search method for symbolic regression that improves efficiency and reduces redundant computations while preserving accuracy.

Findings

SymRegg reduces evaluation redundancy by up to 60%.

It maintains high accuracy across multiple datasets.

The method requires minimal hyperparameter tuning.

Abstract

In Symbolic Regression (SR), Genetic Programming (GP) is a popular search algorithm that delivers state-of-the-art results in term of accuracy. Its success relies on the concept of neutrality, which induces large plateaus that the search can safely navigate to more promising regions. Navigating these plateaus, while necessary, requires the computation of redundant expressions, up to 60% of the total number of evaluation, as noted in a recent study. The equality graph (e-graph) structure can compactly store and group equivalent expressions enabling us to verify if a given expression and their variations were already visited by the search, thus enabling us to avoid unnecessary computation. We propose a new search algorithm for symbolic regression called SymRegg that revolves around the e-graph structure following simple steps: perturb solutions sampled from a selection of expressions stored in the e-graph, if it generates an unvisited expression, insert it into the e-graph and generates its equivalent forms. We show that SymRegg is capable of improving the efficiency of the search, maintaining consistently accurate results across different datasets while requiring a choice of a minimalist set of hyperparameters.