Equality Graph Assisted Symbolic Regression

2025-11-02

AI Summary

In symbolic regression, genetic programming (GP) suffers from severe search inefficiency due to neutrality—up to 60% of expression evaluations are redundant. To address this, we propose SymRegg, the first symbolic regression algorithm systematically integrating equality graphs (e-graphs): it compactly represents and incrementally maintains sets of equivalent expressions to eliminate redundant evaluation, and employs lightweight perturbation and selection strategies for efficient exploration of the expression space. SymRegg achieves GP-level modeling accuracy while reducing expression redundancy by up to 60%, significantly improving search efficiency. It exhibits strong expression preservation, minimal hyperparameters (only population size and number of iterations), and robust generalization across diverse datasets. Extensive experiments on multiple benchmarks demonstrate that SymRegg simultaneously attains high predictive accuracy and low computational overhead.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Cognitive Modeling & Cognitive Systems: Symbolic Representations
• Machine Learning: Graph-based Machine Learning

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

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.

Problem

• Reducing redundant expression evaluations in symbolic regression
• Using equality graphs to compactly store equivalent expressions
• Improving search efficiency while maintaining accuracy across datasets

Innovation

• Equality graph compactly stores equivalent expressions
• SymRegg algorithm perturbs solutions from e-graph
• Avoids redundant computations by tracking visited expressions