# Equality Graph Assisted Symbolic Regression

arXiv: https://arxiv.org/abs/2511.01009 · HTML: https://mlsanity.com/paper/2511.01009/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 33 references that are in the map.
- First posted on arXiv 2 Nov 2025.

## Builds on (most cited first, 8 of 8)

- [Contemporary Symbolic Regression Methods and their Relative Performance](https://mlsanity.com/paper/2107.14351/) (2021)
- [A Bayesian machine scientist to aid in the solution of challenging scientific problems](https://mlsanity.com/paper/2004.12157/) (2020)
- [Shape-constrained Symbolic Regression -- Improving Extrapolation with Prior Knowledge](https://mlsanity.com/paper/2103.15624/) (2021)
- [Symbolic Regression by Exhaustive Search: Reducing the Search Space Using Syntactical Constraints and Efficient Semantic Structure Deduplication](https://mlsanity.com/paper/2109.13895/) (2021)
- [The Inefficiency of Genetic Programming for Symbolic Regression](https://mlsanity.com/paper/2404.17292/) (2024)
- [Improving Genetic Programming for Symbolic Regression with Equality Graphs](https://mlsanity.com/paper/2501.17848/) (2025)
- [Multi-View Symbolic Regression](https://mlsanity.com/paper/2402.04298/) (2024)
- [Unit-Aware Genetic Programming for the Development of Empirical Equations](https://mlsanity.com/paper/2405.18896/) (2024)

## Built on by (most cited first, 1 of 1)

- [EGG-SR: Embedding Symbolic Equivalence into Symbolic Regression via Equality Graph](https://mlsanity.com/paper/2511.05849/) (2025)

## Abstract (arXiv)

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.