# Hash-Based Tree Similarity and Simplification in Genetic Programming for Symbolic Regression

arXiv: https://arxiv.org/abs/2107.10640 · HTML: https://mlsanity.com/paper/2107.10640/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 0 of its 13 references that are in the map.
- First posted on arXiv 22 Jul 2021.

## Built on by (most cited first, 5 of 5)

- [Exhaustive Symbolic Regression](https://mlsanity.com/paper/2211.11461/) (2022)
- [Symbolic Regression by Exhaustive Search: Reducing the Search Space Using Syntactical Constraints and Efficient Semantic Structure Deduplication](https://mlsanity.com/paper/2109.13895/) (2021)
- [Improving Genetic Programming for Symbolic Regression with Equality Graphs](https://mlsanity.com/paper/2501.17848/) (2025)
- [Inexact Simplification of Symbolic Regression Expressions with Locality-sensitive Hashing](https://mlsanity.com/paper/2404.05898/) (2024)
- [Evaluation of Population Initialization Methods for Genetic Programming-based Symbolic Regression](https://mlsanity.com/paper/2606.31990/) (2026)

## Abstract (arXiv)

We introduce in this paper a runtime-efficient tree hashing algorithm for the identification of isomorphic subtrees, with two important applications in genetic programming for symbolic regression: fast, online calculation of population diversity and algebraic simplification of symbolic expression trees. Based on this hashing approach, we propose a simple diversity-preservation mechanism with promising results on a collection of symbolic regression benchmark problems.