# Scaling Up Unbiased Search-based Symbolic Regression

arXiv: https://arxiv.org/abs/2506.19626 · HTML: https://mlsanity.com/paper/2506.19626/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 42 references that are in the map.
- First posted on arXiv 24 Jun 2025.

## Builds on (most cited first, 14 of 14)

- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradients](https://mlsanity.com/paper/1912.04871/) (2019)
- [Contemporary Symbolic Regression Methods and their Relative Performance](https://mlsanity.com/paper/2107.14351/) (2021)
- [End-to-end symbolic regression with transformers](https://mlsanity.com/paper/2204.10532/) (2022)
- [AI Feynman 2.0: Pareto-optimal symbolic regression exploiting graph modularity](https://mlsanity.com/paper/2006.10782/) (2020)
- [Symbolic Regression via Neural-Guided Genetic Programming Population Seeding](https://mlsanity.com/paper/2111.00053/) (2021)
- [Bayesian Symbolic Regression](https://mlsanity.com/paper/1910.08892/) (2019)
- [AI Poincar'e: Machine Learning Conservation Laws from Trajectories](https://mlsanity.com/paper/2011.04698/) (2020)
- [A Bayesian machine scientist to aid in the solution of challenging scientific problems](https://mlsanity.com/paper/2004.12157/) (2020)
- [Epsilon-Lexicase Selection for Regression](https://mlsanity.com/paper/1905.13266/) (2019)
- [Machine-learning hidden symmetries](https://mlsanity.com/paper/2109.09721/) (2021)
- [A computational framework for physics-informed symbolic regression with straightforward integration of domain knowledge](https://mlsanity.com/paper/2209.06257/) (2022)
- [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)

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

- [Analyzing Generalization in Pre-Trained Symbolic Regression](https://mlsanity.com/paper/2509.19849/) (2025)
- [Data-driven discovery of governing differential equations across physical systems](https://mlsanity.com/paper/2606.09638/) (2026)
- [EGG-SR: Embedding Symbolic Equivalence into Symbolic Regression via Equality Graph](https://mlsanity.com/paper/2511.05849/) (2025)
- [ERBench: A Benchmark and Testsuite for Equation Discovery Algorithms](https://mlsanity.com/paper/2606.09276/) (2026)
- [EvoMO-SR: Multiobjective LLM-based Evolution of Symbolic Expressions with substructure guidance](https://mlsanity.com/paper/2609.36187/) (2026)

## Abstract (arXiv)

In a regression task, a function is learned from labeled data to predict the labels at new data points. The goal is to achieve small prediction errors. In symbolic regression, the goal is more ambitious, namely, to learn an interpretable function that makes small prediction errors. This additional goal largely rules out the standard approach used in regression, that is, reducing the learning problem to learning parameters of an expansion of basis functions by optimization. Instead, symbolic regression methods search for a good solution in a space of symbolic expressions. To cope with the typically vast search space, most symbolic regression methods make implicit, or sometimes even explicit, assumptions about its structure. Here, we argue that the only obvious structure of the search space is that it contains small expressions, that is, expressions that can be decomposed into a few subexpressions. We show that systematically searching spaces of small expressions finds solutions that are more accurate and more robust against noise than those obtained by state-of-the-art symbolic regression methods. In particular, systematic search outperforms state-of-the-art symbolic regressors in terms of its ability to recover the true underlying symbolic expressions on established benchmark data sets.