# Racing Control Variable Genetic Programming for Symbolic Regression

arXiv: https://arxiv.org/abs/2309.07934 · HTML: https://mlsanity.com/paper/2309.07934/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 54 references that are in the map.
- First posted on arXiv 13 Sep 2023.

## Builds on (most cited first, 17 of 17)

- [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)
- [Neural Symbolic Regression that Scales](https://mlsanity.com/paper/2106.06427/) (2021)
- [Learning to Branch](https://mlsanity.com/paper/1803.10150/) (2018)
- [Symbolic Regression is NP-hard](https://mlsanity.com/paper/2207.01018/) (2022)
- [Symbolic Physics Learner: Discovering governing equations via Monte Carlo tree search](https://mlsanity.com/paper/2205.13134/) (2022)
- [A Bayesian machine scientist to aid in the solution of challenging scientific problems](https://mlsanity.com/paper/2004.12157/) (2020)
- [Monte Carlo Tree Search based Variable Selection for High Dimensional Bayesian Optimization](https://mlsanity.com/paper/2210.01628/) (2022)
- [Neural Program Synthesis with Priority Queue Training](https://mlsanity.com/paper/1801.03526/) (2018)
- [Taylor Genetic Programming for Symbolic Regression](https://mlsanity.com/paper/2205.09751/) (2022)
- [GSR: A Generalized Symbolic Regression Approach](https://mlsanity.com/paper/2205.15569/) (2022)
- [Elite Bases Regression: A Real-time Algorithm for Symbolic Regression](https://mlsanity.com/paper/1704.07313/) (2017)
- [Symbolic Regression via Control Variable Genetic Programming](https://mlsanity.com/paper/2306.08057/) (2023)
- [Learning Variable Ordering Heuristics for Solving Constraint Satisfaction Problems](https://mlsanity.com/paper/1912.10762/) (2019)
- [Neural-Network-Directed Genetic Programmer for Discovery of Governing Equations](https://mlsanity.com/paper/2203.08808/) (2022)

## Built on by (most cited first, 4 of 4)

- [Knowledge Integration for Physics-informed Symbolic Regression Using Pre-trained Large Language Models](https://mlsanity.com/paper/2509.03036/) (2025)
- [LLM-Meta-SR: In-Context Learning for Evolving Selection Operators in Symbolic Regression](https://mlsanity.com/paper/2505.18602/) (2025)
- [Prompting Neural-Guided Equation Discovery Based on Residuals](https://mlsanity.com/paper/2511.05586/) (2025)
- [Discovering Multiscale Deep Formulas in Complex Systems via Neural-Guided Lambda Calculus](https://mlsanity.com/paper/2606.07426/) (2026)

## Abstract (arXiv)

Symbolic regression, as one of the most crucial tasks in AI for science, discovers governing equations from experimental data. Popular approaches based on genetic programming, Monte Carlo tree search, or deep reinforcement learning learn symbolic regression from a fixed dataset. They require massive datasets and long training time especially when learning complex equations involving many variables. Recently, Control Variable Genetic Programming (CVGP) has been introduced which accelerates the regression process by discovering equations from designed control variable experiments. However, the set of experiments is fixed a-priori in CVGP and we observe that sub-optimal selection of experiment schedules delay the discovery process significantly. To overcome this limitation, we propose Racing Control Variable Genetic Programming (Racing-CVGP), which carries out multiple experiment schedules simultaneously. A selection scheme similar to that used in selecting good symbolic equations in the genetic programming process is implemented to ensure that promising experiment schedules eventually win over the average ones. The unfavorable schedules are terminated early to save time for the promising ones. We evaluate Racing-CVGP on several synthetic and real-world datasets corresponding to true physics laws. We demonstrate that Racing-CVGP outperforms CVGP and a series of symbolic regressors which discover equations from fixed datasets.