# GFN-SR: Symbolic Regression with Generative Flow Networks

arXiv: https://arxiv.org/abs/2312.00396 · HTML: https://mlsanity.com/paper/2312.00396/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 22 references that are in the map.
- First posted on arXiv 1 Dec 2023.

## Builds on (most cited first, 13 of 13)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Flow Network based Generative Models for Non-Iterative Diverse Candidate Generation](https://mlsanity.com/paper/2106.04399/) (2021)
- [Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradients](https://mlsanity.com/paper/1912.04871/) (2019)
- [GFlowNet Foundations](https://mlsanity.com/paper/2111.09266/) (2021)
- [Trajectory balance: Improved credit assignment in GFlowNets](https://mlsanity.com/paper/2201.13259/) (2022)
- [Contemporary Symbolic Regression Methods and their Relative Performance](https://mlsanity.com/paper/2107.14351/) (2021)
- [AI Feynman 2.0: Pareto-optimal symbolic regression exploiting graph modularity](https://mlsanity.com/paper/2006.10782/) (2020)
- [The Optimal Reward Baseline for Gradient-Based Reinforcement Learning](https://mlsanity.com/paper/1301.2315/) (2013)
- [Bayesian Symbolic Regression](https://mlsanity.com/paper/1910.08892/) (2019)
- [Symbolic Regression is NP-hard](https://mlsanity.com/paper/2207.01018/) (2022)
- [Deep symbolic regression for physics guided by units constraints: toward the automated discovery of physical laws](https://mlsanity.com/paper/2303.03192/) (2023)
- [Recovering Quantitative Models of Human Information Processing with Differentiable Architecture Search](https://mlsanity.com/paper/2103.13939/) (2021)

## Built on by (most cited first, 6 of 6)

- [Hybrid-Balance GFlowNet for Solving Vehicle Routing Problems](https://mlsanity.com/paper/2510.04792/) (2025)
- [Streaming Bayes GFlowNets](https://mlsanity.com/paper/2411.05899/) (2024)
- [Generalizing the SINDy approach with nested neural networks](https://mlsanity.com/paper/2404.15742/) (2024)
- [Flow of Spans: Generalizing Language Models to Dynamic Span-Vocabulary via GFlowNets](https://mlsanity.com/paper/2602.10583/) (2026)
- [Bayesian Symbolic Regression with Entropic Reinforcement Learning](https://mlsanity.com/paper/2608.09617/) (2026)
- [Learning a Mixture of GFlowNets](https://mlsanity.com/paper/2610.07562/) (2026)

## Abstract (arXiv)

Symbolic regression (SR) is an area of interpretable machine learning that aims to identify mathematical expressions, often composed of simple functions, that best fit in a given set of covariates X and response y. In recent years, deep symbolic regression (DSR) has emerged as a popular method in the field by leveraging deep reinforcement learning to solve the complicated combinatorial search problem. In this work, we propose an alternative framework (GFN-SR) to approach SR with deep learning. We model the construction of an expression tree as traversing through a directed acyclic graph (DAG) so that GFlowNet can learn a stochastic policy to generate such trees sequentially. Enhanced with an adaptive reward baseline, our method is capable of generating a diverse set of best-fitting expressions. Notably, we observe that GFN-SR outperforms other SR algorithms in noisy data regimes, owing to its ability to learn a distribution of rewards over a space of candidate solutions.