# Graph-Eq: Discovering Mathematical Equations using Graph Generative Models

arXiv: https://arxiv.org/abs/2503.23617 · HTML: https://mlsanity.com/paper/2503.23617/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 28 references that are in the map.
- First posted on arXiv 30 Mar 2025.

## Builds on (most cited first, 18 of 18)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [MolGAN: An implicit generative model for small molecular graphs](https://mlsanity.com/paper/1805.11973/) (2018)
- [PDE-Net: Learning PDEs from Data](https://mlsanity.com/paper/1710.09668/) (2017)
- [Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradients](https://mlsanity.com/paper/1912.04871/) (2019)
- [Grammar Variational Autoencoder](https://mlsanity.com/paper/1703.01925/) (2017)
- [Deep Learning for Symbolic Mathematics](https://mlsanity.com/paper/1912.01412/) (2019)
- [Contemporary Symbolic Regression Methods and their Relative Performance](https://mlsanity.com/paper/2107.14351/) (2021)
- [Neural Symbolic Regression that Scales](https://mlsanity.com/paper/2106.06427/) (2021)
- [Learning Equations for Extrapolation and Control](https://mlsanity.com/paper/1806.07259/) (2018)
- [Extrapolation and learning equations](https://mlsanity.com/paper/1610.02995/) (2016)
- [SymbolicGPT: A Generative Transformer Model for Symbolic Regression](https://mlsanity.com/paper/2106.14131/) (2021)
- [D-VAE: A Variational Autoencoder for Directed Acyclic Graphs](https://mlsanity.com/paper/1904.11088/) (2019)
- [Symbolic Regression is NP-hard](https://mlsanity.com/paper/2207.01018/) (2022)
- [Deep Symbolic Regression for Recurrent Sequences](https://mlsanity.com/paper/2201.04600/) (2022)
- [PACE: A Parallelizable Computation Encoder for Directed Acyclic Graphs](https://mlsanity.com/paper/2203.10304/) (2022)
- [GINN-LP: A Growing Interpretable Neural Network for Discovering Multivariate Laurent Polynomial Equations](https://mlsanity.com/paper/2312.10913/) (2023)
- [GINN-KAN: Interpretability pipelining with applications in Physics Informed Neural Networks](https://mlsanity.com/paper/2408.14780/) (2024)

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

- [Learning the Geometry of Admissible Hypotheses through Inductive Bias in Training Distributions](https://mlsanity.com/paper/2608.31028/) (2026)

## Abstract (arXiv)

The ability to discover meaningful, accurate, and concise mathematical equations that describe datasets is valuable across various domains. Equations offer explicit relationships between variables, enabling deeper insights into underlying data patterns. Most existing equation discovery methods rely on genetic programming, which iteratively searches the equation space but is often slow and prone to overfitting. By representing equations as directed acyclic graphs, we leverage the use of graph neural networks to learn the underlying semantics of equations, and generate new, previously unseen equations. Although graph generative models have been shown to be successful in discovering new types of graphs in many fields, there application in discovering equations remains largely unexplored. In this work, we propose Graph-EQ, a deep graph generative model designed for efficient equation discovery. Graph-EQ uses a conditional variational autoencoder (CVAE) to learn a rich latent representation of the equation space by training it on a large corpus of equations in an unsupervised manner. Instead of directly searching the equation space, we employ Bayesian optimization to efficiently explore this learned latent space. We show that the encoder-decoder architecture of Graph-Eq is able to accurately reconstruct input equations. Moreover, we show that the learned latent representation can be sampled and decoded into valid equations, including new and previously unseen equations in the training data. Finally, we assess Graph-Eq's ability to discover equations that best fit a dataset by exploring the latent space using Bayesian optimization. Latent space exploration is done on 20 dataset with known ground-truth equations, and Graph-Eq is shown to successfully discover the grountruth equation in the majority of datasets.