# Deep Variational Inference Symbolic Regression

arXiv: https://arxiv.org/abs/2605.01067 · HTML: https://mlsanity.com/paper/2605.01067/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 29 references that are in the map.
- First posted on arXiv 1 May 2026.

## Builds on (most cited first, 19 of 19)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [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)
- [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)
- [Integration of Neural Network-Based Symbolic Regression in Deep Learning for Scientific Discovery](https://mlsanity.com/paper/1912.04825/) (2019)
- [Symbolic Regression with a Learned Concept Library](https://mlsanity.com/paper/2409.09359/) (2024)
- [Transformer-based Planning for Symbolic Regression](https://mlsanity.com/paper/2303.06833/) (2023)
- [Bayesian Symbolic Regression](https://mlsanity.com/paper/1910.08892/) (2019)
- [A Bayesian machine scientist to aid in the solution of challenging scientific problems](https://mlsanity.com/paper/2004.12157/) (2020)
- [Deep Generative Symbolic Regression](https://mlsanity.com/paper/2401.00282/) (2023)
- [Deep Learning and Symbolic Regression for Discovering Parametric Equations](https://mlsanity.com/paper/2207.00529/) (2022)
- [Bayesian polynomial neural networks and polynomial neural ordinary differential equations](https://mlsanity.com/paper/2308.10892/) (2023)
- [Flexible Bayesian Nonlinear Model Configuration](https://mlsanity.com/paper/2003.02929/) (2020)
- [Symbolic expression generation via Variational Auto-Encoder](https://mlsanity.com/paper/2301.06064/) (2023)
- [Complexity-Aware Deep Symbolic Regression with Robust Risk-Seeking Policy Gradients](https://mlsanity.com/paper/2406.06751/) (2024)

## Abstract (arXiv)

Symbolic regression discovers explicit, interpretable equations without assuming a functional form in advance. A Bayesian approach strengthens this through probability distributions over candidate expressions, thus quantifying uncertainty in the presence of noisy and limited data. Deep Symbolic Regression (DSR) uses a neural network to generate symbolic expressions, but it is designed to identify a single best-fitting expression rather than infer a posterior distribution over models. We introduce Deep Variational Inference Symbolic Regression (DVISR), a variational Bayesian extension of DSR. DVISR replaces the original reward with the integrand of the evidence lower bound. It also extends the network architecture to output distributions over constants within expressions, enabling posterior inference over both expression trees and their associated constants. We show that DVISR can recover the true posterior in simple settings, both with and without constant tokens, and we examine how its performance changes as the size of the expression space increases. These results position DVISR as a step toward scalable Bayesian symbolic regression with uncertainty over full symbolic models.