# VaSST: Variational Inference for Symbolic Regression using Soft Symbolic Trees

arXiv: https://arxiv.org/abs/2602.23561 · HTML: https://mlsanity.com/paper/2602.23561/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 43 references that are in the map.
- First posted on arXiv 27 Feb 2026.

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

- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [DARTS: Differentiable Architecture Search](https://mlsanity.com/paper/1806.09055/) (2018)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Black Box Variational Inference](https://mlsanity.com/paper/1401.0118/) (2013)
- [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)
- [Automatic Differentiation Variational Inference](https://mlsanity.com/paper/1603.00788/) (2016)
- [Bayesian Symbolic Regression](https://mlsanity.com/paper/1910.08892/) (2019)
- [Symbolic Regression is NP-hard](https://mlsanity.com/paper/2207.01018/) (2022)
- [A Bayesian machine scientist to aid in the solution of challenging scientific problems](https://mlsanity.com/paper/2004.12157/) (2020)
- [An Approach to Symbolic Regression Using Feyn](https://mlsanity.com/paper/2104.05417/) (2021)
- [Black Box Variational Inference with a Deterministic Objective: Faster, More Accurate, and Even More Black Box](https://mlsanity.com/paper/2304.05527/) (2023)

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

- [Are you sure? A Comprehensive and Comprehensible Survey of Uncertainty Quantification in Symbolic Regression](https://mlsanity.com/paper/2606.06567/) (2026)

## Abstract (arXiv)

Symbolic regression (SR) has gained recent traction in AI-driven scientific discovery for learning closed-form physical laws. Yet existing methods are dominated by heuristic search or data-intensive approaches that often assume low-noise regimes and lack principled uncertainty quantification, while fully probabilistic SR formulations remain scarce. We introduce a scalable probabilistic framework for SR, VaSST, based on variational inference. VaSST uses soft symbolic trees, a continuous relaxation of symbolic expression trees in which discrete operator and feature assignments are replaced by probability distributions over allowable components. This transforms combinatorial symbolic search through an astronomically large expression space into efficient gradient-based optimization while preserving a coherent probabilistic interpretation. The learned soft representations induce posterior distributions over symbolic structures, enabling uncertainty quantification across plausible symbolic forms through posterior-aware symbolic model selection. On simulated experiments and the Feynman Symbolic Regression Database, VaSST achieves strong structural recovery and predictive accuracy compared to state-of-the-art competing SR methods.