# Probabilistic Regular Tree Priors for Scientific Symbolic Reasoning

arXiv: https://arxiv.org/abs/2306.08506 · HTML: https://mlsanity.com/paper/2306.08506/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Knowledge- and tool-augmented reasoning, one of 17 directions in LLM reasoning.
- Builds on 17 of its 51 references that are in the map.
- First posted on arXiv 14 Jun 2023.

## Placed in

- LLM reasoning / [Knowledge- and tool-augmented reasoning](https://mlsanity.com/lr/knowledge-and-tool-augmented-reasoning/)

## 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)
- [Grammar Variational Autoencoder](https://mlsanity.com/paper/1703.01925/) (2017)
- [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)
- [Learning Equations for Extrapolation and Control](https://mlsanity.com/paper/1806.07259/) (2018)
- [AI Feynman 2.0: Pareto-optimal symbolic regression exploiting graph modularity](https://mlsanity.com/paper/2006.10782/) (2020)
- [SymbolicGPT: A Generative Transformer Model for Symbolic Regression](https://mlsanity.com/paper/2106.14131/) (2021)
- [Bayesian Symbolic Regression](https://mlsanity.com/paper/1910.08892/) (2019)
- [On scientific understanding with artificial intelligence](https://mlsanity.com/paper/2204.01467/) (2022)
- [A Bayesian machine scientist to aid in the solution of challenging scientific problems](https://mlsanity.com/paper/2004.12157/) (2020)
- [A-NICE-MC: Adversarial Training for MCMC](https://mlsanity.com/paper/1706.07561/) (2017)
- [Probabilistic Grammars for Equation Discovery](https://mlsanity.com/paper/2012.00428/) (2020)
- [TensorNetwork: A Library for Physics and Machine Learning](https://mlsanity.com/paper/1905.01330/) (2019)
- [Duality of Graphical Models and Tensor Networks](https://mlsanity.com/paper/1710.01437/) (2017)
- [Efficient Generator of Mathematical Expressions for Symbolic Regression](https://mlsanity.com/paper/2302.09893/) (2023)
- [Deep Involutive Generative Models for Neural MCMC](https://mlsanity.com/paper/2006.15167/) (2020)

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

- [Symbolic Density Estimation for Discrete Distributions](https://mlsanity.com/paper/2605.21813/) (2026)

## Abstract (arXiv)

Symbolic Regression (SR) allows for the discovery of scientific equations from data. To limit the large search space of possible equations, prior knowledge has been expressed in terms of formal grammars that characterize subsets of arbitrary strings. However, there is a mismatch between context-free grammars required to express the set of syntactically correct equations, missing closure properties of the former, and a tree structure of the latter. Our contributions are to (i) compactly express experts' prior beliefs about which equations are more likely to be expected by probabilistic Regular Tree Expressions (pRTE), and (ii) adapt Bayesian inference to make such priors efficiently available for symbolic regression encoded as finite state machines. Our scientific case studies show its effectiveness in soil science to find sorption isotherms and for modeling hyper-elastic materials.