# Parsing the Language of Expression: Enhancing Symbolic Regression with Domain-Aware Symbolic Priors

arXiv: https://arxiv.org/abs/2503.09592 · HTML: https://mlsanity.com/paper/2503.09592/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 36 references that are in the map.
- First posted on arXiv 12 Mar 2025.

## Builds on (most cited first, 17 of 17)

- [Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradients](https://mlsanity.com/paper/1912.04871/) (2019)
- [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)
- [Symbolic Regression via Neural-Guided Genetic Programming Population Seeding](https://mlsanity.com/paper/2111.00053/) (2021)
- [Transformer-based Planning for Symbolic Regression](https://mlsanity.com/paper/2303.06833/) (2023)
- [Bayesian Symbolic Regression](https://mlsanity.com/paper/1910.08892/) (2019)
- [Symbolic Physics Learner: Discovering governing equations via Monte Carlo tree search](https://mlsanity.com/paper/2205.13134/) (2022)
- [SymFormer: End-to-end symbolic regression using transformer-based architecture](https://mlsanity.com/paper/2205.15764/) (2022)
- [Deep symbolic regression for physics guided by units constraints: toward the automated discovery of physical laws](https://mlsanity.com/paper/2303.03192/) (2023)
- [Monotonic Calibrated Interpolated Look-Up Tables](https://mlsanity.com/paper/1505.06378/) (2015)
- [In-Context Symbolic Regression: Leveraging Large Language Models for Function Discovery](https://mlsanity.com/paper/2404.19094/) (2024)
- [Shape-constrained Symbolic Regression -- Improving Extrapolation with Prior Knowledge](https://mlsanity.com/paper/2103.15624/) (2021)
- [Finite Expression Method for Solving High-Dimensional Partial Differential Equations](https://mlsanity.com/paper/2206.10121/) (2022)
- [Controllable Neural Symbolic Regression](https://mlsanity.com/paper/2304.10336/) (2023)
- [Machine learning of Kondo physics using variational autoencoders and symbolic regression](https://mlsanity.com/paper/2107.08013/) (2021)
- [Incorporating domain knowledge into neural-guided search](https://mlsanity.com/paper/2107.09182/) (2021)
- [Complexity-Aware Deep Symbolic Regression with Robust Risk-Seeking Policy Gradients](https://mlsanity.com/paper/2406.06751/) (2024)

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

- [Aligning Perception, Reasoning, Modeling and Interaction: A Survey on Physical AI](https://mlsanity.com/paper/2510.04978/) (2025)

## Abstract (arXiv)

Symbolic regression is essential for deriving interpretable expressions that elucidate complex phenomena by exposing the underlying mathematical and physical relationships in data. In this paper, we present an advanced symbolic regression method that integrates symbol priors from diverse scientific domains - including physics, biology, chemistry, and engineering - into the regression process. By systematically analyzing domain-specific expressions, we derive probability distributions of symbols to guide expression generation. We propose novel tree-structured recurrent neural networks (RNNs) that leverage these symbol priors, enabling domain knowledge to steer the learning process. Additionally, we introduce a hierarchical tree structure for representing expressions, where unary and binary operators are organized to facilitate more efficient learning. To further accelerate training, we compile characteristic expression blocks from each domain and include them in the operator dictionary, providing relevant building blocks. Experimental results demonstrate that leveraging symbol priors significantly enhances the performance of symbolic regression, resulting in faster convergence and higher accuracy.