# Symbolic Regression for Shared Expressions: Introducing Partial Parameter Sharing

arXiv: https://arxiv.org/abs/2601.04051 · HTML: https://mlsanity.com/paper/2601.04051/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 29 references that are in the map.
- First posted on arXiv 7 Jan 2026.

## Builds on (most cited first, 15 of 15)

- [Discovering Symbolic Models from Deep Learning with Inductive Biases](https://mlsanity.com/paper/2006.11287/) (2020)
- [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)
- [Neural Symbolic Regression that Scales](https://mlsanity.com/paper/2106.06427/) (2021)
- [SymbolicGPT: A Generative Transformer Model for Symbolic Regression](https://mlsanity.com/paper/2106.14131/) (2021)
- [Rediscovering orbital mechanics with machine learning](https://mlsanity.com/paper/2202.02306/) (2022)
- [Exhaustive Symbolic Regression](https://mlsanity.com/paper/2211.11461/) (2022)
- [Analytical Modelling of Exoplanet Transit Specroscopy with Dimensional Analysis and Symbolic Regression](https://mlsanity.com/paper/2112.11600/) (2021)
- [Call for Action: towards the next generation of symbolic regression benchmark](https://mlsanity.com/paper/2505.03977/) (2025)
- [Predicting Friction System Performance with Symbolic Regression and Genetic Programming with Factor Variables](https://mlsanity.com/paper/2107.09484/) (2021)
- [Class Symbolic Regression: Gotta Fit 'Em All](https://mlsanity.com/paper/2312.01816/) (2023)
- [Improving Genetic Programming for Symbolic Regression with Equality Graphs](https://mlsanity.com/paper/2501.17848/) (2025)
- [Introducing Thermodynamics-Informed Symbolic Regression -- A Tool for Thermodynamic Equations of State Development](https://mlsanity.com/paper/2309.02805/) (2023)
- [Alpha Zero for Physics: Application of Symbolic Regression with Alpha Zero to find the analytical methods in physics](https://mlsanity.com/paper/2311.12713/) (2023)
- [A Search for the Underlying Equation Governing Similar Systems](https://mlsanity.com/paper/1908.10673/) (2019)

## Abstract (arXiv)

Symbolic regression aims to find symbolic expressions that describe datasets. Due to its inherent interpretability, symbolic regression (SR) is a powerful paradigm for scientific discovery. Recent advances have expanded SR to describe related phenomena using a single expression with varying sets of parameters, thereby introducing a single categorical variable. To illustrate, this enables the search for a single expression describing temperaturedependent viscosity across multiple fluids, while simultaneously identifying a distinct set of fluid-specific parameters. We expand upon prior efforts by considering multiple categorical variables and introducing intermediate levels of parameter sharing. Rather than parameters being either entirely universal or entirely unique, some parameters can also be shared across specific categories while remaining distinct for others. This allows for separating universal effects (shared parameters), category-specific trends (partially-shared parameters), and category interactions (non-shared parameters). We test the limits of this setup in terms of reducing data requirements and transfer learning using a synthetic, fitting-only example. Furthermore, we apply the method to an astrophysics dataset also used in a previous single-category study. In comparison, we achieve similar fit quality with significantly fewer parameters while extracting additional information about the problem.