# Class Symbolic Regression: Gotta Fit 'Em All

arXiv: https://arxiv.org/abs/2312.01816 · HTML: https://mlsanity.com/paper/2312.01816/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 31 references that are in the map.
- First posted on arXiv 4 Dec 2023.

## Builds on (most cited first, 5 of 5)

- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Extrapolation and learning equations](https://mlsanity.com/paper/1610.02995/) (2016)
- [Deep symbolic regression for physics guided by units constraints: toward the automated discovery of physical laws](https://mlsanity.com/paper/2303.03192/) (2023)
- [Probabilistic Grammars for Equation Discovery](https://mlsanity.com/paper/2012.00428/) (2020)
- [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)

## Built on by (most cited first, 6 of 6)

- [Multi-View Symbolic Regression](https://mlsanity.com/paper/2402.04298/) (2024)
- [Generalizing the SINDy approach with nested neural networks](https://mlsanity.com/paper/2404.15742/) (2024)
- [Exploring Multi-view Symbolic Regression methods in physical sciences](https://mlsanity.com/paper/2509.10500/) (2025)
- [Constraining dark matter halo profiles with symbolic regression](https://mlsanity.com/paper/2511.23073/) (2025)
- [Symbolic Regression for Shared Expressions: Introducing Partial Parameter Sharing](https://mlsanity.com/paper/2601.04051/) (2026)
- [Shared Symbolic Backbones for Physically Consistent Multi-Output Symbolic Regression](https://mlsanity.com/paper/2607.26528/) (2026)

## Abstract (arXiv)

We introduce 'Class Symbolic Regression' (Class SR) a first framework for automatically finding a single analytical functional form that accurately fits multiple datasets - each realization being governed by its own (possibly) unique set of fitting parameters. This hierarchical framework leverages the common constraint that all the members of a single class of physical phenomena follow a common governing law. Our approach extends the capabilities of our earlier Physical Symbolic Optimization (Phi-SO) framework for Symbolic Regression, which integrates dimensional analysis constraints and deep reinforcement learning for unsupervised symbolic analytical function discovery from data. Additionally, we introduce the first Class SR benchmark, comprising a series of synthetic physical challenges specifically designed to evaluate such algorithms. We demonstrate the efficacy of our novel approach by applying it to these benchmark challenges and showcase its practical utility for astrophysics by successfully extracting an analytic galaxy potential from a set of simulated orbits approximating stellar streams.