# Is the Machine Smarter than the Theorist: Deriving Formulas for Particle Kinematics with Symbolic Regression

arXiv: https://arxiv.org/abs/2211.08420 · HTML: https://mlsanity.com/paper/2211.08420/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 68 references that are in the map.
- First posted on arXiv 15 Nov 2022.

## Builds on (most cited first, 18 of 18)

- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Interaction Networks for Learning about Objects, Relations and Physics](https://mlsanity.com/paper/1612.00222/) (2016)
- [Discovering Symbolic Models from Deep Learning with Inductive Biases](https://mlsanity.com/paper/2006.11287/) (2020)
- [End-to-end symbolic regression with transformers](https://mlsanity.com/paper/2204.10532/) (2022)
- [A Compositional Object-Based Approach to Learning Physical Dynamics](https://mlsanity.com/paper/1612.00341/) (2016)
- [Discovering physical concepts with neural networks](https://mlsanity.com/paper/1807.10300/) (2018)
- [Rediscovering orbital mechanics with machine learning](https://mlsanity.com/paper/2202.02306/) (2022)
- [A Bayesian machine scientist to aid in the solution of challenging scientific problems](https://mlsanity.com/paper/2004.12157/) (2020)
- [Deep Symbolic Regression for Recurrent Sequences](https://mlsanity.com/paper/2201.04600/) (2022)
- [Learning Symbolic Physics with Graph Networks](https://mlsanity.com/paper/1909.05862/) (2019)
- [Rethinking Symbolic Regression Datasets and Benchmarks for Scientific Discovery](https://mlsanity.com/paper/2206.10540/) (2022)
- [AI Poincar'e 2.0: Machine Learning Conservation Laws from Differential Equations](https://mlsanity.com/paper/2203.12610/) (2022)
- [Analytical Modelling of Exoplanet Transit Specroscopy with Dimensional Analysis and Symbolic Regression](https://mlsanity.com/paper/2112.11600/) (2021)
- [Simplifying Polylogarithms with Machine Learning](https://mlsanity.com/paper/2206.04115/) (2022)
- [SYMBA: Symbolic Computation of Squared Amplitudes in High Energy Physics with Machine Learning](https://mlsanity.com/paper/2206.08901/) (2022)
- [Fundamental limits to learning closed-form mathematical models from data](https://mlsanity.com/paper/2204.02704/) (2022)
- [Accelerating Understanding of Scientific Experiments with End to End Symbolic Regression](https://mlsanity.com/paper/2112.04023/) (2021)
- [Symbolic Expression Transformer: A Computer Vision Approach for Symbolic Regression](https://mlsanity.com/paper/2205.11798/) (2022)

## Built on by (most cited first, 8 of 8)

- [Deep Learning Symmetries and Their Lie Groups, Algebras, and Subalgebras from First Principles](https://mlsanity.com/paper/2301.05638/) (2023)
- [Quantum Vision Transformers for Quark-Gluon Classification](https://mlsanity.com/paper/2405.10284/) (2024)
- [Oracle-Preserving Latent Flows](https://mlsanity.com/paper/2302.00806/) (2023)
- [Exploring the Truth and Beauty of Theory Landscapes with Machine Learning](https://mlsanity.com/paper/2401.11513/) (2024)
- [Iterated Agent for Symbolic Regression](https://mlsanity.com/paper/2510.08317/) (2025)
- [Seeking Truth and Beauty in Flavor Physics with Machine Learning](https://mlsanity.com/paper/2311.00087/) (2023)
- [Discovering Nuclear Models from Symbolic Machine Learning](https://mlsanity.com/paper/2404.11477/) (2024)
- [Symbolic Classification-Enabled LHC Limits for BSM Global Fits](https://mlsanity.com/paper/2605.22330/) (2026)

## Abstract (arXiv)

We demonstrate the use of symbolic regression in deriving analytical formulas, which are needed at various stages of a typical experimental analysis in collider phenomenology. As a first application, we consider kinematic variables like the stransverse mass, MT2, which are defined algorithmically through an optimization procedure and not in terms of an analytical formula. We then train a symbolic regression and obtain the correct analytical expressions for all known special cases of MT2 in the literature. As a second application, we reproduce the correct analytical expression for a next-to-leading order (NLO) kinematic distribution from data, which is simulated with a NLO event generator. Finally, we derive analytical approximations for the NLO kinematic distributions after detector simulation, for which no known analytical formulas currently exist.