# Learning the S-matrix from data: Rediscovering gravity from gauge theory via symbolic regression

arXiv: https://arxiv.org/abs/2602.15169 · HTML: https://mlsanity.com/paper/2602.15169/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 41 references that are in the map.
- First posted on arXiv 16 Feb 2026.

## Builds on (most cited first, 7 of 7)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Rediscovering orbital mechanics with machine learning](https://mlsanity.com/paper/2202.02306/) (2022)
- [Learning the Simplicity of Scattering Amplitudes](https://mlsanity.com/paper/2408.04720/) (2024)
- [A Perspective on Symbolic Machine Learning in Physical Sciences](https://mlsanity.com/paper/2502.17993/) (2025)
- [Versor: A Geometric Sequence Architecture](https://mlsanity.com/paper/2602.10195/) (2026)

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

- [Efficient AI-Inspired Reduction of Feynman Integrals via Tube Seeding](https://mlsanity.com/paper/2606.10698/) (2026)

## Abstract (arXiv)

We demonstrate that modern machine-learning methods can autonomously reconstruct several flagship analytic structures in scattering amplitudes directly from numerical on-shell data. In particular, we show that the Kawai--Lewellen--Tye (KLT) relations can be rediscovered using symbolic regression applied to colour-ordered Yang--Mills amplitudes with Mandelstam invariants as input features. Using standard feature-selection techniques, specifically column-pivoted QR factorisation, we simultaneously recover the Kleiss--Kuijf and Bern--Carrasco--Johansson (BCJ) relations, identifying a minimal basis of partial amplitudes without any group-theoretic input. We obtain the tree-level KLT relations with high numerical accuracy up to five external legs, using only minimal theoretical priors, and we comment on the obstacles to generalising the method to higher multiplicity. Our results establish symbolic regression as a practical tool for exploring the analytic structure of the scattering-amplitude landscape, and suggests a general data-driven strategy for uncovering hidden relations in general theories. For comparison, we benchmark this general approach with a recently introduced neural-network based method.