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[2602.15169] Learning the S-matrix from data: Rediscovering gravity from gauge theory via symbolic regression
Summary
This article presents a novel approach using symbolic regression to reconstruct key analytic structures in scattering amplitudes from numerical data, highlighting its implications for understanding gravity and gauge theory.
Why It Matters
The research demonstrates the potential of machine learning, specifically symbolic regression, to uncover fundamental relationships in high-energy physics. This could lead to new insights in theoretical physics and enhance our understanding of gravity, making it relevant for both physicists and data scientists exploring complex systems.
Key Takeaways
- Symbolic regression can autonomously reconstruct analytic structures in scattering amplitudes.
- The study successfully recovers KLT relations using minimal theoretical priors.
- The method shows promise for uncovering hidden relations in various physical theories.
- Benchmarking against neural-network methods highlights its effectiveness.
- The research opens avenues for further exploration in high-energy physics using data-driven approaches.
High Energy Physics - Theory arXiv:2602.15169 (hep-th) [Submitted on 16 Feb 2026] Title:Learning the S-matrix from data: Rediscovering gravity from gauge theory via symbolic regression Authors:Nathan Moynihan View a PDF of the paper titled Learning the S-matrix from data: Rediscovering gravity from gauge theory via symbolic regression, by Nathan Moynihan View PDF HTML (experimental) Abstract: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 th...
