# Learning Standard Model structure from LHC data with Riemannian flow matching

arXiv: https://arxiv.org/abs/2607.16144 · HTML: https://mlsanity.com/paper/2607.16144/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 30 of its 92 references that are in the map.
- First posted on arXiv 17 Jul 2026.

## Builds on (most cited first, 30 of 30)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Flow Matching on General Geometries](https://mlsanity.com/paper/2302.03660/) (2023)
- [Particle Transformer for Jet Tagging](https://mlsanity.com/paper/2202.03772/) (2022)
- [A Living Review of Machine Learning for Particle Physics](https://mlsanity.com/paper/2102.02770/) (2021)
- [Anomaly Detection with Density Estimation](https://mlsanity.com/paper/2001.04990/) (2020)
- [Accelerating Science with Generative Adversarial Networks: An Application to 3D Particle Showers in Multi-Layer Calorimeters](https://mlsanity.com/paper/1705.02355/) (2017)
- [Score-based Generative Models for Calorimeter Shower Simulation](https://mlsanity.com/paper/2206.11898/) (2022)
- [Machine Learning in the Search for New Fundamental Physics](https://mlsanity.com/paper/2112.03769/) (2021)
- [CaloFlow: Fast and Accurate Generation of Calorimeter Showers with Normalizing Flows](https://mlsanity.com/paper/2106.05285/) (2021)
- [Masked Particle Modeling on Sets: Towards Self-Supervised High Energy Physics Foundation Models](https://mlsanity.com/paper/2401.13537/) (2024)
- [Classification without labels: Learning from mixed samples in high energy physics](https://mlsanity.com/paper/1708.02949/) (2017)
- [OmniJet-α: The first cross-task foundation model for particle physics](https://mlsanity.com/paper/2403.05618/) (2024)
- [Lorentz-Equivariant Geometric Algebra Transformers for High-Energy Physics](https://mlsanity.com/paper/2405.14806/) (2024)
- [CaloChallenge 2022: A Community Challenge for Fast Calorimeter Simulation](https://mlsanity.com/paper/2410.21611/) (2024)
- [Evaluating generative models in high energy physics](https://mlsanity.com/paper/2211.10295/) (2022)
- [Performance of a Geometric Deep Learning Pipeline for HL-LHC Particle Tracking](https://mlsanity.com/paper/2103.06995/) (2021)
- [Machine Learning for Anomaly Detection in Particle Physics](https://mlsanity.com/paper/2312.14190/) (2023)
- [Simulation Assisted Likelihood-free Anomaly Detection](https://mlsanity.com/paper/2001.05001/) (2020)
- [PC-JeDi: Diffusion for Particle Cloud Generation in High Energy Physics](https://mlsanity.com/paper/2303.05376/) (2023)
- [EPiC-ly Fast Particle Cloud Generation with Flow-Matching and Diffusion](https://mlsanity.com/paper/2310.00049/) (2023)
- [Aspen Open Jets: Unlocking LHC Data for Foundation Models in Particle Physics](https://mlsanity.com/paper/2412.10504/) (2024)
- [Large Physics Models: Towards a collaborative approach with Large Language Models and Foundation Models](https://mlsanity.com/paper/2501.05382/) (2025)
- [Improving new physics searches with diffusion models for event observables and jet constituents](https://mlsanity.com/paper/2312.10130/) (2023)
- [A Language Model for Particle Tracking](https://mlsanity.com/paper/2402.10239/) (2024)
- [Foundation models for high-energy physics](https://mlsanity.com/paper/2509.21434/) (2025)
- [Refereeing the Referees: Evaluating Two-Sample Tests for Validating Generators in Precision Sciences](https://mlsanity.com/paper/2409.16336/) (2024)
- [EveNet: A Foundation Model for Particle Collision Data Analysis](https://mlsanity.com/paper/2601.17126/) (2026)
- [PC-Droid: Faster diffusion and improved quality for particle cloud generation](https://mlsanity.com/paper/2307.06836/) (2023)

## Abstract (arXiv)

In this work we demonstrate that a single transformer-based generative model can capture Standard Model structure spanning five decades of invariant mass, from the sub-GeV regime to the TeV continuum, a range that no single Monte Carlo sample covers. To achieve this we design textscShellFlow, a Riemannian conditional flow matching model that, given the recorded event composition, generates each particle on its on-shell manifold. Its only physics priors are the on-shell condition and the invariant-mass formula. The model is trained on ~ 109 real pp collision events from the ATLAS Open Data 13~TeV release and told nothing else. From a single training run, the model learns to reproduce all of the following: intra-particle kinematics, the dilepton resonances (J/psi, Upsilon, Z) at their PDG positions, the leptonic Weinberg angle, the W and top-quark masses, and inter-particle correlations that enter no training objective. A substantial fraction of the Standard Model is thus learnable directly from recorded collision data.