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Multimodal Generative Flows for LHC Jets

Darius A. Faroughy, Manfred Opper, Cesar Ojeda

TL;DR

The paper tackles LHC jet generation with hybrid data consisting of continuous kinematics and discrete flavor tokens by introducing a multimodal flow that combines flow-matching with a continuous-time Markov jump bridge over the hybrid space $\mathbb{R}^3 \otimes \mathcal{F}$, learning a probability path $P_t$ with velocity $\mathbf{u}_t$ and discrete rates $\mathbf{W}_t$. A novel Multimodal ParticleFormer architecture jointly learns these generators via mode-specific encoders and a fused encoder, optimizing a joint MMF loss that balances continuous and discrete objectives and adapts through time-dependent uncertainty weights. Evaluations on the AspenOpenJets dataset from CMS Open Data show improved fidelity in jet kinematics, substructure, and flavor distributions, demonstrating realistic cross-modal correlations and potential for data-driven jet simulations and anomaly detection. The framework provides a principled path toward scalable, hybrid-modality generative modeling in high-energy physics with practical implications for LHC analyses and foundation-model-like jet generation. The use of a Markov-bridge-based discrete dynamics and a permutation-equivariant Transformer enables modeling of complex inter-particle correlations while remaining tractable for large jet showers.

Abstract

Generative modeling of high-energy collisions at the Large Hadron Collider (LHC) offers a data-driven route to simulations, anomaly detection, among other applications. A central challenge lies in the hybrid nature of particle-cloud data: each particle carries continuous kinematic features and discrete quantum numbers such as charge and flavor. We introduce a transformer-based multimodal flow that extends flow-matching with a continuous-time Markov jump bridge to jointly model LHC jets with both modalities. Trained on CMS Open Data, our model can generate high fidelity jets with realistic kinematics, jet substructure and flavor composition.

Multimodal Generative Flows for LHC Jets

TL;DR

The paper tackles LHC jet generation with hybrid data consisting of continuous kinematics and discrete flavor tokens by introducing a multimodal flow that combines flow-matching with a continuous-time Markov jump bridge over the hybrid space , learning a probability path with velocity and discrete rates . A novel Multimodal ParticleFormer architecture jointly learns these generators via mode-specific encoders and a fused encoder, optimizing a joint MMF loss that balances continuous and discrete objectives and adapts through time-dependent uncertainty weights. Evaluations on the AspenOpenJets dataset from CMS Open Data show improved fidelity in jet kinematics, substructure, and flavor distributions, demonstrating realistic cross-modal correlations and potential for data-driven jet simulations and anomaly detection. The framework provides a principled path toward scalable, hybrid-modality generative modeling in high-energy physics with practical implications for LHC analyses and foundation-model-like jet generation. The use of a Markov-bridge-based discrete dynamics and a permutation-equivariant Transformer enables modeling of complex inter-particle correlations while remaining tractable for large jet showers.

Abstract

Generative modeling of high-energy collisions at the Large Hadron Collider (LHC) offers a data-driven route to simulations, anomaly detection, among other applications. A central challenge lies in the hybrid nature of particle-cloud data: each particle carries continuous kinematic features and discrete quantum numbers such as charge and flavor. We introduce a transformer-based multimodal flow that extends flow-matching with a continuous-time Markov jump bridge to jointly model LHC jets with both modalities. Trained on CMS Open Data, our model can generate high fidelity jets with realistic kinematics, jet substructure and flavor composition.

Paper Structure

This paper contains 34 sections, 49 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. CMS Open Data
  3. Multimodal flows for particle clouds
  4. Conditional dynamics
  5. Multimodal objective
  6. Multimodal ParticleFormer
  7. Sampling
  8. Experiments
  9. Aspen Open Jets
  10. Discussion
  11. Related Work
  12. Generative modeling with bridge processes
  13. Continuous random variables
  14. Conditional Flow-Matching
  15. Discrete random variables
  16. ...and 19 more sections

Figures (4)

  • Figure 1: Visualizations of 10 CMS jets in the $(\eta,\phi)$-plane taken from the AspenOpenJets dataset. Each particle cloud is centered around the jet axis. The size of each marker is proportional to the particle's transverse momentum ($p_T$), while the shape and color encode electric charge and flavor, respectively. The upper right corner of each panel indicates the total number of constituents in the respective jet.
  • Figure 2: Multi-modal particle transformer architecture. Additional details are provided App. \ref{['app:architecture']}.
  • Figure 3: Performance comparison between generated samples from our particle transformer MMF model (orange) and the EPiC-FM baseline (blue) for various high-level jet observables. The corresponding Wasserstein distance between the generated and test distributions are shown in Table \ref{['tab:results']}.
  • Figure 4: Detail of the particle self-attention block used for our MMF model and the EPiC encoder used for our baseline model.