Versatile Energy-Based Probabilistic Models for High Energy Physics

TL;DR

This work introduces a versatile energy-based probabilistic framework for LHC events that uses a transformer-based energy function to model higher-order inter-particle interactions and to support implicit generation via short-run Langevin dynamics. It demonstrates three capabilities: parameterized event generation, model-independent anomaly detection free from spurious correlations, and a hybrid classifier-EBM (EBM-CLF) that unifies jet classification with generation. The approach offers a data-driven path toward fast, reliable physics event simulation and robust new-physics searches, with evidence of realistic jet generation and improved OOD tagging. Overall, the framework provides a multitasking, physics-informed alternative to traditional Monte Carlo methods for high-energy physics analyses.

Abstract

As a classical generative modeling approach, energy-based models have the natural advantage of flexibility in the form of the energy function. Recently, energy-based models have achieved great success in modeling high-dimensional data in computer vision and natural language processing. In line with these advancements, we build a multi-purpose energy-based probabilistic model for High Energy Physics events at the Large Hadron Collider. This framework builds on a powerful generative model and describes higher-order inter-particle interactions. It suits different encoding architectures and builds on implicit generation. As for applicative aspects, it can serve as a powerful parameterized event generator for physics simulation, a generic anomalous signal detector free from spurious correlations, and an augmented event classifier for particle identification.

Figures (9)

• Figure 1: Schematic of the EBM model. The energy function $E({\mathbf{x}}, y)$ is estimated with a transformer. The training procedure is governed by Contrastive Divergence (the vertical dimension), for which the model distribution estimation $q_\theta({\mathbf{x}})$ is obtained with Langevin Dynamics (the horizontal dimension), evolving samples from random noises ${\mathbf{x}}_0^-$.
• Figure 2: Top: Input feature distributions of jet constituents for the data and the model generation. Bottom: High-level feature distributions for the data and the model generation.
• Figure 3: Left: Energy distributions for random samples, background QCD jets, and novel signals. Right: Correlation between the jet mass $M_J$ and the energy $E$.
• Figure 4: Left: ROC Curves for EBM and EBM-CLF with the energy $E({\mathbf{x}})$ as the anomaly score. The grey line denotes the case of random guessing. Right: Background mass distributions under different acceptance rates $\epsilon$ after cutting on the energy score from the EBM-CLF.
• Figure 5: Typical high-level observable distributions for MLP-based models.