# Energy Flow Networks: Deep Sets for Particle Jets

arXiv: https://arxiv.org/abs/1810.05165 · HTML: https://mlsanity.com/paper/1810.05165/

## Key facts

- Cited by 84 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Oct 2018.

## Built on by (most cited first, 30 of 84)

- [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)
- [Clifford Group Equivariant Neural Networks](https://mlsanity.com/paper/2305.11141/) (2023)
- [Machine Learning in the Search for New Fundamental Physics](https://mlsanity.com/paper/2112.03769/) (2021)
- [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)
- [MLPF: Efficient machine-learned particle-flow reconstruction using graph neural networks](https://mlsanity.com/paper/2101.08578/) (2021)
- [The Dark Machines Anomaly Score Challenge: Benchmark Data and Model Independent Event Classification for the Large Hadron Collider](https://mlsanity.com/paper/2105.14027/) (2021)
- [A Lorentz-Equivariant Transformer for All of the LHC](https://mlsanity.com/paper/2411.00446/) (2024)
- [PC-JeDi: Diffusion for Particle Cloud Generation in High Energy Physics](https://mlsanity.com/paper/2303.05376/) (2023)
- [PELICAN: Permutation Equivariant and Lorentz Invariant or Covariant Aggregator Network for Particle Physics](https://mlsanity.com/paper/2211.00454/) (2022)
- [Explainable Equivariant Neural Networks for Particle Physics: PELICAN](https://mlsanity.com/paper/2307.16506/) (2023)
- [Point Cloud Transformers applied to Collider Physics](https://mlsanity.com/paper/2102.05073/) (2021)
- [EPiC-GAN: Equivariant Point Cloud Generation for Particle Jets](https://mlsanity.com/paper/2301.08128/) (2023)
- [Topological Obstructions to Autoencoding](https://mlsanity.com/paper/2102.08380/) (2021)
- [Deep Generative Models for Detector Signature Simulation: A Taxonomic Review](https://mlsanity.com/paper/2312.09597/) (2023)
- [Finetuning Foundation Models for Joint Analysis Optimization](https://mlsanity.com/paper/2401.13536/) (2024)
- [E Pluribus Unum Ex Machina: Learning from Many Collider Events at Once](https://mlsanity.com/paper/2101.07263/) (2021)
- [Lorentz group equivariant autoencoders](https://mlsanity.com/paper/2212.07347/) (2022)
- [Graph Neural Networks in Particle Physics: Implementations, Innovations, and Challenges](https://mlsanity.com/paper/2203.12852/) (2022)
- [Ultrafast jet classification on FPGAs for the HL-LHC](https://mlsanity.com/paper/2402.01876/) (2024)
- [Lorentz Local Canonicalization: How to Make Any Network Lorentz-Equivariant](https://mlsanity.com/paper/2505.20280/) (2025)
- [Snowmass 2021 Computational Frontier CompF03 Topical Group Report: Machine Learning](https://mlsanity.com/paper/2209.07559/) (2022)
- [Scaffolding Simulations with Deep Learning for High-dimensional Deconvolution](https://mlsanity.com/paper/2105.04448/) (2021)
- [Particle Convolution for High Energy Physics](https://mlsanity.com/paper/2107.02908/) (2021)
- [An Exploration of Learnt Representations of W Jets](https://mlsanity.com/paper/2109.10919/) (2021)
- [IRC-safe Graph Autoencoder for unsupervised anomaly detection](https://mlsanity.com/paper/2204.12231/) (2022)
- [A Detailed Study of Interpretability of Deep Neural Network based Top Taggers](https://mlsanity.com/paper/2210.04371/) (2022)
- [A Comparison Between Invariant and Equivariant Classical and Quantum Graph Neural Networks](https://mlsanity.com/paper/2311.18672/) (2023)
- [Scaling Laws in Jet Classification](https://mlsanity.com/paper/2312.02264/) (2023)

## Abstract (arXiv)

A key question for machine learning approaches in particle physics is how to best represent and learn from collider events. As an event is intrinsically a variable-length unordered set of particles, we build upon recent machine learning efforts to learn directly from sets of features or "point clouds". Adapting and specializing the "Deep Sets" framework to particle physics, we introduce Energy Flow Networks, which respect infrared and collinear safety by construction. We also develop Particle Flow Networks, which allow for general energy dependence and the inclusion of additional particle-level information such as charge and flavor. These networks feature a per-particle internal (latent) representation, and summing over all particles yields an overall event-level latent representation. We show how this latent space decomposition unifies existing event representations based on detector images and radiation moments. To demonstrate the power and simplicity of this set-based approach, we apply these networks to the collider task of discriminating quark jets from gluon jets, finding similar or improved performance compared to existing methods. We also show how the learned event representation can be directly visualized, providing insight into the inner workings of the model. These architectures lend themselves to efficiently processing and analyzing events for a wide variety of tasks at the Large Hadron Collider. Implementations and examples of our architectures are available online in our EnergyFlow package.