# Particle Convolution for High Energy Physics

arXiv: https://arxiv.org/abs/2107.02908 · HTML: https://mlsanity.com/paper/2107.02908/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 51 references that are in the map.
- First posted on arXiv 5 Jul 2021.

## Builds on (most cited first, 12 of 12)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [A General Theory of Equivariant CNNs on Homogeneous Spaces](https://mlsanity.com/paper/1811.02017/) (2018)
- [Learning Steerable Filters for Rotation Equivariant CNNs](https://mlsanity.com/paper/1711.07289/) (2017)
- [Lorentz Group Equivariant Neural Network for Particle Physics](https://mlsanity.com/paper/2006.04780/) (2020)
- [Energy Flow Networks: Deep Sets for Particle Jets](https://mlsanity.com/paper/1810.05165/) (2018)
- [ParticleNet: Jet Tagging via Particle Clouds](https://mlsanity.com/paper/1902.08570/) (2019)
- [Jet-Images -- Deep Learning Edition](https://mlsanity.com/paper/1511.05190/) (2015)
- [QCD-Aware Recursive Neural Networks for Jet Physics](https://mlsanity.com/paper/1702.00748/) (2017)
- [Long Short-Term Memory (LSTM) networks with jet constituents for boosted top tagging at the LHC](https://mlsanity.com/paper/1711.09059/) (2017)
- [Recursive Neural Networks in Quark/Gluon Tagging](https://mlsanity.com/paper/1711.02633/) (2017)

## Built on by (most cited first, 8 of 8)

- [Particle Transformer for Jet Tagging](https://mlsanity.com/paper/2202.03772/) (2022)
- [Machine Learning in the Search for New Fundamental Physics](https://mlsanity.com/paper/2112.03769/) (2021)
- [PC-JeDi: Diffusion for Particle Cloud Generation in High Energy Physics](https://mlsanity.com/paper/2303.05376/) (2023)
- [Snowmass 2021 Computational Frontier CompF03 Topical Group Report: Machine Learning](https://mlsanity.com/paper/2209.07559/) (2022)
- [PCN: A Deep Learning Approach to Jet Tagging Utilizing Novel Graph Construction Methods and Chebyshev Graph Convolutions](https://mlsanity.com/paper/2309.08630/) (2023)
- [KIGNet: Physics-Motivated Multi-Graph Representation Learning for Explainable Jet Tagging](https://mlsanity.com/paper/2512.07420/) (2025)
- [Rethinking SO(3)-equivariance with Bilinear Tensor Networks](https://mlsanity.com/paper/2303.11288/) (2023)
- [Predict before you train: Scaling Laws for particle physics foundation models](https://mlsanity.com/paper/2607.23377/) (2026)

## Abstract (arXiv)

We introduce the Particle Convolution Network (PCN), a new type of equivariant neural network layer suitable for many tasks in jet physics. The particle convolution layer can be viewed as an extension of Deep Sets and Energy Flow network architectures, in which the permutation-invariant operator is promoted to a group convolution. While the PCN can be implemented for various kinds of symmetries, we consider the specific case of rotation about the jet axis the η - φ plane. In two standard benchmark tasks, q/g tagging and top tagging, we show that the rotational PCN (rPCN) achieves performance comparable to graph networks such as ParticleNet. Moreover, we show that it is possible to implement an IRC-safe rPCN, which significantly outperforms existing IRC-safe tagging methods on both tasks. We speculate that by generalizing the PCN to include additional convolutional symmetries relevant to jet physics, it may outperform the current state-of-the-art set by graph networks, while offering a new degree of control over physically-motivated inductive biases.