Machine learning algorithms are heavily relied on to understand the vast
amounts of data from high-energy particle collisions at the CERN Large Hadron
Collider (LHC). The data from such collision events can naturally be
represented with graph structures. Therefore, deep geometric methods, such as
graph neural networks (GNNs), have been leveraged for various data analysis
tasks in high-energy physics. One typical task is jet tagging, where jets are
viewed as point clouds with distinct features and edge connections between
their constituent particles. The increasing size and complexity of the LHC
particle datasets, as well as the computational models used for their analysis,
greatly motivate the development of alternative fast and efficient
computational paradigms such as quantum computation. In addition, to enhance
the validity and robustness of deep networks, one can leverage the fundamental
symmetries present in the data through the use of invariant inputs and
equivariant layers. In this paper, we perform a fair and comprehensive
comparison between classical graph neural networks (GNNs) and equivariant graph
neural networks (EGNNs) and their quantum counterparts: quantum graph neural
networks (QGNNs) and equivariant quantum graph neural networks (EQGNN). The
four architectures were benchmarked on a binary classification task to classify
the parton-level particle initiating the jet. Based on their AUC scores, the
quantum networks were shown to outperform the classical networks. However,
seeing the computational advantage of the quantum networks in practice may have
to wait for the further development of quantum technology and its associated
APIs.

机器学习算法、图神经网络、量子计算、等变图神经网络和二元分类任务是本文的关键词和研究主题。

不变量和等变量的经典与量子图神经网络比较

A Comparison Between Invariant and Equivariant Classical and Quantum  Graph Neural Networks

Convolutional neural networks revolutionized computer vision and natrual
language processing. Their efficiency, as compared to fully connected neural
networks, has its origin in the architecture, where convolutions reflect the
translation invariance in space and time in pattern or speech recognition
tasks. Recently, Cohen and Welling have put this in the broader perspective of
invariance under symmetry groups, which leads to the concept of group
equivaiant neural networks and more generally steerable neural networks. In
this article, we review the architecture of such networks including equivariant
layers and filter banks, activation with capsules and group pooling. We apply
this formalism to the symmetric group, for which we work out a number of
details on representations and capsules that are not found in the literature.

本研究论文探讨卷积神经网络在对称群中的应用，提出了群等变神经网络的概念和架构，以及使用多种层和滤波器的方法，为对称群的表示和胶囊的细节做出了数学分析。