The Weisfeiler-Leman algorithm ($1$-WL) is a well-studied heuristic for the graph isomorphism problem. Recently, the algorithm has played a prominent role in understanding the expressive power of message-passing graph neural networks (MPNNs) and being effective as a graph kernel. Despite its success, $1$-WL faces challenges in distinguishing non-isomorphic graphs, leading to the development of more expressive MPNN and kernel architectures. However, the relationship between enhanced expressivity and improved generalization performance remains unclear. Here, we show that an architecture's expressivity offers limited insights into its generalization performance when viewed through graph isomorphism. Moreover, we focus on augmenting $1$-WL and MPNNs with subgraph information and employ classical margin theory to investigate the conditions under which an architecture's increased expressivity aligns with improved generalization performance. In addition, we show that gradient flow pushes the MPNN's weights toward the maximum margin solution. Further, we introduce variations of expressive $1$-WL-based kernel and MPNN architectures with provable generalization properties. Our empirical study confirms the validity of our theoretical findings.
Institute for Mathematical and Computational Engineering, PUC Chile（智利天主教大学数学与计算工程研究所）；IMFD Chile（智利数据基础研究所）；CENIA Chile（智利国家人工智能中心）；Mila Quebec AI Institute（魁北克人工智能研究所Mila）；McGill University（麦吉尔大学）；RWTH Aachen University（亚琛工业大学）；Universidad Adolfo Ibáñez（阿道夫·伊瓦涅斯大学）
Weisfeiler and Leman Follow the Arrow of Time: Expressive Power of Message Passing in Temporal Event Graphs
Chair of Machine Learning for Complex Networks（复杂网络机器学习教授席）；Center for AI and Data Science (CAIDAS)（人工智能与数据科学中心（CAIDAS））；University of Würzburg（乌尔姆大学）；Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院）；University of Karlsruhe（卡尔斯鲁厄大学）；Institute for Computer Science 1（计算机科学研究所1）；University of Bonn（波恩大学）
Weisfeiler Leman for Euclidean Equivariant Machine Learning
Faculty of Mathematics, Technion - Israel Institute of Technology（以色列理工学院数学学院）；Faculty of Computer Science, Technion - Israel Institute of Technology（以色列理工学院计算机科学学院）
Scalable Message-Passing Quantum Graph Neural Networks in the Weisfeiler-Leman Hierarchy
LIP6, CNRS, Sorbonne Université, Paris, France（巴黎大学LIP6研究所、法国国家科学研究中心、索邦大学）；QC Ware, Palo Alto, USA and Paris, France（QC Ware公司，美国帕洛阿尔托及法国巴黎）；School of Informatics, University of Edinburgh, Edinburgh, UK（爱丁堡大学信息学院，英国爱丁堡）；Fujitsu Research of Europe Ltd., United Kingdom（日本富士通欧洲研究有限公司，英国）；Terra Quantum GmbH, Germany（德国Terra Quantum GmbH公司）；Quantum Research Center, Technology Innovation Institute, Abu Dhabi, UAE（阿布扎赫尔技术创新研究所量子研究中心，阿联酋）
POSTECH（浦项科技大学）；Center for Geometry and Physics, Institute for Basic Science (IBS)（基础科学研究院几何与物理中心）；Korea Advanced Institute of Science and Technology (KAIST)（韩国科学技术院）
Weisfeiler and Leman go Machine Learning: The Story so far
RWTH Aachen University（亚琛工业大学）；Meta AI Research（Meta人工智能研究院）；Weizmann Institute of Science（魏茨曼科学研究所）；NVIDIA Research（英伟达研究院）；Helmholtz Zentrum München（慕尼黑亥姆霍兹中心）；Technical University of Munich（慕尼黑工业大学）；University of Vienna（维也纳大学）；ETH Zürich（苏黎世联邦理工学院）；Swiss Institute of Bioinformatics（瑞士生物信息学研究所）；Max Planck Institute of Biochemistry（马克斯·普朗克生物化学研究所）
A Unifying Relational Perspective on Expressive Lottery Tickets
Faculty of Computer Science, University of Vienna（维也纳大学计算机科学学院）；Doctoral School Computer Science, University of Vienna（维也纳大学计算机科学博士学院）；CeMM Research Center for Molecular Medicine of the Austrian Academy of Sciences（奥地利科学院CeMM分子医学研究中心）；CISPA Helmholtz Center for Information Security（CISPA亥姆霍兹信息安全中心）；School of Electronic Engineering and Computer Science, Queen Mary University of London（伦敦大学玛丽女王学院电子工程与计算机科学学院）；Research Network Data Science, University of Vienna（维也纳大学数据科学研究网络）
Attacking Graph Neural Networks with Bit Flips: Weisfeiler and Lehman Go Indifferent
University of Vienna（维也纳大学）；Doctoral School Computer Science, Faculty of Computer Science, University of Vienna（维也纳大学计算机学院计算机科学博士学院）；Christian Doppler Laboratory for Assurance and Transparency in Software Protection, Faculty of Computer Science, University of Vienna（维也纳大学计算机学院克里斯蒂安·多普勒软件保护保障与透明度实验室）；Research Network Data Science, Faculty of Computer Science, University of Vienna（维也纳大学计算机学院数据科学研究网络）
该研究提出首个专门针对图神经网络的Injectivity Bit Flip Attack，通过攻击量化消息传递神经网络的邻域聚合函数削弱其结构区分能力，仅翻转少量比特就能让高表达力的图同构网络输出随机结果，破坏力优于迁移自CNN的位翻转攻击。
Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networks
University of Cambridge（剑桥大学）；Twitter（推特）；Imperial College London（帝国理工学院）；University of New South Wales（新南威尔士大学）；Max Planck Institute for Mathematics in the Sciences（马克斯·普朗克数学科学研究所）；Shanghai Jiao Tong University（上海交通大学）；University of California, Los Angeles（加州大学洛杉矶分校）
Expressivity and Generalization: Fragment-Biases for Molecular GNNs
School of Computation, Information & Technology, Technical University of Munich（慕尼黑工业大学计算、信息与技术学院）；Munich Data Science Institute（慕尼黑数据科学研究所）；Helmholtz Center for Computational Health（亥姆霍兹计算健康中心）
On the Rademacher Complexity of Graph Neural Networks: Unifying Expressivity and Geometry
University of Fribourg（弗里堡大学）；Johns Hopkins University（约翰·霍普金斯大学）；Université Paris-Saclay（巴黎萨克雷大学）；University of Ferrara（费拉拉大学）；Technical University of Munich（慕尼黑技术大学）；University of Siena（锡耶纳大学）
