Fine-Grained Expressive Power of Weisfeiler-Leman: A Homomorphism Counting Perspective

• URL: http://arxiv.org/abs/2410.03517v1
• Date: Fri, 4 Oct 2024 15:36:48 GMT
• Title: Fine-Grained Expressive Power of Weisfeiler-Leman: A Homomorphism Counting Perspective
• Authors: Junru Zhou, Muhan Zhang,
• Abstract summary: We provide a theoretical framework to determine the homomorphism counting power of an arbitrary class of graph neural networks (GNNs) As the considered design space is large enough to accommodate almost all known powerful GNNs, our result greatly extends all existing works, and may find its application in the automation of GNN model design.
• Score: 24.729126775414922
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The ability of graph neural networks (GNNs) to count homomorphisms has recently been proposed as a practical and fine-grained measure of their expressive power. Although several existing works have investigated the homomorphism counting power of certain GNN families, a simple and unified framework for analyzing the problem is absent. In this paper, we first propose \emph{generalized folklore Weisfeiler-Leman (GFWL)} algorithms as a flexible design basis for expressive GNNs, and then provide a theoretical framework to algorithmically determine the homomorphism counting power of an arbitrary class of GNN within the GFWL design space. As the considered design space is large enough to accommodate almost all known powerful GNNs, our result greatly extends all existing works, and may find its application in the automation of GNN model design.

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