Graph Neural Networks (GNNs) have demonstrated strong performance in graph
mining tasks due to their message-passing mechanism, which is aligned with the
homophily assumption that adjacent nodes exhibit similar behaviors. However, in
many real-world graphs, connected nodes may display contrasting behaviors,
termed as heterophilous patterns, which has attracted increased interest in
heterophilous GNNs (HTGNNs). Although the message-passing mechanism seems
unsuitable for heterophilous graphs due to the propagation of class-irrelevant
information, it is still widely used in many existing HTGNNs and consistently
achieves notable success. This raises the question: why does message passing
remain effective on heterophilous graphs? To answer this question, in this
paper, we revisit the message-passing mechanisms in heterophilous graph neural
networks and reformulate them into a unified heterophilious message-passing
(HTMP) mechanism. Based on HTMP and empirical analysis, we reveal that the
success of message passing in existing HTGNNs is attributed to implicitly
enhancing the compatibility matrix among classes. Moreover, we argue that the
full potential of the compatibility matrix is not completely achieved due to
the existence of incomplete and noisy semantic neighborhoods in real-world
heterophilous graphs. To bridge this gap, we introduce a new approach named
CMGNN, which operates within the HTMP mechanism to explicitly leverage and
improve the compatibility matrix. A thorough evaluation involving 10 benchmark
datasets and comparative analysis against 13 well-established baselines
highlights the superior performance of the HTMP mechanism and CMGNN method.

基于对异构图神经网络中的消息传递机制的研究，本文提出了统一异质消息传递（HTMP）机制以及一种名为 CMGNN 的新方法，通过显式利用和改进兼容性矩阵，实现了在真实世界的异质图中消息传递机制和 CMGNN 方法的卓越性能。

异质图神经网络中的消息传递再探

Revisiting the Message Passing in Heterophilous Graph Neural Networks

Graph Neural Networks (GNNs) have proven to be useful for many different
practical applications. However, many existing GNN models have implicitly
assumed homophily among the nodes connected in the graph, and therefore have
largely overlooked the important setting of heterophily, where most connected
nodes are from different classes. In this work, we propose a novel framework
called CPGNN that generalizes GNNs for graphs with either homophily or
heterophily. The proposed framework incorporates an interpretable compatibility
matrix for modeling the heterophily or homophily level in the graph, which can
be learned in an end-to-end fashion, enabling it to go beyond the assumption of
strong homophily. Theoretically, we show that replacing the compatibility
matrix in our framework with the identity (which represents pure homophily)
reduces to GCN. Our extensive experiments demonstrate the effectiveness of our
approach in more realistic and challenging experimental settings with
significantly less training data compared to previous works: CPGNN variants
achieve state-of-the-art results in heterophily settings with or without
contextual node features, while maintaining comparable performance in homophily
settings.

本研究提出了 CPGNN 框架，它使用可解释的兼容性矩阵来建模图中异相性（heterophily）或同相性（homophily）水平，并证明了该框架在更现实和具有挑战性的实验设置下比以前的作品要有效。