  Graph neural networks (GNNs) have achieved great success in various graph
problems. However, most GNNs are Message Passing Neural Networks (MPNNs) based
on the homophily assumption, where nodes with the same label are connected in
graphs. Real-world problems bring us heterophily problems, where nodes with
different labels are connected in graphs. MPNNs fail to address the heterophily
problem because they mix information from different distributions and are not
good at capturing global patterns. Therefore, we investigate a novel Graph
Memory Networks model on Heterophilous Graphs (HP-GMN) to the heterophily
problem in this paper. In HP-GMN, local information and global patterns are
learned by local statistics and the memory to facilitate the prediction. We
further propose regularization terms to help the memory learn global
information. We conduct extensive experiments to show that our method achieves
state-of-the-art performance on both homophilous and heterophilous graphs.
