Rethinking heterophilic graph learning via graph curvature

The performance of graph neural networks is limited on heterophilic graphs since heterophilic connections hinder the transport of supervision signals related to downstream tasks. In recent years, most existing works based on node-pair heterophily “transform” heterophilic graphs into special homophilic graphs, which often increase homophilic connectivity and remove heterophilic edges, thereby converting highly heterophilic graphs into highly homophilic ones. They only consider the label difference between node pairs while overlooking the change in the label distribution between their neighborhoods. They need to provide some heuristic priors or complex designs to alleviate the lack of underlying understanding of the heterophilic information propagation, which leads to the issue of heterophily inconsistency. To address the issue of heterophily inconsistency, based on optimal transport theory, we extend the definition of curvature and propose the Heterophily Curvature Graph Representation Learning framework (HetCurv) to optimize the information transport structure and learn better node representations simultaneously. HetCurv perceives the variation of supervision signals on heterophilic graphs through heterophily curvature, and learns the optimal information transport pattern for specific downstream tasks. Extensive experiments demonstrate the superiority of the proposed method in comparison to state-of-the-art baselines across various node classification benchmarks.