Hyperbolic-Euclidean Deep Mutual Learning

Graph neural networks (GNNs) exhibit powerful performance in handling graph data, with Euclidean and hyperbolic variants excelling in processing grid-based and hierarchical structures, respectively. However, existing methods focus on learning specific structures linked to the inherent properties of the underlying space, failing to fully exploit their complementary properties in distinct geometric spaces, thus limiting their ability to efficiently model complex graph structures. In this paper, we propose a Hyperbolic-Euclidean Deep Mutual Learning (H-EDML) framework, which leverages the unique properties of hyperbolic space to effectively capture the hierarchical relationships present in graph data, while also utilizes the familiar Euclidean space to handle local interactions. Specifically, We design a topology mutual learning module to bolster the capacity of each single model to perceive the holistic topological structure of the graph. Then, we integrate a decision mutual learning module to further advance the models' comprehensive judgment capabilities towards graph data, thereby strengthening the robustness and generalization. Furthermore, we employ an attention-based probabilistic integration strategy for the final prediction to alleviate potential disparities in decision-making among different models. Extensive experiments on node classification are conducted on five real-world graph datasets and the results show that our proposed H-EDML achieves competitive performances compared to the state-of-the-art methods. The source code will be available at: https://github.com/caohaifang123/H-EDML.