Geometry Awakening: Cross-Geometry Learning Exhibits Superiority over Individual Structures

Recent research has underscored the efficacy of Graph Neural Networks (GNNs) in modeling diverse geometric structures within graph data. However, real-world graphs typically exhibit geometrically heterogeneous characteristics, rendering the confinement to a single geometric paradigm insufficient for capturing their intricate structural complexities. To address this limitation, we examine the performance of GNNs across various geometries through the lens of knowledge distillation (KD) and introduce a novel cross-geometric framework. This framework encodes graphs by integrating both Euclidean and hyperbolic geometries in a space-mixing fashion. Our approach employs multiple teacher models, each generating hint embeddings that encapsulate distinct geometric properties. We then implement a structure-wise knowledge transfer module that optimally leverages these embeddings within their respective geometric contexts, thereby enhancing the training efficacy of the student model. Additionally, our framework incorporates a geometric optimization network designed to bridge the distributional disparities among these embeddings. Experimental results demonstrate that our model-agnostic framework more effectively captures topological graph knowledge, resulting in superior performance of the student models when compared to traditional KD methodologies.