Discrete Curvature Graph Information Bottleneck
This work addresses graph learning bottlenecks for researchers and practitioners by improving GNN performance and interpretability, though it is incremental as it builds on existing curvature and information bottleneck methods.
The paper tackles the problem of inefficient information propagation in graph neural networks (GNNs) by proposing the Discrete Curvature Graph Information Bottleneck (CurvGIB) framework, which optimizes graph curvature to learn better node representations and achieves superior effectiveness in experiments.
Graph neural networks(GNNs) have been demonstrated to depend on whether the node effective information is sufficiently passing. Discrete curvature (Ricci curvature) is used to study graph connectivity and information propagation efficiency with a geometric perspective, and has been raised in recent years to explore the efficient message-passing structure of GNNs. However, most empirical studies are based on directly observed graph structures or heuristic topological assumptions and lack in-depth exploration of underlying optimal information transport structures for downstream tasks. We suggest that graph curvature optimization is more in-depth and essential than directly rewiring or learning for graph structure with richer message-passing characterization and better information transport interpretability. From both graph geometry and information theory perspectives, we propose the novel Discrete Curvature Graph Information Bottleneck (CurvGIB) framework to optimize the information transport structure and learn better node representations simultaneously. CurvGIB advances the Variational Information Bottleneck (VIB) principle for Ricci curvature optimization to learn the optimal information transport pattern for specific downstream tasks. The learned Ricci curvature is used to refine the optimal transport structure of the graph, and the node representation is fully and efficiently learned. Moreover, for the computational complexity of Ricci curvature differentiation, we combine Ricci flow and VIB to deduce a curvature optimization approximation to form a tractable IB objective function. Extensive experiments on various datasets demonstrate the superior effectiveness and interpretability of CurvGIB.