Discrete Curvature Graph Information Bottleneck

TL;DR

This paper introduces CurvGIB, a novel framework that uses discrete Ricci curvature to optimize graph information transport, enhancing node representations and interpretability in graph neural networks.

Contribution

It proposes a new curvature-based information bottleneck method that improves message-passing efficiency and interpretability for GNNs, integrating Ricci curvature optimization with variational principles.

Findings

CurvGIB outperforms baseline models on multiple datasets.

The framework enhances interpretability of message-passing structures.

Ricci curvature optimization improves downstream task performance.

Abstract

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.