Hierarchical graph structure learning with nonlinear information bottleneck

In recent years, graph neural networks (GNNs) have become extremely popular due to their powerful expressive capabilities and widespread availability. They have been successful in various real-world applications. GNNs work by learning the node representations through message passing along with the structure. Most empirical studies of GNNs assume that the observed graph structure perfectly depicts the accurate and complete relations between nodes. However, in real-world scenarios, graphs are often noisy, incomplete, or manipulated by adversaries. This noise and interference can affect the quality of graph representations during information aggregation. In this paper, we propose a method called NIB-HGSL, which is a hierarchical graph structure learning method based on the nonlinear information bottleneck principle. NIB-HGSL aims to learn robust graph representations without noisy information, obtaining the minimum sufficient structure for downstream tasks through a balanced optimization of relevant information preservation and noisy information compression. Our comprehensive empirical evaluations demonstrate the effectiveness and robustness of NIB-HGSL, enhancing the power of GNNs for in-the-wild extrapolation.