Improving hierarchical graph pooling with information bottleneck

Jun Long, Zidong Wang, Tingxuan Chen, Yang Liu

Abstract: Hierarchical graph pooling has received significant attention in recent years due to its capability to capture hierarchical structures and deliver superior performance on graph-level tasks. However, most existing methods design pooling layers empirically and lack a unified theoretical framework. Consequently, the coarsened graphs generated by these methods frequently contain redundant information, leading to significant semantic bias. In this paper, we propose the principle of “minimal sufficient coarsened graph” to precisely define the desired properties of coarsened graphs. Guided by this principle, we introduce a novel Graph Pooling Information Bottleneck (GPIB) for hierarchical graph pooling. GPIB aims to achieve the desired attributes of minimality and sufficiency in coarsened graphs. Specifically, we first incorporate node degree properties to enrich node representations and introduce a dynamic generation mechanism. This mechanism regulates the information flow, ensuring substantial auxiliary knowledge for downstream tasks and enhancing information sufficiency. Then, we introduce a parameter-learning noise distribution, forcing the elimination of redundant information and thus, facilitating minimality and robustness in our model. Remarkably, we theoretically demonstrate that imposing constraints only on the coarsened graph produced by the final pooling layer equates to constraining all coarsened graphs. This insight simplifies the constraint procedure while ensuring its effectiveness. Extensive experiments on six real-world datasets validate the effectiveness of our proposed model, which consistently outperforms the baseline methods and produces high-quality coarsened graphs.