BN-Pool: a Bayesian Nonparametric Approach to Graph Pooling

Abstract

We introduce BN-Pool, the first clustering-based pooling method for Graph Neural Networks (GNNs) that adaptively determines the number of supernodes in a coarsened graph. By leveraging a Bayesian non-parametric framework, BN-Pool employs a generative model capable of partitioning graph nodes into an unbounded number of clusters. During training, we learn the node-to-cluster assignments by combining the supervised loss of the downstream task with an unsupervised auxiliary term, which encourages the reconstruction of the original graph topology while penalizing unnecessary proliferation of clusters. This adaptive strategy allows BN-Pool to automatically discover an optimal coarsening level, offering enhanced flexibility and removing the need to specify sensitive pooling ratios. We show that BN-Pool achieves superior performance across diverse benchmarks.