Hierarchical Graph Neural Nets can Capture Long-Range Interactions

Graph neural networks (GNNs) based on message passing between neighboring nodes are known to be insufficient for capturing long-range interactions in graphs. In this paper we study hierarchical message passing models that leverage a multi-resolution representation of a given graph. This facilitates learning of features that span large receptive fields without loss of local information, an aspect not studied in preceding work on hierarchical GNNs. We introduce Hierarchical Graph Net (HGNet), which for any two connected nodes guarantees existence of message-passing paths of at most logarithmic length w.r.t. the input graph size. Yet, under mild assumptions, its internal hierarchy maintains asymptotic size equivalent to that of the input graph. We observe that our HGNet outperforms conventional stacking of GCN layers particularly in molecular property prediction benchmarks. Finally, we propose two benchmarking tasks designed to elucidate capability of GNNs to leverage long-range interactions in graphs.