Hierarchical graph neural nets can capture long-range interactions

TL;DR

This paper introduces Hierarchical Graph Net (HGNet), a novel hierarchical GNN model that efficiently captures long-range interactions in graphs, outperforming traditional GCNs especially in molecular property prediction tasks.

Contribution

The paper proposes HGNet, a hierarchical GNN architecture with logarithmic message-passing paths, and introduces benchmarking tasks to evaluate long-range interaction capabilities.

Findings

HGNet guarantees message paths of logarithmic length between nodes.

HGNet outperforms traditional GCNs in molecular property prediction.

New benchmarks effectively assess GNNs' ability to leverage long-range interactions.

Abstract

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 project 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.