Next Level Message-Passing with Hierarchical Support Graphs

TL;DR

This paper introduces Hierarchical Support Graphs (HSGs), a novel extension of virtual nodes created through recursive graph coarsening, to improve information exchange in Message-Passing Neural Networks, achieving state-of-the-art results.

Contribution

The paper proposes HSGs, a new hierarchical framework that enhances message passing in GNNs beyond existing virtual node methods, with theoretical analysis and empirical validation.

Findings

HSGs outperform existing virtual node methods.

HSGs achieve state-of-the-art results on multiple datasets.

HSGs improve information flow in graph neural networks.

Abstract

Message-Passing Neural Networks (MPNNs) are extensively employed in graph learning tasks but suffer from limitations such as the restricted scope of information exchange, by being confined to neighboring nodes during each round of message passing. Various strategies have been proposed to address these limitations, including incorporating virtual nodes to facilitate global information exchange. In this study, we introduce the Hierarchical Support Graph (HSG), an extension of the virtual node concept created through recursive coarsening of the original graph. This approach provides a flexible framework for enhancing information flow in graphs, independent of the specific MPNN layers utilized. We present a theoretical analysis of HSGs, investigate their empirical performance, and demonstrate that HSGs can surpass other methods augmented with virtual nodes, achieving state-of-the-art results across multiple datasets.