Half-Hop: A graph upsampling approach for slowing down message passing

TL;DR

Half-Hop introduces a graph upsampling method that adds 'slow nodes' to edges, slowing message passing to improve learning, especially in heterophilic graphs, and enhances self-supervised graph representations.

Contribution

The paper proposes a novel, plug-and-play graph upsampling framework with theoretical and empirical validation, improving message passing in heterophilic and self-supervised settings.

Findings

Improves performance on heterophilic graph benchmarks.

Enhances self-supervised learning with multi-scale graph augmentations.

Demonstrates theoretical benefits of slowed message passing.

Abstract

Message passing neural networks have shown a lot of success on graph-structured data. However, there are many instances where message passing can lead to over-smoothing or fail when neighboring nodes belong to different classes. In this work, we introduce a simple yet general framework for improving learning in message passing neural networks. Our approach essentially upsamples edges in the original graph by adding "slow nodes" at each edge that can mediate communication between a source and a target node. Our method only modifies the input graph, making it plug-and-play and easy to use with existing models. To understand the benefits of slowing down message passing, we provide theoretical and empirical analyses. We report results on several supervised and self-supervised benchmarks, and show improvements across the board, notably in heterophilic conditions where adjacent nodes are more likely to have different labels. Finally, we show how our approach can be used to generate augmentations for self-supervised learning, where slow nodes are randomly introduced into different edges in the graph to generate multi-scale views with variable path lengths.