Two Sides of the Same Coin: Heterophily and Oversmoothing in Graph Convolutional Neural Networks

TL;DR

This paper provides a unified node-level explanation for the oversmoothing and heterophily problems in graph convolutional neural networks, proposing strategies to mitigate both issues simultaneously.

Contribution

It introduces a theoretical framework linking node degree and heterophily to GCN performance, and proposes combined correction strategies for both problems.

Findings

The theory predicts GCN performance based on node metrics.

Edge correction strategies improve GCN robustness.

GGCN outperforms existing methods in heterophily and oversmoothing scenarios.

Abstract

In node classification tasks, graph convolutional neural networks (GCNs) have demonstrated competitive performance over traditional methods on diverse graph data. However, it is known that the performance of GCNs degrades with increasing number of layers (oversmoothing problem) and recent studies have also shown that GCNs may perform worse in heterophilous graphs, where neighboring nodes tend to belong to different classes (heterophily problem). These two problems are usually viewed as unrelated, and thus are studied independently, often at the graph filter level from a spectral perspective. We are the first to take a unified perspective to jointly explain the oversmoothing and heterophily problems at the node level. Specifically, we profile the nodes via two quantitative metrics: the relative degree of a node (compared to its neighbors) and the node-level heterophily. Our theory shows that the interplay of these two profiling metrics defines three cases of node behaviors, which explain the oversmoothing and heterophily problems jointly and can predict the performance of GCNs. Based on insights from our theory, we show theoretically and empirically the effectiveness of two strategies: structure-based edge correction, which learns corrected edge weights from structural properties (i.e., degrees), and feature-based edge correction, which learns signed edge weights from node features. Compared to other approaches, which tend to handle well either heterophily or oversmoothing, we show that {our model, GGCN}, which incorporates the two strategies performs well in both problems.