What Do Graph Convolutional Neural Networks Learn?

TL;DR

This paper investigates the learning mechanisms of Graph Convolutional Neural Networks (GCNs) in semi-supervised node classification, revealing how embedding similarity and neighborhood structure influence performance.

Contribution

It provides the first detailed analysis of what GCNs learn, linking embedding similarity and neighborhood structure to classification success.

Findings

Embedding similarity correlates with GCN performance.

Neighborhood structure consistency impacts GCN effectiveness.

GCNs perform well under certain structural conditions.

Abstract

Graph neural networks (GNNs) have gained traction over the past few years for their superior performance in numerous machine learning tasks. Graph Convolutional Neural Networks (GCN) are a common variant of GNNs that are known to have high performance in semi-supervised node classification (SSNC), and work well under the assumption of homophily. Recent literature has highlighted that GCNs can achieve strong performance on heterophilous graphs under certain "special conditions". These arguments motivate us to understand why, and how, GCNs learn to perform SSNC. We find a positive correlation between similarity of latent node embeddings of nodes within a class and the performance of a GCN. Our investigation on underlying graph structures of a dataset finds that a GCN's SSNC performance is significantly influenced by the consistency and uniqueness in neighborhood structure of nodes within a class.