[Paper Review] Is Homophily a Necessity for Graph Neural Networks?

Yao Ma, Xiaorui Liu+2 more|arXiv (Cornell University)|Jun 11, 2021

Advanced Graph Neural NetworksComputer Science48 references58 citations

TL;DR

The paper shows that GCNs can perform well on heterophilous graphs under certain conditions, and it analyzes when homophily is or isn’t necessary for strong SSNC performance.

ABSTRACT

Graph neural networks (GNNs) have shown great prowess in learning representations suitable for numerous graph-based machine learning tasks. When applied to semi-supervised node classification, GNNs are widely believed to work well due to the homophily assumption ("like attracts like"), and fail to generalize to heterophilous graphs where dissimilar nodes connect. Recent works design new architectures to overcome such heterophily-related limitations, citing poor baseline performance and new architecture improvements on a few heterophilous graph benchmark datasets as evidence for this notion. In our experiments, we empirically find that standard graph convolutional networks (GCNs) can actually achieve better performance than such carefully designed methods on some commonly used heterophilous graphs. This motivates us to reconsider whether homophily is truly necessary for good GNN performance. We find that this claim is not quite true, and in fact, GCNs can achieve strong performance on heterophilous graphs under certain conditions. Our work carefully characterizes these conditions, and provides supporting theoretical understanding and empirical observations. Finally, we examine existing heterophilous graphs benchmarks and reconcile how the GCN (under)performs on them based on this understanding.

Motivation & Objective

• Investigate the role of homophily in GCN performance for semi-supervised node classification.
• Characterize conditions under which GCNs can perform well on heterophilous graphs.
• Provide theoretical explanations based on embedding behavior and neighborhood distributions.
• Evaluate GCNs on real-world and synthetic heterophilous graphs and compare with heterophily-specific models.

Proposed method

• Theoretically analyze GCN embeddings under assumptions about feature and neighbor distributions.
• Use a Contextual Stochastic Block Model (CSBM) to study linear separability after GCN smoothing.
• Derive bounds showing same-label embeddings concentrate and neighboring distributions influence separability.
• Empirically create synthetic heterophilous graphs by targeted edge addition and controlled noise to study performance trends.
• Compare GCN with MLP and heterophily-focused architectures on standard benchmarks.

Experimental results

Research questions

• RQ1 Under what heterophily conditions can a standard GCN achieve strong SSNC performance?
• RQ2 How do node degree and neighborhood distribution distinguishability affect GCN effectiveness?
• RQ3 What explanations can account for observed GCN performance on heterophilous real-world graphs?
• RQ4 How do synthetic perturbations to neighborhood patterns impact GCN versus specialized models?

Key findings

• GCN can outperform heterophily-tailored models on some heterophilous graphs with proper hyperparameter tuning.
• Same-label nodes can have similar GCN embeddings if their neighborhood patterns are similarly distributed, enabling good SSNC.
• Performance improves for high-degree nodes when neighbor distributions are distinguishable; very similar distributions yield limited benefits.
• There exist both “good” and “bad” heterophily; heterophily is not sufficient for poor GCN performance.
• On real benchmarks, GCN fares better than MLP on some heterophilous graphs (e.g., Squirrel, Chameleon) and worse on others.
• Adding edges according to target neighborhood distributions can create V-shaped performance trends, highlighting phase transitions in reliance on topology.