Generalization of Spectral Graph Neural Networks

Fangbing Liu, Qing Wang

Keywords: graph learning, graph neural networks, generalization, node classification, uniform stability

TL;DR: We study the generalization of spectral graph neural networks in node classification tasks, especially how the generalization is affected by the graph homophily and the architecture of spectral GNNs.

Abstract: Spectral graph neural networks (GNNs) have achieved remarkable success across various applications, yet their generalization properties remain poorly understood. This paper bridges this gap by analyzing the impact of graph homophily and architectural choices on the generalization of spectral GNNs. We derive a general form of uniform transductive stability for spectral GNNs and provide an explicit stability analysis for graphs with two node classes, providing a comprehensive framework to understand their generalization. Based on this stability analysis, we establish a generalization error bound, demonstrating that better stability leads to improved generalization. Our theoretical findings reveal that spectral GNNs generalize well on graphs with strong homophily or heterophily but struggle on graphs with weaker structural properties. We also identify conditions under which increasing the polynomial order in spectral GNN architectures may degrade generalization. Empirical results on synthetic and real-world benchmark datasets align closely with our theoretical findings.

Primary Area: learning on graphs and other geometries & topologies

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Submission Number: 6170