Generalization Bound for GNNs on Transductive Node Classification: A View from Optimal Transport

MoonJeong Park, Seungbeom Lee, Kyungmin Kim, Jaeseung Heo, Seunghyuk Cho, Shouheng Li, Sangdon Park, Dongwoo Kim

Keywords: gnn, generalization bound, transductive setting

Abstract: The generalization ability of graph neural networks (GNNs) remains insufficiently understood, especially for node classification where node embeddings are inherently dependent on the entire graph structure. In this work, we establish new generalization error bounds for GNNs in the transductive node classification setting. Building on distribution-free transductive learning theory, we derive global and class-wise bounds expressed in terms of the Wasserstein distance of node features' distribution. Our analysis reveals how the GNN aggregation process transforms representation distributions and enables rigorous control of the generalization gap. We further specialize our results to the case of Simple Graph Convolution, providing explicit spectral characterizations of the bound. Empirical evaluations across homophilic and heterophilic benchmark datasets confirm that the proposed bounds accurately capture generalization behavior. These results advance the theoretical understanding of GNNs by providing the first Wasserstein-based generalization guarantees tailored to node classification.

Primary Area: learning on graphs and other geometries & topologies

Submission Number: 9058