Transductive Generalization for GNNs via Optimal Transport

Analyzing the generalization of graph neural networks (GNNs) on node classification is challenging: message passing induces dependencies that break the i.i.d. assumption underlying standard inductive generalization theory. While distribution-free transductive theory resolves this dependency issue, existing classical bounds are either intractable or correlate poorly with empirical generalization. To fill this gap, we propose a transductive generalization bound based on optimal transport, connecting generalization to intra-class concentration and inter-class separation in the feature space. Empirically, our bound aligns strongly with the generalization gap. Building on this representation-based approach, we analyze how feature geometry evolves under repeated message passing. This explains the non-monotonic relationship between GNN depth and generalization, providing new insights into oversmoothing research. Practically, our bound serves as a geometry-aware regularizer that corrects the harmful behavior of message passing, yielding consistent performance improvements.