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This paper introduces novel distribution-free transductive generalization bounds based on optimal transport (OT) for graph node classification, where test features are available during training and representations are dependent. The bounds, expressed as Wasserstein distances between encoded feature distributions, are efficiently computable and correlate well with empirical generalization, outperforming classical complexity measures. The analysis reveals a depth-dependent trade-off between intra-class concentration and inter-class separation induced by GNN aggregation, explaining the non-monotonic relationship between depth and generalization error.
Optimal transport provides a surprisingly tight and efficiently computable bound on transductive generalization in graph node classification, revealing how GNN depth impacts representation geometry.
Many existing transductive bounds rely on classical complexity measures that are computationally intractable and often misaligned with empirical behavior. In this work, we establish new representation-based generalization bounds in a distribution-free transductive setting, where learned representations are dependent, and test features are accessible during training. We derive global and class-wise bounds via optimal transport, expressed in terms of Wasserstein distances between encoded feature distributions. We demonstrate that our bounds are efficiently computable and strongly correlate with empirical generalization in graph node classification, improving upon classical complexity measures. Additionally, our analysis reveals how the GNN aggregation process transforms the representation distributions, inducing a trade-off between intra-class concentration and inter-class separation. This yields depth-dependent characterizations that capture the non-monotonic relationship between depth and generalization error observed in practice. The code is available at https://github.com/ml-postech/Transductive-OT-Gen-Bound.
