Transductive Generalization via Optimal Transport and Its Application to Graph Node Classification
This work addresses the challenge of providing practical generalization guarantees for transductive learning, particularly in graph node classification, offering insights into GNN behavior, but it is incremental as it builds on existing transductive and optimal transport frameworks.
The paper tackles the problem of deriving computationally tractable generalization bounds for transductive learning, where test features are accessible during training, by establishing new bounds based on optimal transport and Wasserstein distances between encoded feature distributions. The result shows that these bounds are efficiently computable and strongly correlate with empirical generalization in graph node classification, improving upon classical complexity measures and capturing depth-dependent trade-offs in GNNs.
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.