Transductive Generalization via Optimal Transport and Its Application to Graph Node Classification

2026-03-10

AI Summary

This work addresses the limitations of existing transductive learning generalization bounds, which rely on classical complexity measures that are computationally intractable and poorly aligned with empirical performance. Under a distribution-free transductive setting, the authors propose a novel generalization bound grounded in optimal transport theory, leveraging the Wasserstein distance to quantify the discrepancy between encoded feature distributions. This bound is efficiently computable, exhibits strong correlation with empirical generalization error, and reveals a representation trade-off in graph neural networks (GNNs)—namely, the balance between intra-class aggregation and inter-class separation during message passing. The proposed measure significantly outperforms conventional metrics, effectively explaining the non-monotonic relationship between GNN depth and generalization error, and demonstrates strong predictive power on node classification tasks.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

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.

Problem

• transductive generalization
• graph node classification
• generalization bounds
• optimal transport
• Wasserstein distance

Innovation

• Optimal Transport
• Transductive Generalization
• Wasserstein Distance
• Graph Neural Networks
• Representation Distribution