← 研踪 PaperTrailarXiv:2603.09257 · v2
Transductive Generalization for GNNs via Optimal Transport
首次提交 2026-03-10 14:43
版本更新 2026-11-09 00:32
雷达观测 2026-11-10 12:16
摘要
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. The code is available at https://github.com/ml-postech/Transductive-OT-Gen-Bound.
作者备注：accepted to NeurIPS 2026
观测到的版本
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v2 · 2026-11-09 00:32 · 最新观测版本
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. The code is available at https://github.com/ml-postech/Transductive-OT-Gen-Bound.
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