Transductive Generalization via Optimal Transport and Its Application to Graph Node Classification
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arXiv
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| Autores principales: | , , , , , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866910047388303360 |
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| author | Park, MoonJeong Lee, Seungbeom Kim, Kyungmin Heo, Jaeseung Cho, Seunghyuk Li, Shouheng Park, Sangdon Kim, Dongwoo |
| author_facet | Park, MoonJeong Lee, Seungbeom Kim, Kyungmin Heo, Jaeseung Cho, Seunghyuk Li, Shouheng Park, Sangdon Kim, Dongwoo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_09257 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Transductive Generalization via Optimal Transport and Its Application to Graph Node Classification Park, MoonJeong Lee, Seungbeom Kim, Kyungmin Heo, Jaeseung Cho, Seunghyuk Li, Shouheng Park, Sangdon Kim, Dongwoo Machine Learning 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. |
| title | Transductive Generalization via Optimal Transport and Its Application to Graph Node Classification |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2603.09257 |