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Data"],"published-print":{"date-parts":[[2026,1,31]]},"abstract":"<jats:p>\n                    Graph neural networks (GNNs) have essentially taken over as the\n                    <jats:italic toggle=\"yes\">de facto<\/jats:italic>\n                    model for learning graph-structured data. However, the majority of existing methods perform transductive learning in a known graph, which is unable to tackle abundant in-the-wild unseen graphs with potential domain shifts. Even worse, these graphs, accompanied by domain shifts on structural topology and node attributes, bring in vulnerable data bias and thus a huge drop in performance. To tackle this, we propose a novel GNN method named spectral optimal transport (SPOT) for effective domain generalization on graphs. Our method is motivated by the fact that the high-frequency graph spectrum is more likely to indicate domain differences. In particular, we formulate the structural augmentation as an optimal transport problem to retain low-frequency key knowledge and solve the problem using Sinkhorn-Knopp algorithm. In addition, we incorporate an adaptive perturbation strategy to deep features, where the direction of the additive noise is determined by the homophily degrees to maintain semantic properties. Accordingly, we meticulously construct a collection of real-world benchmark datasets to assess the domain generalization capability of our model on graphs, and extensive experiments confirm the effectiveness of our proposed SPOT.\n                  <\/jats:p>","DOI":"10.1145\/3772720","type":"journal-article","created":{"date-parts":[[2025,10,23]],"date-time":"2025-10-23T14:20:26Z","timestamp":1761229226000},"page":"1-22","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["SPOT: Spectral Optimal Transport for Graph Domain Generalization"],"prefix":"10.1145","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0830-0468","authenticated-orcid":false,"given":"Yusheng","family":"Zhao","sequence":"first","affiliation":[{"name":"State Key Laboratory for Multimedia Information Processing, School of Computer Science, PKU-Anker LLM Lab, Peking University, Beijing, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7987-3714","authenticated-orcid":false,"given":"Xiao","family":"Luo","sequence":"additional","affiliation":[{"name":"Department of Statistics, University of Wisconsin\u2013Madison, Madison, Wisconsin, USA"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-6894-1144","authenticated-orcid":false,"given":"Junyu","family":"Luo","sequence":"additional","affiliation":[{"name":"State Key Laboratory for Multimedia Information Processing, School of Computer Science, PKU-Anker LLM Lab, Peking University, Beijing, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9657-951X","authenticated-orcid":false,"given":"Wei","family":"Ju","sequence":"additional","affiliation":[{"name":"State Key Laboratory for Multimedia Information Processing, School of Computer Science, PKU-Anker LLM Lab, Peking University, Beijing, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6142-4358","authenticated-orcid":false,"given":"Zhonghui","family":"Gu","sequence":"additional","affiliation":[{"name":"Peking-Tsinghua Center for Life Sciences, Academy for Advanced Interdisciplinary Studies, Peking University, Beijing, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8583-4789","authenticated-orcid":false,"given":"Zhiping","family":"Xiao","sequence":"additional","affiliation":[{"name":"Paul G. Allen School of Computer Science and Engineering, University of Washington, Seattle, Washington, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8232-5049","authenticated-orcid":false,"given":"Xian-Sheng","family":"Hua","sequence":"additional","affiliation":[{"name":"Terminus Group, Beijing, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9809-3430","authenticated-orcid":false,"given":"Ming","family":"Zhang","sequence":"additional","affiliation":[{"name":"State Key Laboratory for Multimedia Information Processing, School of Computer Science, PKU-Anker LLM Lab, Peking University, Beijing, China"}]}],"member":"320","published-online":{"date-parts":[[2025,11,21]]},"reference":[{"key":"e_1_3_2_2_2","unstructured":"Isabela Albuquerque Jo\u00e3o Monteiro Mohammad Darvishi Tiago H. Falk and Ioannis Mitliagkas. 2019. Generalizing to unseen domains via distribution matching. arXiv:1911.00804. 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Retrieved from https:\/\/arxiv.org\/abs\/1412.6980"},{"key":"e_1_3_2_42_2","volume-title":"ICLR","author":"Kipf Thomas N.","year":"2017","unstructured":"Thomas N. Kipf and Max Welling. 2017. Semi-supervised classification with graph convolutional networks. In ICLR."},{"issue":"22","key":"e_1_3_2_43_2","first-page":"1","article-title":"A unified framework for structured graph learning via spectral constraints","volume":"21","author":"Kumar Sandeep","year":"2020","unstructured":"Sandeep Kumar, Jiaxi Ying, Jos\u00e9 Vin\u00edcius de M. Cardoso, and Daniel P. Palomar. 2020. A unified framework for structured graph learning via spectral constraints. Journal of Machine Learning Research 21, 22 (2020), 1\u201360.","journal-title":"Journal of Machine Learning Research"},{"key":"e_1_3_2_44_2","first-page":"11906","volume-title":"ICML","author":"Lan Shiyong","year":"2022","unstructured":"Shiyong Lan, Yitong Ma, Weikang Huang, Wenwu Wang, Hongyu Yang, and Pyang Li. 2022. 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PALA: Class-imbalanced graph domain adaptation via prototype-anchored learning and alignment. In IJCAI, 3198\u20133207."},{"key":"e_1_3_2_62_2","doi-asserted-by":"publisher","DOI":"10.1109\/ICCV48922.2021.00656"},{"key":"e_1_3_2_63_2","unstructured":"Hoang Nt and Takanori Maehara. 2019. Revisiting graph neural networks: All we have is low-pass filters. arXiv:1905.09550. Retrieved from https:\/\/arxiv.org\/abs\/1905.09550"},{"key":"e_1_3_2_64_2","doi-asserted-by":"publisher","DOI":"10.1109\/JPROC.2018.2820126"},{"key":"e_1_3_2_65_2","first-page":"309","volume-title":"MM","author":"Pang Jinhui","year":"2023","unstructured":"Jinhui Pang, Zixuan Wang, Jiliang Tang, Mingyan Xiao, and Nan Yin. 2023. Sa-gda: Spectral augmentation for graph domain adaptation. 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Retrieved from https:\/\/arxiv.org\/abs\/1710.10903"},{"key":"e_1_3_2_79_2","volume-title":"ICLR","author":"Veli\u010dkovi\u0107 Petar","year":"2018","unstructured":"Petar Veli\u010dkovi\u0107, Guillem Cucurull, Arantxa Casanova, Adriana Romero, Pietro Lio, and Yoshua Bengio. 2018. Graph attention networks. In ICLR."},{"key":"e_1_3_2_80_2","volume-title":"NeurIPS","author":"Volpi Riccardo","year":"2018","unstructured":"Riccardo Volpi, Hongseok Namkoong, Ozan Sener, John C. Duchi, Vittorio Murino, and Silvio Savarese. 2018. Generalizing to unseen domains via adversarial data augmentation. In NeurIPS."},{"key":"e_1_3_2_81_2","first-page":"2215","article-title":"On calibration and out-of-domain generalization","volume":"34","author":"Wald Yoav","year":"2021","unstructured":"Yoav Wald, Amir Feder, Daniel Greenfeld, and Uri Shalit. 2021. On calibration and out-of-domain generalization. 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In ICLR."},{"key":"e_1_3_2_96_2","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR46437.2021.01415"},{"key":"e_1_3_2_97_2","doi-asserted-by":"publisher","DOI":"10.1038\/s42256-024-00899-3"},{"key":"e_1_3_2_98_2","first-page":"25261","volume-title":"ICML","author":"Yang Mingqi","year":"2022","unstructured":"Mingqi Yang, Yanming Shen, Rui Li, Heng Qi, Qiang Zhang, and Baocai Yin. 2022. A new perspective on the effects of spectrum in graph neural networks. In ICML. PMLR, 25261\u201325279."},{"key":"e_1_3_2_99_2","doi-asserted-by":"publisher","DOI":"10.1145\/3641549"},{"key":"e_1_3_2_100_2","doi-asserted-by":"crossref","first-page":"103708","DOI":"10.1016\/j.artint.2022.103708","article-title":"Multi-view graph convolutional networks with attention mechanism","volume":"307","author":"Yao Kaixuan","year":"2022","unstructured":"Kaixuan Yao, Jiye Liang, Jianqing Liang, Ming Li, and Feilong Cao. 2022. Multi-view graph convolutional networks with attention mechanism. 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Retrieved from https:\/\/arxiv.org\/abs\/2505.17599"},{"key":"e_1_3_2_117_2","unstructured":"Xin Zheng Yi Wang Yixin Liu Ming Li Miao Zhang Di Jin Philip S. Yu and Shirui Pan. 2022. Graph neural networks for graphs with heterophily: A survey. arXiv:2202.07082. Retrieved from https:\/\/arxiv.org\/abs\/2202.07082"},{"issue":"3","key":"e_1_3_2_118_2","first-page":"1","article-title":"Mixstyle neural networks for domain generalization and adaptation","volume":"132","author":"Zhou Kaiyang","year":"2023","unstructured":"Kaiyang Zhou, Yongxin Yang, Yu Qiao, and Tao Xiang. 2023. Mixstyle neural networks for domain generalization and adaptation. International Journal of Computer Vision 132, 3 (2023), 1\u201315.","journal-title":"International Journal of Computer Vision"},{"key":"e_1_3_2_119_2","volume-title":"IZCLR","author":"Zhu Ronghang","year":"2022","unstructured":"Ronghang Zhu and Sheng Li. 2022. 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