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Knowl. Discov. Data"],"published-print":{"date-parts":[[2024,7,31]]},"abstract":"<jats:p>\n            Multiple recent studies show a paradox in graph convolutional networks (GCNs)\u2014that is, shallow architectures limit the capability of learning information from high-order neighbors, whereas deep architectures suffer from over-smoothing or over-squashing. To enjoy the simplicity of shallow architectures and overcome their limits of neighborhood extension, in this work we introduce a\n            <jats:italic>biaffine<\/jats:italic>\n            technique to improve the expressiveness of GCNs with a shallow architecture. The core design of our method is to learn direct dependency on long-distance neighbors for nodes, with which only 1-hop message passing is capable of capturing rich information for node representation. Besides, we propose a multi-view contrastive learning method to exploit the representations learned from long-distance dependencies. Extensive experiments on nine graph benchmark datasets suggest that the shallow biaffine graph convolutional networks (BAGCN) significantly outperform state-of-the-art GCNs (with deep or shallow architectures) on semi-supervised node classification. We further verify the effectiveness of biaffine design in node representation learning and the performance consistency on different sizes of training data.\n          <\/jats:p>","DOI":"10.1145\/3650113","type":"journal-article","created":{"date-parts":[[2024,3,1]],"date-time":"2024-03-01T12:10:40Z","timestamp":1709295040000},"page":"1-21","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":4,"title":["Building Shortcuts between Distant Nodes with Biaffine Mapping for Graph Convolutional Networks"],"prefix":"10.1145","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0009-0001-6654-8664","authenticated-orcid":false,"given":"Acong","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Computer Science and Software Engineering, Southwest Petroleum University, Chengdu, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8181-9410","authenticated-orcid":false,"given":"Jincheng","family":"Huang","sequence":"additional","affiliation":[{"name":"School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8391-6510","authenticated-orcid":false,"given":"Ping","family":"Li","sequence":"additional","affiliation":[{"name":"School of Computer Science and Software Engineering, Southwest Petroleum University, Chengdu, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6297-4423","authenticated-orcid":false,"given":"Kai","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology, East China Normal University, Shanghai, China"}]}],"member":"320","published-online":{"date-parts":[[2024,4,12]]},"reference":[{"key":"e_1_3_3_2_2","doi-asserted-by":"publisher","DOI":"10.1109\/TKDE.2018.2807452"},{"key":"e_1_3_3_3_2","article-title":"Deep learning on graphs: A survey","author":"Zhang Ziwei","year":"2020","unstructured":"Ziwei Zhang, Peng Cui, and Wenwu Zhu. 2020. 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In Proceedings of the International Conference on Machine Learning. 448\u2013456."},{"key":"e_1_3_3_55_2","volume-title":"Proceedings of the 3rd International Conference on Learning Representations: Conference Track (ICLR\u201915)","author":"Kingma Diederik P.","year":"2015","unstructured":"Diederik P. Kingma and Jimmy Ba. 2015. Adam: A method for stochastic optimization. In Proceedings of the 3rd International Conference on Learning Representations: Conference Track (ICLR\u201915)."},{"key":"e_1_3_3_56_2","article-title":"Deep graph contrastive representation learning","author":"Zhu Yanqiao","year":"2020","unstructured":"Yanqiao Zhu, Yichen Xu, Feng Yu, Qiang Liu, Shu Wu, and Liang Wang. 2020. 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