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Data"],"published-print":{"date-parts":[[2025,9,30]]},"abstract":"<jats:p>Graph Transformers have demonstrated outstanding performance across various graph-based applications. Despite their success, applying them to large-scale graphs presents significant scalability challenges, limiting their practical use in industrial environments. Recent studies have attempted to overcome this challenge by focusing on the spatial domain of graphs, leading to the development of various scalable models. However, these approaches neglect the spectral characteristics of graphs, which are crucial for adaptively extracting information from full-frequency bands based on the graph\u2019s inherent properties. As a result, existing scalable Graph Transformers tend to rely heavily on low-frequency features, overlooking valuable mid- and high-frequency information.<\/jats:p>\n          <jats:p>This article proposes the Graph Filter Transformer (GFformer), a framework designed to effectively extract full-frequency information from large-scale graphs. Unlike existing Graph Transformers, GFformer integrates graph filters into the Transformer architecture, thereby enhancing its ability to model both structural and frequency-related properties. Utilizing the proposed Spectral Token Converter (ST-converter), GFformer generates a unique spectral token sequence for each node by incorporating features from diverse frequencies that act as tokens. This design enables the independent learning of node representations in parallel and supports mini-batch training with flexible batch sizes, making GFformer highly scalable. ST-converter employs spectral graph filters, including low-, mid-, and high-pass filters, to extract features serving as tokens. Consequently, each sequence encompasses features from various frequencies, enabling GFformer to capture comprehensive frequency information effectively. Extensive experiments on datasets of varying scales, including both homophilic and heterophilic graphs, consistently demonstrate that GFformer outperforms existing representative methods.<\/jats:p>","DOI":"10.1145\/3750051","type":"journal-article","created":{"date-parts":[[2025,7,23]],"date-time":"2025-07-23T16:54:51Z","timestamp":1753289691000},"page":"1-20","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":2,"title":["GFformer: A Graph Transformer for Extracting All Frequency Information from Large-scale Graphs"],"prefix":"10.1145","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3096-8261","authenticated-orcid":false,"given":"Qi","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Information Science and Technology, Beijing University of Technology, Beijing, China and School of Information Science and Engineering, Shandong Agricultural University, Tai\u2019an, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0007-0685-8672","authenticated-orcid":false,"given":"Mengmeng","family":"Si","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Henan Normal University, Xinxiang, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0872-384X","authenticated-orcid":false,"given":"Yanfeng","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Information Science and Technology, Beijing University of Technology, Beijing, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3045-624X","authenticated-orcid":false,"given":"Shaofan","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Information Science and Technology, Beijing University of Technology, Beijing, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9803-0256","authenticated-orcid":false,"given":"Junbin","family":"Gao","sequence":"additional","affiliation":[{"name":"The University of Sydney Business School, The University of Sydney, Sydney, Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3121-1823","authenticated-orcid":false,"given":"Baocai","family":"Yin","sequence":"additional","affiliation":[{"name":"School of Information Science and Technology, Beijing University of Technology, Beijing, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2025,9,8]]},"reference":[{"key":"e_1_3_1_2_2","first-page":"1","volume-title":"Proceedings of the International Conference on Learning Representations","author":"Alon Uri","year":"2021","unstructured":"Uri Alon and Eran Yahav. 2021. 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