{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/graph-kernel-attention-transformers","title":"From block-Toeplitz matrices to differential equations on graphs: towards a general theory for scalable masked Transformers","arxiv_id":"2107.07999","date":"2021-07-16","proceeding":null,"authors":["Krzysztof Choromanski","Han Lin","Haoxian Chen","Tianyi Zhang","Arijit Sehanobish","Valerii Likhosherstov","Jack Parker-Holder","Tamas Sarlos","Adrian Weller","Thomas Weingarten"],"abstract":"In this paper we provide, to the best of our knowledge, the first comprehensive approach for incorporating various masking mechanisms into Transformers architectures in a scalable way. We show that recent results on linear causal attention (Choromanski et al., 2021) and log-linear RPE-attention (Luo et al., 2021) are special cases of this general mechanism. However by casting the problem as a topological (graph-based) modulation of unmasked attention, we obtain several results unknown before, including efficient d-dimensional RPE-masking and graph-kernel masking. We leverage many mathematical techniques ranging from spectral analysis through dynamic programming and random walks to new algorithms for solving Markov processes on graphs. We provide a corresponding empirical evaluation.","url_abs":"https://arxiv.org/abs/2107.07999v8","url_pdf":"https://arxiv.org/pdf/2107.07999v8.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"graph-kernel-attention-transformers","repo_url":"https://github.com/hl-hanlin/gkat","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[{"task_slug":"graph-attention","task_name":"Graph Attention"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2107.07999","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}