{"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/deep-quaternion-networks","title":"Deep Quaternion Networks","arxiv_id":"1712.04604","date":"2017-12-13","proceeding":null,"authors":["Chase Gaudet","Anthony Maida"],"abstract":"The field of deep learning has seen significant advancement in recent years.\nHowever, much of the existing work has been focused on real-valued numbers.\nRecent work has shown that a deep learning system using the complex numbers can\nbe deeper for a fixed parameter budget compared to its real-valued counterpart.\nIn this work, we explore the benefits of generalizing one step further into the\nhyper-complex numbers, quaternions specifically, and provide the architecture\ncomponents needed to build deep quaternion networks. We develop the theoretical\nbasis by reviewing quaternion convolutions, developing a novel quaternion\nweight initialization scheme, and developing novel algorithms for quaternion\nbatch-normalization. These pieces are tested in a classification model by\nend-to-end training on the CIFAR-10 and CIFAR-100 data sets and a segmentation\nmodel by end-to-end training on the KITTI Road Segmentation data set. These\nquaternion networks show improved convergence compared to real-valued and\ncomplex-valued networks, especially on the segmentation task, while having\nfewer parameters","url_abs":"http://arxiv.org/abs/1712.04604v3","url_pdf":"http://arxiv.org/pdf/1712.04604v3.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":"deep-quaternion-networks","repo_url":"https://github.com/gaudetcj/DeepQuaternionNetworks","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"deep-quaternion-networks","repo_url":"https://github.com/heheqianqian/DeepQuaternionNetworks","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"unanswered"}}],"tasks":[{"task_slug":"road-segementation","task_name":"Road Segmentation"},{"task_slug":"segmentation","task_name":"Segmentation"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1712.04604","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1712.04604"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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