{"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/group-equivariant-capsule-networks","title":"Group Equivariant Capsule Networks","arxiv_id":"1806.05086","date":"2018-06-13","proceeding":"NeurIPS 2018 12","authors":["Jan Eric Lenssen","Matthias Fey","Pascal Libuschewski"],"abstract":"We present group equivariant capsule networks, a framework to introduce\nguaranteed equivariance and invariance properties to the capsule network idea.\nOur work can be divided into two contributions. First, we present a generic\nrouting by agreement algorithm defined on elements of a group and prove that\nequivariance of output pose vectors, as well as invariance of output\nactivations, hold under certain conditions. Second, we connect the resulting\nequivariant capsule networks with work from the field of group convolutional\nnetworks. Through this connection, we provide intuitions of how both methods\nrelate and are able to combine the strengths of both approaches in one deep\nneural network architecture. The resulting framework allows sparse evaluation\nof the group convolution operator, provides control over specific equivariance\nand invariance properties, and can use routing by agreement instead of pooling\noperations. In addition, it is able to provide interpretable and equivariant\nrepresentation vectors as output capsules, which disentangle evidence of object\nexistence from its pose.","url_abs":"http://arxiv.org/abs/1806.05086v2","url_pdf":"http://arxiv.org/pdf/1806.05086v2.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":"group-equivariant-capsule-networks","repo_url":"https://github.com/mrjel/group_equivariant_capsules_pytorch","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[],"methods":[{"method_slug":"fixcaps","method_name":"Capsule Network"},{"method_slug":"convolution","method_name":"Convolution"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1806.05086","atlas_url":"https://app.syntology.ai/?focus=1806.05086","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}