{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T00:35:29Z","timestamp":1787013329262,"version":"build-2736575974"},"reference-count":41,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","issue":"2","license":[{"start":{"date-parts":[[2022,2,1]],"date-time":"2022-02-01T00:00:00Z","timestamp":1643673600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"},{"start":{"date-parts":[[2022,2,1]],"date-time":"2022-02-01T00:00:00Z","timestamp":1643673600000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"},{"start":{"date-parts":[[2022,2,1]],"date-time":"2022-02-01T00:00:00Z","timestamp":1643673600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2022,2,1]],"date-time":"2022-02-01T00:00:00Z","timestamp":1643673600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["IIS-1724174"],"award-info":[{"award-number":["IIS-1724174"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE Trans. Pattern Anal. Mach. Intell."],"published-print":{"date-parts":[[2022,2,1]]},"DOI":"10.1109\/tpami.2020.3035130","type":"journal-article","created":{"date-parts":[[2020,11,3]],"date-time":"2020-11-03T16:04:44Z","timestamp":1604419484000},"page":"823-833","source":"Crossref","is-referenced-by-count":10,"title":["VolterraNet: A Higher Order Convolutional Network With Group Equivariance for Homogeneous Manifolds"],"prefix":"10.1109","volume":"44","author":[{"given":"Monami","family":"Banerjee","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0448-911X","authenticated-orcid":false,"given":"Rudrasis","family":"Chakraborty","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jose","family":"Bouza","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1400-5844","authenticated-orcid":false,"given":"Baba C.","family":"Vemuri","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"263","reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1109\/5.726791"},{"key":"ref2","article-title":"Learning multiple layers of features from tiny images","author":"Krizhevsky","year":"2009"},{"key":"ref3","volume-title":"Theory of Functionals and of Integral and Integro-Differential Equations","author":"Volterra","year":"2005"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2017.758"},{"key":"ref5","first-page":"1","article-title":"Spherical CNNs","volume-title":"Proc. Int. Conf. Learn. Representations","author":"Cohen"},{"key":"ref6","first-page":"1","article-title":"Convolutional networks for spherical signals","volume-title":"Proc. 1st Workshop Principled Approaches Deep Learn. Int. Conf. Mach. Learn.","author":"Cohen"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-01261-8_4"},{"key":"ref8","article-title":"Clebsch-gordan nets: A fully fourier space spherical convolutional neural network","author":"Kondor","year":"2018"},{"key":"ref9","article-title":"Polar transformer networks","author":"Esteves","year":"2017"},{"key":"ref10","first-page":"2017","article-title":"Spatial transformer networks","volume-title":"Proc. 28th Int. Conf. Neural Inf. Process. Syst.","author":"Jaderberg"},{"key":"ref11","article-title":"On the generalization of equivariance and convolution in neural networks to the action of compact groups","author":"Kondor","year":"2018"},{"key":"ref12","article-title":"A general theory of equivariant CNNs on homogeneous spaces","author":"Cohen","year":"2018"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1006\/aama.1994.1008"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2009.5206837"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2011.225"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1109\/ACSSC.1991.186623"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1109\/ICCV.2017.510"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1090\/chel\/341"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1109\/ISBI.2019.8759558"},{"key":"ref20","volume-title":"Abstract Algebra","volume":"3","author":"Dummit","year":"2004"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-40409-6"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1090\/gsm\/093"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1016\/j.jco.2007.03.007"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1207\/s15516709cog1402_1"},{"key":"ref25","article-title":"Convolutional sequence modeling revisited","author":"Bai","year":"2018"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1017\/cbo9780511707162"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1109\/MFI.2017.8170406"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1137\/110853376"},{"key":"ref29","article-title":"A method for stochastic optimization","volume-title":"Proc. Int. Conf. Learn. Representations","volume":"5","author":"Kinga"},{"key":"ref30","article-title":"Large-scale 3D shape reconstruction and segmentation from shapenet core55","author":"Yi","year":"2017"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.1007\/s00371-008-0304-2"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.5244\/C.30.121"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2016.609"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2015.7298682"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1021\/ja902302h"},{"key":"ref36","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.108.058301"},{"key":"ref37","first-page":"440","article-title":"Learning invariant representations of molecules for atomization energy prediction","volume-title":"Proc. 25th Int. Conf. Neural Inf. Process. Syst.","author":"Montavon"},{"key":"ref38","article-title":"Local group invariant representations via orbit embeddings","author":"Raj","year":"2016"},{"key":"ref39","article-title":"Statistical recurrent models on manifold valued data","author":"Chakraborty","year":"2018","journal-title":"arXiv:1805.11204v1"},{"key":"ref40","doi-asserted-by":"publisher","DOI":"10.1093\/cercor\/bhx066"},{"key":"ref41","doi-asserted-by":"publisher","DOI":"10.3390\/econometrics4030032"}],"container-title":["IEEE Transactions on Pattern Analysis and Machine Intelligence"],"original-title":[],"link":[{"URL":"https:\/\/ieeexplore.ieee.org\/ielam\/34\/9674188\/9247263-aam.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"http:\/\/xplorestaging.ieee.org\/ielx7\/34\/9674188\/09247263.pdf?arnumber=9247263","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,1,9]],"date-time":"2024-01-09T17:42:57Z","timestamp":1704822177000},"score":1,"resource":{"primary":{"URL":"https:\/\/ieeexplore.ieee.org\/document\/9247263\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,2,1]]},"references-count":41,"journal-issue":{"issue":"2"},"URL":"https:\/\/doi.org\/10.1109\/tpami.2020.3035130","relation":{},"ISSN":["0162-8828","2160-9292","1939-3539"],"issn-type":[{"value":"0162-8828","type":"print"},{"value":"2160-9292","type":"electronic"},{"value":"1939-3539","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,2,1]]}}}