{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T03:45:20Z","timestamp":1774928720846,"version":"3.50.1"},"reference-count":76,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","issue":"1","license":[{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"},{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62431017"],"award-info":[{"award-number":["62431017"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62320106003"],"award-info":[{"award-number":["62320106003"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["U24A20251"],"award-info":[{"award-number":["U24A20251"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62125109"],"award-info":[{"award-number":["62125109"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62120106007"],"award-info":[{"award-number":["62120106007"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62371288"],"award-info":[{"award-number":["62371288"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62301299"],"award-info":[{"award-number":["62301299"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62401366"],"award-info":[{"award-number":["62401366"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62401357"],"award-info":[{"award-number":["62401357"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62401367"],"award-info":[{"award-number":["62401367"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Program of Shanghai Science and Technology Innovation Project","award":["24BC3200800"],"award-info":[{"award-number":["24BC3200800"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE Trans. Pattern Anal. Mach. Intell."],"published-print":{"date-parts":[[2026,1]]},"DOI":"10.1109\/tpami.2025.3603601","type":"journal-article","created":{"date-parts":[[2025,8,27]],"date-time":"2025-08-27T18:30:27Z","timestamp":1756319427000},"page":"251-269","source":"Crossref","is-referenced-by-count":1,"title":["Hierarchical Spherical CNNs With Lifting-Based Adaptive Wavelets for Pooling and Unpooling"],"prefix":"10.1109","volume":"48","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2883-1802","authenticated-orcid":false,"given":"Mingxing","family":"Xu","sequence":"first","affiliation":[{"name":"Department of Electronic Engineering, Shanghai Jiao Tong University, Shanghai, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2888-594X","authenticated-orcid":false,"given":"Chenglin","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Electronic Engineering, Shanghai Jiao Tong University, Shanghai, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2522-5778","authenticated-orcid":false,"given":"Wenrui","family":"Dai","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9144-0583","authenticated-orcid":false,"given":"Siheng","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Electronic Engineering, Shanghai Jiao Tong University, Shanghai, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9694-9880","authenticated-orcid":false,"given":"Junni","family":"Zou","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4010-714X","authenticated-orcid":false,"given":"Pascal","family":"Frossard","sequence":"additional","affiliation":[{"name":"Signal Processing Laboratory (LTS4), École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4552-0029","authenticated-orcid":false,"given":"Hongkai","family":"Xiong","sequence":"additional","affiliation":[{"name":"Department of Electronic Engineering, Shanghai Jiao Tong University, Shanghai, China"}]}],"member":"263","reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-01240-3_32"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2018.2858783"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1109\/TITS.2006.883116"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1109\/IROS.2010.5650380"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1177\/0278364913491297"},{"key":"ref6","first-page":"3405","article-title":"ExtremeWeather: A large-scale climate dataset for semi-supervised detection, localization, and understanding of extreme weather events","volume-title":"Proc. Adv. Neural Inf. Process. Syst.","author":"Racah"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1016\/j.ascom.2019.03.004"},{"key":"ref8","first-page":"3436","article-title":"Spherical convolutions and their application in molecular modeling","volume-title":"Proc. Adv. Neural Inf. Process. Syst.","author":"Boomsma"},{"key":"ref9","article-title":"Efficient generalized spherical CNNs","volume-title":"Proc. Int. Conf. Learn. Representations","author":"Cobb"},{"key":"ref10","first-page":"1321","article-title":"Gauge equivariant convolutional networks and the icosahedral CNN","volume-title":"Proc. Int. Conf. Mach. Learn.","author":"Cohen"},{"key":"ref11","article-title":"Spherical CNNs","volume-title":"Proc. Int. Conf. Learn. Representations","author":"Cohen"},{"key":"ref12","article-title":"DeepSphere: A graph-based spherical CNN","volume-title":"Proc. Int. Conf. Learn. Representations","author":"Defferrard"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-01261-8_4"},{"key":"ref14","first-page":"8614","article-title":"Spin-weighted spherical CNNs","volume-title":"Proc. Adv. Neural Inf. Process. Syst.","author":"Esteves"},{"key":"ref15","article-title":"Spherical CNNs on unstructured grids","volume-title":"Proc. Int. Conf. Learn. Representations","author":"Jiang"},{"key":"ref16","first-page":"10138","article-title":"Clebsch\u2013Gordan Nets: A fully fourier space spherical convolutional neural network","volume-title":"Proc. Adv. Neural Inf. Process. Syst.","author":"Kondor"},{"key":"ref17","article-title":"Scattering networks on the sphere for scalable and rotationally equivariant spherical CNNs","volume-title":"Proc. Int. Conf. Learn. Representations","author":"McEwen"},{"key":"ref18","first-page":"5105","article-title":"PointNet : Deep hierarchical feature learning on point sets in a metric space","volume-title":"Proc. Adv. Neural Inf. Process. Syst.","author":"Qi"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2020.2997045"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-24574-4_28"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2021.3081010"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR46437.2021.01458"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2016.2644615"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2016.80"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2017.698"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1137\/0722066"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1006\/aama.1994.1008"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1086\/427976"},{"key":"ref29","article-title":"LiftPool: Bidirectional convnet pooling","volume-title":"Proc. Int. Conf. Learn. Representations","author":"Zhao"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.5244\/C.35.334"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.24963\/ijcai.2018\/167"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1109\/tpami.2021.3113612"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2021.3100259"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1111\/j.1365-2966.2008.13448.x"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2016.03.009"},{"key":"ref36","doi-asserted-by":"publisher","DOI":"10.1063\/1.532481"},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1006\/acha.1999.0272"},{"key":"ref38","article-title":"A directional continuous wavelet transform on the sphere","author":"McEwen","year":"2006"},{"key":"ref39","doi-asserted-by":"publisher","DOI":"10.1006\/acha.1996.0015"},{"key":"ref40","doi-asserted-by":"publisher","DOI":"10.1137\/S0036141095289051"},{"key":"ref41","doi-asserted-by":"publisher","DOI":"10.1145\/218380.218439"},{"key":"ref42","first-page":"998","article-title":"Wavelets on graphs via deep learning","volume-title":"Proc. Adv. Neural Inf. Process. Syst.","author":"Rustamov"},{"key":"ref43","doi-asserted-by":"publisher","DOI":"10.1109\/TSIPN.2022.3140477"},{"key":"ref44","doi-asserted-by":"publisher","DOI":"10.1109\/WACV45572.2020.9093580"},{"key":"ref45","article-title":"Semi-supervised classification with graph convolutional networks","volume-title":"Proc. 5th Int. Conf. Learn. Representation","author":"Kipf"},{"key":"ref46","first-page":"1024","article-title":"Inductive representation learning on large graphs","volume-title":"Proc. Adv. Neural Inf. Process. Syst.","author":"Hamilton"},{"key":"ref47","article-title":"Graph attention networks","volume-title":"Proc. Int. Conf. Learn. Representations","author":"Veli\u010dkovi\u0107"},{"key":"ref48","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2020.2978386"},{"key":"ref49","doi-asserted-by":"publisher","DOI":"10.5555\/3294771.3294822"},{"key":"ref50","article-title":"","author":"Jacobson","year":"2012"},{"key":"ref51","first-page":"869","article-title":"Graph-based classification of omnidirectional images","volume-title":"Proc. IEEE Int. Conf. Comput. Vis. Workshops","author":"Khasanova"},{"key":"ref52","doi-asserted-by":"publisher","DOI":"10.1609\/aaai.v35i11.17154"},{"key":"ref53","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR42600.2020.00436"},{"key":"ref54","doi-asserted-by":"publisher","DOI":"10.1109\/ICCV.2019.00363"},{"key":"ref55","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2022.3202357"},{"key":"ref56","first-page":"396","article-title":"Handwritten digit recognition with a back-propagation network","volume-title":"Proc. Adv. Neural Inf. Process. Syst.","author":"LeCun"},{"key":"ref57","doi-asserted-by":"publisher","DOI":"10.1109\/ICCV.2009.5459469"},{"key":"ref58","first-page":"464","article-title":"Generalizing pooling functions in convolutional neural networks: Mixed, gated, and tree","volume-title":"Proc. Artif. Intell. Statist.","author":"Lee"},{"key":"ref59","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-11740-9_34"},{"key":"ref60","first-page":"307","article-title":"Signal recovery from pooling representations","volume-title":"Proc. Int. Conf. Mach. Learn.","author":"Estrach"},{"key":"ref61","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-44848-9_34"},{"key":"ref62","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2018.00949"},{"key":"ref63","article-title":"Wavelet pooling for convolutional neural networks","volume-title":"Proc. Int. Conf. Learn. Representations","author":"Williams"},{"key":"ref64","first-page":"1936","article-title":"Adaptive wavelet pooling for convolutional neural networks","volume-title":"Proc. Int. Conf. Artif. Intell. Statist.","author":"Wolter"},{"key":"ref65","doi-asserted-by":"publisher","DOI":"10.1016\/b978-0-12-374370-1.x0001-8"},{"key":"ref66","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2002.1011203"},{"key":"ref67","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2003.817237"},{"key":"ref68","doi-asserted-by":"publisher","DOI":"10.1109\/ICOSP.2004.1452654"},{"key":"ref69","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2021.3082465"},{"key":"ref70","first-page":"13578","article-title":"Graph normalizing flows","volume-title":"Proc. Adv. Neural Inf. Process. Syst.","author":"Liu"},{"key":"ref71","article-title":"Nice: Non-linear independent components estimation","volume-title":"Proc. Int. Conf. Learn. Representations Workshops","author":"Dinh"},{"key":"ref72","article-title":"Density estimation using real NVP","volume-title":"Proc. Int. Conf. Learn. Representations","author":"Dinh"},{"key":"ref73","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2012.2188718"},{"key":"ref74","article-title":"Learning multiple layers of features from tiny images","author":"Krizhevsky","year":"2009"},{"key":"ref75","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2015.7298801"},{"key":"ref76","article-title":"Joint 2D-3D-semantic data for indoor scene understanding","author":"Armeni","year":"2017"}],"container-title":["IEEE Transactions on Pattern Analysis and Machine Intelligence"],"original-title":[],"link":[{"URL":"http:\/\/xplorestaging.ieee.org\/ielx8\/34\/11275622\/11142951.pdf?arnumber=11142951","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,12,4]],"date-time":"2025-12-04T07:57:14Z","timestamp":1764835034000},"score":1,"resource":{"primary":{"URL":"https:\/\/ieeexplore.ieee.org\/document\/11142951\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,1]]},"references-count":76,"journal-issue":{"issue":"1"},"URL":"https:\/\/doi.org\/10.1109\/tpami.2025.3603601","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":[[2026,1]]}}}