{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,25]],"date-time":"2026-02-25T22:02:57Z","timestamp":1772056977700,"version":"3.50.1"},"reference-count":61,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","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\/501100012166","name":"National Key R&D Program of China","doi-asserted-by":"publisher","award":["2025YFF0515602"],"award-info":[{"award-number":["2025YFF0515602"]}],"id":[{"id":"10.13039\/501100012166","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":["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":["62125109"],"award-info":[{"award-number":["62125109"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE Trans. Signal Process."],"published-print":{"date-parts":[[2026]]},"DOI":"10.1109\/tsp.2026.3660885","type":"journal-article","created":{"date-parts":[[2026,2,4]],"date-time":"2026-02-04T20:49:53Z","timestamp":1770238193000},"page":"701-716","source":"Crossref","is-referenced-by-count":0,"title":["Stable Representation Learning via Generalized Learnable Graph Scattering Transform"],"prefix":"10.1109","volume":"74","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-4083-1792","authenticated-orcid":false,"given":"Shiyu","family":"Liu","sequence":"first","affiliation":[{"name":"Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2522-5778","authenticated-orcid":false,"given":"Wenrui","family":"Dai","sequence":"additional","affiliation":[{"name":"Department of Electronic Engineering, Shanghai Jiao Tong University, Shanghai, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9650-8874","authenticated-orcid":false,"given":"Shaohui","family":"Li","sequence":"additional","affiliation":[{"name":"College of Information Science and Electronic Engineering, Zhejiang University, Hangzhou, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9923-8016","authenticated-orcid":false,"given":"Ziyang","family":"Zheng","sequence":"additional","affiliation":[{"name":"Department of Electronic Engineering, Shanghai Jiao Tong University, Shanghai, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9694-9880","authenticated-orcid":false,"given":"Junni","family":"Zou","sequence":"additional","affiliation":[{"name":"Department of Electronic Engineering, Shanghai Jiao Tong University, Shanghai, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"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"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"263","reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2012.230"},{"key":"ref2","first-page":"14498","article-title":"Scattering GCN: Overcoming oversmoothness in graph convolutional networks","volume-title":"Proc. Adv. Neural Inf. Process. Syst.","volume":"33","author":"Min","year":"2020"},{"key":"ref3","first-page":"8038","article-title":"Stability of graph scattering transforms","volume-title":"Proc. Adv. Neural Inf. Process. Syst.","volume":"32","author":"Gama","year":"2019"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2019.06.003"},{"key":"ref5","first-page":"2122","article-title":"Geometric scattering for graph data analysis","volume-title":"Proc. 36th Int. Conf. Mach. Learn.","author":"Gao","year":"2019"},{"key":"ref6","article-title":"Diffusion scattering transforms on graphs","volume-title":"Proc. 7th Int. Conf. Learn. Representations","author":"Gama","year":"2019"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2006.04.004"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1109\/ISIT.2015.7282648"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2017.2776228"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2020.3026980"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2010.04.005"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2021.3098936"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.11650\/twjm\/1500406535"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1190\/1.1437843"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1186\/s13660-022-02809-w"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1023\/A:1026553619983"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1109\/ICASSP40776.2020.9054072"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1109\/5.726791"},{"key":"ref19","article-title":"Pruned graph scattering transforms","volume-title":"Proc. 8th Int. Conf. Learn. Representations","author":"Ioannidis","year":"2020"},{"key":"ref20","article-title":"Spectral networks and locally connected networks on graphs","volume-title":"Proc. 2nd Int. Conf. Learn. Representations","author":"Bruna","year":"2014"},{"key":"ref21","first-page":"3844","article-title":"Convolutional neural networks on graphs with fast localized spectral filtering","volume-title":"Proc. Adv. Neural Inf. Process. Syst.","volume":"29","author":"Defferrard","year":"2016"},{"key":"ref22","article-title":"Semi-supervised classification with graph convolutional networks","volume-title":"Proc. 5th Int. Conf. Learn. Representations","author":"Kipf","year":"2017"},{"key":"ref23","article-title":"Graph attention networks","volume-title":"Proc. 6th Int. Conf. Learn. Representations","author":"Veli\u010dkovi\u0107","year":"2018"},{"key":"ref24","article-title":"LanczosNet: Multi-scale deep graph convolutional networks","volume-title":"Proc. 7th Int. Conf. Learn. Representations","author":"Liao","year":"2019"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2018.2879624"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2021.3054830"},{"key":"ref27","first-page":"6009","article-title":"DFNets: Spectral CNNs for graphs with feedback-looped filters","volume-title":"Proc. Adv. Neural Inf. Process. Syst.","volume":"32","author":"Wijesinghe","year":"2019"},{"key":"ref28","article-title":"Graph wavelet neural network","volume-title":"Proc. 7th Int. Conf. Learn. Representations","author":"Xu","year":"2019"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1117\/12.2186921"},{"issue":"1","key":"ref30","first-page":"876","article-title":"Group invariance, stability to deformations, and complexity of deep convolutional representations","volume":"20","author":"Bietti","year":"2019","journal-title":"J. Mach. Learn. Res."},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2019.2961812"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1109\/TSIPN.2021.3109820"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1007\/s11222-007-9033-z"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1109\/TNN.2008.2005605"},{"key":"ref35","first-page":"1025","article-title":"Inductive representation learning on large graphs","volume-title":"Proc. Adv. Neural Inf. Process. Syst.","volume":"30","author":"Hamilton","year":"2017"},{"key":"ref36","first-page":"499","article-title":"Dual graph convolutional networks for graph-based semi-supervised classification","volume-title":"Proc. World Wide Web Conf.","author":"Chenyi","year":"2018"},{"key":"ref37","article-title":"Order matters: Sequence to sequence for sets","volume-title":"Proc. 3rd Int. Conf. Learn. Representations","author":"Vinyals","year":"2015"},{"key":"ref38","article-title":"graph2vec: Learning distributed representations of graphs","volume-title":"Proc. 13th Int. Workshop Min. Learn. Graphs (MLG)","author":"Narayanan","year":"2017"},{"key":"ref39","article-title":"Benchmark data sets for graph kernels","author":"Kersting","year":"2016"},{"key":"ref40","doi-asserted-by":"publisher","DOI":"10.1109\/mlsp52302.2021.9596169"},{"key":"ref41","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2024.3378001"},{"key":"ref42","doi-asserted-by":"publisher","DOI":"10.1609\/aaai.v32i1.11782"},{"key":"ref43","article-title":"Invariant and equivariant graph networks","volume-title":"Proc. 7th Int. Conf. Learn. Representations","author":"Maron","year":"2019"},{"key":"ref44","doi-asserted-by":"publisher","DOI":"10.1109\/ICCV.2019.00936"},{"key":"ref45","first-page":"21","article-title":"MixHop: Higher-order graph convolutional architectures via sparsified neighborhood mixing","volume-title":"Proc. 36th Int. Conf. Mach. Learn.","author":"Abu-El-Haija","year":"2019"},{"key":"ref46","first-page":"8376","article-title":"Revisiting graph neural networks: All we have is low-pass filters","volume-title":"Proc. 25th Int. Conf. Pattern Recognit. (ICPR)","author":"Hoang","year":"2020"},{"key":"ref47","doi-asserted-by":"publisher","DOI":"10.23919\/EUSIPCO55093.2022.9909669"},{"key":"ref48","doi-asserted-by":"publisher","DOI":"10.1109\/ICASSP39728.2021.9414557"},{"key":"ref49","doi-asserted-by":"publisher","DOI":"10.1109\/ICASSP43922.2022.9747790"},{"key":"ref50","doi-asserted-by":"publisher","DOI":"10.1093\/imaiai\/iaw007"},{"key":"ref51","doi-asserted-by":"publisher","DOI":"10.1109\/mlsp55214.2022.9943379"},{"key":"ref52","doi-asserted-by":"publisher","DOI":"10.1109\/ICSP58490.2023.10248927"},{"key":"ref53","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2023.3297848"},{"key":"ref54","article-title":"KAN: Kolmogorov\u2013Arnold networks","volume-title":"Proc. 13th Int. Conf. Learn. Representations","author":"Liu","year":"2025"},{"key":"ref55","article-title":"SpecFormer: Spectral graph neural networks meet transformers","volume-title":"Proc. 11th Int. Conf. Learn. Representations","author":"Bo","year":"2023"},{"key":"ref56","article-title":"Pitfalls of graph neural network evaluation","author":"Shchur","year":"2018"},{"key":"ref57","article-title":"A critical look at the evaluation of GNNs under heterophily: Are we really making progress?","volume-title":"Proc. 11th Int. Conf. Learn. Representations","author":"Platonov","year":"2023"},{"key":"ref58","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2024.101635"},{"key":"ref59","first-page":"30219","article-title":"Graph scattering beyond wavelet shackles","volume-title":"Proc. Adv. Neural Inf. Process. Syst.","volume":"35","author":"Koke","year":"2022"},{"key":"ref60","first-page":"23341","article-title":"How powerful are spectral graph neural networks","volume-title":"Proc. 39th Int. Conf. Mach. Learn.","author":"Wang","year":"2022"},{"key":"ref61","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2024.3392360"}],"container-title":["IEEE Transactions on Signal Processing"],"original-title":[],"link":[{"URL":"http:\/\/xplorestaging.ieee.org\/ielx8\/78\/11345506\/11372127.pdf?arnumber=11372127","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,25]],"date-time":"2026-02-25T20:59:04Z","timestamp":1772053144000},"score":1,"resource":{"primary":{"URL":"https:\/\/ieeexplore.ieee.org\/document\/11372127\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026]]},"references-count":61,"URL":"https:\/\/doi.org\/10.1109\/tsp.2026.3660885","relation":{},"ISSN":["1053-587X","1941-0476"],"issn-type":[{"value":"1053-587X","type":"print"},{"value":"1941-0476","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026]]}}}