{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,9]],"date-time":"2026-03-09T23:33:49Z","timestamp":1773099229633,"version":"3.50.1"},"reference-count":56,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","issue":"9","license":[{"start":{"date-parts":[[2023,9,1]],"date-time":"2023-09-01T00:00:00Z","timestamp":1693526400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"},{"start":{"date-parts":[[2023,9,1]],"date-time":"2023-09-01T00:00:00Z","timestamp":1693526400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2023,9,1]],"date-time":"2023-09-01T00:00:00Z","timestamp":1693526400000},"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":["12131004"],"award-info":[{"award-number":["12131004"]}],"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":["11971052"],"award-info":[{"award-number":["11971052"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004826","name":"Beijing Natural Science Foundation","doi-asserted-by":"publisher","award":["Z190002"],"award-info":[{"award-number":["Z190002"]}],"id":[{"id":"10.13039\/501100004826","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE Trans. Neural Netw. Learning Syst."],"published-print":{"date-parts":[[2023,9]]},"DOI":"10.1109\/tnnls.2021.3131406","type":"journal-article","created":{"date-parts":[[2021,12,13]],"date-time":"2021-12-13T20:52:25Z","timestamp":1639428745000},"page":"5882-5896","source":"Crossref","is-referenced-by-count":6,"title":["Recursion Newton-Like Algorithm for <i>l<\/i>\n                  <sub>2,0<\/sub>-ReLU Deep Neural Networks"],"prefix":"10.1109","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5699-9242","authenticated-orcid":false,"given":"Hui","family":"Zhang","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics, Beijing Jiaotong University, Beijing, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhengpeng","family":"Yuan","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, Beijing Jiaotong University, Beijing, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3129-2005","authenticated-orcid":false,"given":"Naihua","family":"Xiu","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, Beijing Jiaotong University, Beijing, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"263","reference":[{"key":"ref13","first-page":"1","article-title":"Understanding deep neural networks with rectified linear units","author":"arora","year":"2016","journal-title":"Proc ICML"},{"key":"ref12","article-title":"Optimization for deep learning: Theory and algorithms","author":"sun","year":"2019","journal-title":"arXiv 1912 08957"},{"key":"ref56","doi-asserted-by":"publisher","DOI":"10.1080\/02331934.2015.1032286"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1007\/s10994-019-05839-6"},{"key":"ref14","article-title":"Complexity of training ReLU neural network","author":"boob","year":"2018","journal-title":"arXiv 1809 10787"},{"key":"ref53","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-92775-6"},{"key":"ref52","doi-asserted-by":"publisher","DOI":"10.1007\/s10462-020-09825-6"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1007\/s11590-020-01579-y"},{"key":"ref55","first-page":"211","article-title":"On nonconvex subdifferential calculus in Banach spaces","volume":"2","author":"mordukhovich","year":"1995","journal-title":"J Convex Anal"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1137\/18M1231559"},{"key":"ref54","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611970142"},{"key":"ref17","article-title":"On the stability of deep networks","author":"giryes","year":"2014","journal-title":"arXiv 1412 5896"},{"key":"ref16","article-title":"A survey on neural network interpretability","author":"zhang","year":"2020","journal-title":"arXiv 2012 14261"},{"key":"ref19","first-page":"7924","article-title":"Robust detection of adversarial attacks by modeling the intrinsic properties of deep neural networks","author":"zheng","year":"2018","journal-title":"Proc NIPS"},{"key":"ref18","article-title":"Intriguing properties of neural networks","author":"szegedy","year":"2013","journal-title":"arXiv 1312 6199"},{"key":"ref51","doi-asserted-by":"publisher","DOI":"10.1109\/5.726791"},{"key":"ref50","doi-asserted-by":"publisher","DOI":"10.1007\/BF00344251"},{"key":"ref46","doi-asserted-by":"publisher","DOI":"10.1109\/SIPROCESS.2019.8868650"},{"key":"ref45","first-page":"1","article-title":"Learning structured sparsity in deep neural networks","author":"wen","year":"2016","journal-title":"Proc NIPS"},{"key":"ref48","first-page":"960","article-title":"Group sparse optimization via $l_{p,q}$\n regularization","volume":"18","author":"hu","year":"2017","journal-title":"J Mach Learn Res"},{"key":"ref47","author":"rockafellar","year":"2009","journal-title":"Variational Analysis"},{"key":"ref42","doi-asserted-by":"publisher","DOI":"10.1145\/3357384.3358114"},{"key":"ref41","first-page":"574","article-title":"Toward compact ConvNets via structure-sparsity regularized filter pruning","volume":"31","author":"lin","year":"2019","journal-title":"IEEE T Neur Net Lear"},{"key":"ref44","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2017.2748585"},{"key":"ref43","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2017.02.029"},{"key":"ref49","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-018-1277-1"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1214\/19-AOS1875"},{"key":"ref7","first-page":"486","article-title":"A theoretical analysis of deep Q-learning","volume":"120","author":"fan","year":"2020","journal-title":"Proc 2nd Conf Learn Dyn Control"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1137\/18M117337X"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1016\/j.neunet.2019.04.024"},{"key":"ref3","doi-asserted-by":"crossref","DOI":"10.1109\/TPAMI.2021.3059968","article-title":"Image segmentation using deep learning: A survey","author":"minaee","year":"2021","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1016\/j.cviu.2019.102897"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1016\/j.patrec.2018.05.018"},{"key":"ref40","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-64580-9_31"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1080\/00207160.2020.1812585"},{"key":"ref34","first-page":"2722","article-title":"Training neural networks without gradients: A scalable ADMM approach","author":"taylor","year":"2016","journal-title":"Proc ICML"},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2016.165"},{"key":"ref36","article-title":"On ADMM in deep learning: Convergence and saturation-avoidance","author":"zeng","year":"2019","journal-title":"arXiv 1902 02060"},{"key":"ref31","article-title":"A proximal block coordinate descent algorithm for deep neural network training","author":"tsz-kit lau","year":"2018","journal-title":"arXiv 1803 09082"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2016.90"},{"key":"ref33","first-page":"1721","article-title":"Convergent block coordinate descent for training Tikhonov regularized deep neural networks","author":"zhang","year":"2017","journal-title":"Proc NIPS"},{"key":"ref32","first-page":"7313","article-title":"Global convergence of block coordinate descent in deep learning","author":"zeng","year":"2019","journal-title":"Proc ICML"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cosrev.2021.100379"},{"key":"ref1","doi-asserted-by":"crossref","first-page":"436","DOI":"10.1038\/nature14539","article-title":"Deep learning","volume":"521","author":"lecun","year":"2015","journal-title":"Nature"},{"key":"ref39","first-page":"97","article-title":"Channel pruning for deep neural networks via a relaxed group-wise splitting method","author":"yang","year":"2019","journal-title":"Proc AI4I"},{"key":"ref38","article-title":"Training skinny deep neural networks with iterative hard thresholding methods","author":"jin","year":"2016","journal-title":"arXiv 1607 05423"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1162\/neco_a_01164"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1162\/neco_a_01234"},{"key":"ref26","first-page":"243","article-title":"Deep compression: Compressing deep neural networks with pruning, trained quantization and Huffman coding","author":"han","year":"2016","journal-title":"Proc ISCA"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1109\/72.279181"},{"key":"ref20","article-title":"Sparsity in deep learning: Pruning and growth for efficient inference and training in neural networks","author":"hoefler","year":"2021","journal-title":"arXiv 2102 00554"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1162\/neco_a_01195"},{"key":"ref21","article-title":"On the convergence of a class of adam-type algorithms for non-convex optimization","author":"chen","year":"2018","journal-title":"arXiv 1808 02941"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1109\/ICCV.2015.123"},{"key":"ref27","first-page":"249","article-title":"Understanding the difficulty of training deep feedforward neural networks","author":"glorot","year":"2010","journal-title":"Proc AISTAT"},{"key":"ref29","first-page":"448","article-title":"Batch normalization: Accelerating deep network training by reducing internal covariate shift","author":"ioffe","year":"2015","journal-title":"Proc ICML"}],"container-title":["IEEE Transactions on Neural Networks and Learning Systems"],"original-title":[],"link":[{"URL":"http:\/\/xplorestaging.ieee.org\/ielx7\/5962385\/10237282\/09648259.pdf?arnumber=9648259","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,25]],"date-time":"2023-09-25T18:30:24Z","timestamp":1695666624000},"score":1,"resource":{"primary":{"URL":"https:\/\/ieeexplore.ieee.org\/document\/9648259\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,9]]},"references-count":56,"journal-issue":{"issue":"9"},"URL":"https:\/\/doi.org\/10.1109\/tnnls.2021.3131406","relation":{},"ISSN":["2162-237X","2162-2388"],"issn-type":[{"value":"2162-237X","type":"print"},{"value":"2162-2388","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,9]]}}}