{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T14:07:16Z","timestamp":1773842836375,"version":"3.50.1"},"reference-count":55,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","issue":"16","license":[{"start":{"date-parts":[[2017,8,15]],"date-time":"2017-08-15T00:00:00Z","timestamp":1502755200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/legalcode"},{"start":{"date-parts":[[2017,8,15]],"date-time":"2017-08-15T00:00:00Z","timestamp":1502755200000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/legalcode"}],"funder":[{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["Ep\/K033166\/1"],"award-info":[{"award-number":["Ep\/K033166\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001736","name":"GIF","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001736","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001736","name":"German-Israeli Foundation for Scientific Research and Development","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001736","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000006","name":"Office of Naval Research","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000006","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000183","name":"ARO","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000183","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000266","name":"NGA","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000266","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE Trans. Signal Process."],"published-print":{"date-parts":[[2017,8,15]]},"DOI":"10.1109\/tsp.2017.2708039","type":"journal-article","created":{"date-parts":[[2017,5,25]],"date-time":"2017-05-25T18:11:11Z","timestamp":1495735871000},"page":"4265-4280","source":"Crossref","is-referenced-by-count":119,"title":["Robust Large Margin Deep Neural Networks"],"prefix":"10.1109","volume":"65","author":[{"given":"Jure","family":"Sokolic","sequence":"first","affiliation":[]},{"given":"Raja","family":"Giryes","sequence":"additional","affiliation":[]},{"given":"Guillermo","family":"Sapiro","sequence":"additional","affiliation":[]},{"given":"Miguel R. D.","family":"Rodrigues","sequence":"additional","affiliation":[]}],"member":"263","reference":[{"key":"ref39","doi-asserted-by":"publisher","DOI":"10.1109\/ICSMC.2008.4811372"},{"key":"ref38","doi-asserted-by":"publisher","DOI":"10.1007\/s10994-007-5025-7"},{"key":"ref33","first-page":"1376","article-title":"Norm-based\n capacity control in neural networks","author":"neyshabur","year":"2015","journal-title":"Proc 28th Conf Learn Theory"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1007\/s10994-011-5268-1"},{"key":"ref31","first-page":"463","article-title":"Rademacher and Gaussian complexities: Risk bounds and structural results","volume":"3","author":"bartlett","year":"2002","journal-title":"J Mach Learn Res"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781107298019"},{"key":"ref37","first-page":"1094","article-title":"Generalization error of\n invariant classifiers","author":"sokoli?","year":"2017","journal-title":"Proc Int Conf Artif Intell Statist"},{"key":"ref36","article-title":"Understanding deep learning requires\n rethinking generalization","author":"zhang","year":"0","journal-title":"Proc Int Conf Learn Representations"},{"key":"ref35","article-title":"Wide residual networks","author":"zagoruyko","year":"0","journal-title":"Proc British Mach Vision Conf"},{"key":"ref34","article-title":"Large margin deep neural networks: Theory and algorithms","author":"sun","year":"2015"},{"key":"ref28","first-page":"1333","article-title":"Discriminative robust transformation\n learning","author":"huang","year":"2015","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref27","first-page":"833","article-title":"Contractive auto-encoders: Explicit invariance during feature\n extraction","author":"rifai","year":"2011","journal-title":"Proc 28th Int Conf Mach Learn"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1109\/72.788640"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1109\/MSP.2012.2205597"},{"key":"ref1","first-page":"1097","article-title":"Imagenet\n classification with deep convolutional neural networks","author":"krizhevsky","year":"2012","journal-title":"Proc 25th Int Conf Adv Neural Inf Process Syst"},{"key":"ref20","article-title":"Exact solutions to the nonlinear dynamics of learning in deep linear neural networks","author":"saxe","year":"2014","journal-title":"Proc Int Conf Learn Representations"},{"key":"ref22","first-page":"2422","article-title":"Path-SGD: Path-normalized optimization in deep neural networks","author":"neyshabur","year":"2015","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1093\/imaiai\/iav006"},{"key":"ref24","first-page":"901","article-title":"Weight normalization: A simple reparameterization to accelerate training of deep neural\n networks","author":"salimans","year":"2016","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref23","first-page":"448","article-title":"Batch normalization: Accelerating deep network training by reducing internal covariate shift","author":"ioffe","year":"2015","journal-title":"Proceedings of the 32nd Intl Conf on Machine Learning"},{"key":"ref26","first-page":"1929","article-title":"Dropout: A simple way to prevent neural networks from\n overfitting","volume":"15","author":"srivastava","year":"2014","journal-title":"J Mach Learn Res"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1109\/ICCV.2015.289"},{"key":"ref50","doi-asserted-by":"publisher","DOI":"10.1109\/5.726791"},{"key":"ref51","article-title":"Learning multiple layers of features from tiny images","author":"krizhevsky","year":"2009","journal-title":"Tech Rep"},{"key":"ref55","article-title":"Theano: A Python framework for fast computation of mathematical\n expressions","year":"2016"},{"key":"ref54","article-title":"Striving for simplicity: The all\n convolutional net","author":"springenberg","year":"2015","journal-title":"Proc Int Conf Learn Representations"},{"key":"ref53","doi-asserted-by":"publisher","DOI":"10.1007\/s11263-015-0816-y"},{"key":"ref52","doi-asserted-by":"publisher","DOI":"10.1145\/2557642.2563669"},{"key":"ref10","first-page":"2924","article-title":"On the number of linear regions of deep\n neural networks","author":"mont\u00fafar","year":"2014","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref11","first-page":"698","article-title":"On the\n expressive power of deep learning: A tensor analysis","author":"cohen","year":"2016","journal-title":"Proc 29th Annu Conf Learn Theory"},{"key":"ref40","doi-asserted-by":"publisher","DOI":"10.1016\/j.neunet.2005.02.006"},{"key":"ref12","first-page":"1517","article-title":"Benefits of depth in neural networks","author":"telgarsky","year":"2016","journal-title":"Proc 29th Annu Conf Learn Theory"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.21413"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2012.230"},{"key":"ref15","article-title":"A mathematical theory of deep convolutional neural networks for feature\n extraction","author":"wiatowski","year":"2015"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2016.2546221"},{"key":"ref17","first-page":"192","article-title":"The loss surfaces of multilayer networks","author":"choromanska","year":"2015","journal-title":"Proc Int Conf Artif Intell Statist"},{"key":"ref18","article-title":"Global optimality in tensor factorization, deep learning, and beyond","author":"haeffele","year":"2015"},{"key":"ref19","article-title":"Tradeoffs between\n convergence speed and reconstruction accuracy in inverse problems","author":"giryes","year":"2016"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2016.90"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1038\/nature14539"},{"key":"ref6","article-title":"Learning\n stable group invariant representations with convolutional networks","author":"bruna","year":"2013","journal-title":"Proc Int Conf Learn Representations"},{"key":"ref5","first-page":"807","article-title":"Rectified linear units improve restricted Boltzmann machines","author":"nair","year":"2010","journal-title":"Proc 27th Int Conf Mach Learn"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1007\/BF02551274"},{"key":"ref7","first-page":"111","article-title":"A\n theoretical analysis of feature pooling in visual recognition","author":"boureau","year":"2010","journal-title":"Proc 27th Int Conf Mach Learn"},{"key":"ref49","first-page":"550","article-title":"Residual\n networks are exponential ensembles of relatively shallow networks","author":"veit","year":"0","journal-title":"Proc Adv Neural Inform Process Syst"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1016\/0893-6080(91)90009-T"},{"key":"ref46","first-page":"630","article-title":"Identity mappings in deep residual networks","author":"he","year":"0","journal-title":"Proc Europ Conf Comput Vision"},{"key":"ref45","article-title":"The matrix cookbook","author":"petersen","year":"2012","journal-title":"Tech Univ"},{"key":"ref48","doi-asserted-by":"publisher","DOI":"10.1561\/2200000006"},{"key":"ref47","doi-asserted-by":"publisher","DOI":"10.1162\/neco.1997.9.8.1735"},{"key":"ref42","first-page":"2415","article-title":"Distance preserving embeddings for general n-dimensional\n manifolds.","volume":"14","author":"verma","year":"2013","journal-title":"J Mach Learn Res"},{"key":"ref41","doi-asserted-by":"publisher","DOI":"10.1007\/s00365-007-9005-8"},{"key":"ref44","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(92)90407-2"},{"key":"ref43","article-title":"Data-dependent path\n normalization in neural networks","author":"neyshabur","year":"2015","journal-title":"Proc Int Conf Learn Representations"}],"container-title":["IEEE Transactions on Signal Processing"],"original-title":[],"link":[{"URL":"https:\/\/ieeexplore.ieee.org\/ielaam\/78\/7942328\/7934087-aam.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"http:\/\/xplorestaging.ieee.org\/ielx7\/78\/7942328\/07934087.pdf?arnumber=7934087","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,4,8]],"date-time":"2022-04-08T18:48:55Z","timestamp":1649443735000},"score":1,"resource":{"primary":{"URL":"https:\/\/ieeexplore.ieee.org\/document\/7934087\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,8,15]]},"references-count":55,"journal-issue":{"issue":"16"},"URL":"https:\/\/doi.org\/10.1109\/tsp.2017.2708039","relation":{},"ISSN":["1053-587X","1941-0476"],"issn-type":[{"value":"1053-587X","type":"print"},{"value":"1941-0476","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,8,15]]}}}