{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,4]],"date-time":"2026-04-04T17:46:51Z","timestamp":1775324811751,"version":"3.50.1"},"reference-count":95,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","license":[{"start":{"date-parts":[[2021,1,1]],"date-time":"2021-01-01T00:00:00Z","timestamp":1609459200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE Trans. Pattern Anal. Mach. Intell."],"published-print":{"date-parts":[[2021]]},"DOI":"10.1109\/tpami.2021.3058891","type":"journal-article","created":{"date-parts":[[2021,2,13]],"date-time":"2021-02-13T02:19:13Z","timestamp":1613182753000},"page":"1-1","source":"Crossref","is-referenced-by-count":54,"title":["Deep Polynomial Neural Networks"],"prefix":"10.1109","author":[{"given":"Grigorios G.","family":"Chrysos","sequence":"first","affiliation":[]},{"given":"Stylianos","family":"Moschoglou","sequence":"additional","affiliation":[]},{"given":"Giorgos","family":"Bouritsas","sequence":"additional","affiliation":[]},{"given":"Jiankang","family":"Deng","sequence":"additional","affiliation":[]},{"given":"Yannis","family":"Panagakis","sequence":"additional","affiliation":[]},{"given":"Stefanos P","family":"Zafeiriou","sequence":"additional","affiliation":[]}],"member":"263","reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1109\/5.726791"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1145\/3065386"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2017.243"},{"key":"ref4","first-page":"1","article-title":"Spectral normalization for generative adversarial networks","volume-title":"Proc. Int. Conf. Learn. Representations","author":"Miyato"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2016.90"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1007\/s13398-014-0173-7.2"},{"key":"ref7","first-page":"1","article-title":"A convergence analysis of gradient descent for deep linear neural networks","author":"Arora","year":"2019","journal-title":"Int. Conf. Learn. Representations"},{"key":"ref8","first-page":"3845","article-title":"Minimax estimation of neural net distance","volume-title":"Proc. Int. Conf. Neural Inf. Process. Syst.","author":"Ji"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2019.00453"},{"key":"ref10","first-page":"1","article-title":"Multiplicative interactions and where to find them","volume-title":"Proc. Int. Conf. Learn. Representations","author":"Jayakumar"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2017.2690524"},{"key":"ref12","article-title":"Polygan: High-order polynomial generators","author":"Chrysos","year":"2019"},{"key":"ref13","first-page":"1","article-title":"Newton residual learning","volume-title":"Proc. Int. Conf. Learn. Representations","author":"Chrysos"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR42600.2020.00735"},{"key":"ref15","first-page":"1","article-title":"On the expressive power of deep polynomial neural networks","volume-title":"Proc. Int. Conf. Neural Inf. Process. Syst.","author":"Kileel"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2009.5206848"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1109\/ICCV.2015.425"},{"key":"ref18","first-page":"1","article-title":"Chainer: A next-generation open source framework for deep learning","volume-title":"Proc. Conf. Neural Inf. Process. Syst.","author":"Tokui"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1017\/9781108924238.008"},{"key":"ref20","first-page":"1","article-title":"Adam: A method for stochastic optimization","volume-title":"Proc. Int. Conf. Learn. Representations","author":"Kingma"},{"key":"ref21","first-page":"1","article-title":"On the convergence of adam and beyond","volume-title":"Proc. Int. Conf. Learn. Representations","author":"Reddi"},{"key":"ref22","first-page":"1","article-title":"Very deep convolutional networks for large-scale image recognition","volume-title":"Proc. Int. Conf. Learn. Representations","author":"Simonyan"},{"key":"ref23","first-page":"249","article-title":"Understanding the difficulty of training deep feedforward neural networks","volume-title":"Proc. 13th Int. Conf. Artif. Intell. Statist.","author":"Glorot"},{"key":"ref24","first-page":"1","article-title":"Exact solutions to the nonlinear dynamics of learning in deep linear neural networks","volume-title":"Proc. Int. Conf. Learn. Representations","author":"Saxe"},{"key":"ref25","article-title":"Instance normalization: The missing ingredient for fast stylization","author":"Ulyanov","year":"2016"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1007\/BF00344251"},{"key":"ref27","article-title":"Searching for activation functions","author":"Ramachandran","year":"2017"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.5555\/3104322.3104425"},{"key":"ref29","first-page":"1","article-title":"Large scale GAN training for high fidelity natural image synthesis","volume-title":"Proc. Int. Conf. Learn. Representations","author":"Brock"},{"key":"ref30","first-page":"4091","article-title":"Learning hierarchical features from deep generative models","volume-title":"Proc. Int. Conf. Mach. Learn.","author":"Zhao"},{"key":"ref31","first-page":"1","article-title":"Progressive growing of GANs for improved quality, stability, and variation","volume-title":"Proc. Int. Conf. Learn. Representations","author":"Karras"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1109\/ICCV.2017.167"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1109\/TSMC.1971.4308320"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1016\/j.neunet.2014.09.003"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1016\/S0045-7906(02)00045-9"},{"key":"ref36","doi-asserted-by":"publisher","DOI":"10.1109\/IJCNN.1991.155142"},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1162\/neco.2007.19.12.3356"},{"key":"ref38","doi-asserted-by":"publisher","DOI":"10.1109\/VIPMC.2003.1220516"},{"key":"ref39","doi-asserted-by":"publisher","DOI":"10.1023\/A:1022967523886"},{"key":"ref40","first-page":"698","article-title":"On the expressive power of deep learning: A tensor analysis","volume-title":"Proc. Conf. Learn. Theory","author":"Cohen"},{"key":"ref41","first-page":"955","article-title":"Convolutional rectifier networks as generalized tensor decompositions","volume-title":"Proc. Int. Conf. Mach. Learn.","author":"Cohen"},{"key":"ref42","article-title":"Neural machine translation by jointly learning to align and translate","volume-title":"Proc. Int. Conf. Learn. Representations","author":"Bahdanau"},{"key":"ref43","article-title":"Highway networks","author":"Srivastava","year":"2015"},{"key":"ref44","first-page":"1431","article-title":"Learning to disentangle factors of variation with manifold interaction","volume-title":"Proc. Int. Conf. Mach. Learn.","author":"Reed"},{"key":"ref45","doi-asserted-by":"publisher","DOI":"10.1137\/07070111x"},{"key":"ref46","doi-asserted-by":"publisher","DOI":"10.2307\/3029337"},{"key":"ref47","volume-title":"Analysis III: Spaces of Differentiable Functions","author":"Nikol\u2019skii","year":"2013"},{"key":"ref48","first-page":"1","article-title":"The lottery ticket hypothesis: Finding sparse, trainable neural networks","volume-title":"Proc. Int. Conf. Learn. Representations","author":"Frankle"},{"key":"ref49","first-page":"1135","article-title":"Learning both weights and connections for efficient neural network","volume-title":"Proc. Int. Conf. Neural Inf. Process. Syst.","author":"Han"},{"key":"ref50","first-page":"395","article-title":"CirCNN: Accelerating and compressing deep neural networks using block-circulant weight matrices","volume-title":"Proc. 50th Annu. IEEE\/ACM Int. Symp. Microarchitecture","author":"Ding"},{"key":"ref51","first-page":"635","article-title":"Sharing residual units through collective tensor factorization in deep neural networks","volume-title":"Proc. Int. Joint Conf. Artif. Intell.","author":"Yunpeng"},{"key":"ref52","first-page":"2148","article-title":"Predicting parameters in deep learning","volume-title":"Proc. Int. Conf. Neural Inf. Process. Syst.","author":"Denil"},{"key":"ref53","first-page":"1","article-title":"Generative adversarial nets","volume-title":"Proc. Int. Conf. Neural Inf. Process. Syst.","author":"Goodfellow"},{"key":"ref54","article-title":"Fashion-mnist: A novel image dataset for benchmarking machine learning algorithms","author":"Xiao","year":"2017"},{"key":"ref55","doi-asserted-by":"publisher","DOI":"10.1109\/34.927464"},{"key":"ref56","article-title":"The cifar-10 dataset","author":"Krizhevsky","year":"2014"},{"key":"ref57","first-page":"2234","article-title":"Improved techniques for training GANs","volume-title":"Proc. Neural Inf. Process. Syst.","author":"Salimans"},{"key":"ref58","first-page":"6626","article-title":"GANs trained by a two time-scale update rule converge to a local nash equilibrium","volume-title":"Proc. Neural Inf. Process. Syst.","author":"Heusel"},{"key":"ref59","doi-asserted-by":"publisher","DOI":"10.4324\/9781410605337-29"},{"key":"ref60","article-title":"Class-splitting generative adversarial networks","author":"Grinblat","year":"2017"},{"key":"ref61","first-page":"5767","article-title":"Improved training of wasserstein GANs","volume-title":"Proc. Neural Inf. Proc. Syst.","author":"Gulrajani"},{"key":"ref62","first-page":"1","article-title":"Implicit generation and generalization in energy-based models","volume-title":"Proc. Int. Conf. Neural Inf. Process. Syst.","author":"Du"},{"key":"ref63","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2019.00596"},{"key":"ref64","article-title":"Adversarial training of partially invertible variational autoencoders","author":"Lucas","year":"2019"},{"key":"ref65","doi-asserted-by":"publisher","DOI":"10.24963\/ijcai.2018\/391"},{"key":"ref66","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2017.634"},{"key":"ref67","doi-asserted-by":"publisher","DOI":"10.1109\/TCSVT.2017.2654543"},{"key":"ref68","doi-asserted-by":"publisher","DOI":"10.5244\/C.30.87"},{"key":"ref69","article-title":"Speech commands: A dataset for limited-vocabulary speech recognition","author":"Warden","year":"2018"},{"key":"ref70","doi-asserted-by":"publisher","DOI":"10.1007\/s11263-015-0816-y"},{"key":"ref71","article-title":"Accurate, large minibatch sgd: Training imagenet in 1 hour","author":"Goyal","year":"2017"},{"key":"ref72","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2018.00745"},{"key":"ref73","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2019.00482"},{"key":"ref74","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-46487-9_6"},{"key":"ref75","doi-asserted-by":"publisher","DOI":"10.1109\/ICCVW.2019.00322"},{"key":"ref76","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR42600.2020.00525"},{"key":"ref77","article-title":"Labeled faces in the wild: A database forstudying face recognition in unconstrained environments","author":"Huang"},{"key":"ref78","doi-asserted-by":"publisher","DOI":"10.1109\/WACV.2016.7477558"},{"key":"ref79","doi-asserted-by":"publisher","DOI":"10.1109\/CVPRW.2017.250"},{"key":"ref80","article-title":"Cross-pose LFW: A database for studying cross-pose face recognition in unconstrained environments","author":"Zheng","year":"2018"},{"key":"ref81","article-title":"Cross-age lfw: A database for studying cross-age face recognition in unconstrained environments","author":"Zheng","year":"2017"},{"key":"ref82","doi-asserted-by":"publisher","DOI":"10.1109\/ICCV.2019.00078"},{"key":"ref83","doi-asserted-by":"publisher","DOI":"10.1109\/CVPRW.2017.87"},{"key":"ref84","doi-asserted-by":"publisher","DOI":"10.1109\/ICB2018.2018.00033"},{"key":"ref85","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2016.527"},{"key":"ref86","article-title":"MxNet: A flexible and efficient machine learning library for heterogeneous distributed systems","author":"Chen"},{"key":"ref87","doi-asserted-by":"publisher","DOI":"10.1109\/ICIP.2014.7025068"},{"key":"ref88","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-01219-9_43"},{"key":"ref89","doi-asserted-by":"publisher","DOI":"10.1109\/ICCV.2019.00731"},{"key":"ref90","article-title":"Graph attention networks","volume-title":"Proc. Int. Conf. Learn. Representations","author":"Veli\u010dkovi\u0107"},{"key":"ref91","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2018.00275"},{"key":"ref92","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2017.576"},{"key":"ref93","first-page":"1","article-title":"Convolutional neural networks on graphs with fast localized spectral filtering","volume-title":"Proc. Int. Conf Neural Inf.. Process. Syst.","author":"Defferrard"},{"key":"ref94","doi-asserted-by":"publisher","DOI":"10.1145\/311535.311556"},{"key":"ref95","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2017.591"}],"container-title":["IEEE Transactions on Pattern Analysis and Machine Intelligence"],"original-title":[],"link":[{"URL":"http:\/\/xplorestaging.ieee.org\/ielx7\/34\/4359286\/09353253.pdf?arnumber=9353253","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,1,9]],"date-time":"2024-01-09T23:43:41Z","timestamp":1704843821000},"score":1,"resource":{"primary":{"URL":"https:\/\/ieeexplore.ieee.org\/document\/9353253\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021]]},"references-count":95,"URL":"https:\/\/doi.org\/10.1109\/tpami.2021.3058891","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":[[2021]]}}}