{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,17]],"date-time":"2026-03-17T17:13:33Z","timestamp":1773767613096,"version":"3.50.1"},"reference-count":25,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2022,9,15]],"date-time":"2022-09-15T00:00:00Z","timestamp":1663200000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2022,9,15]],"date-time":"2022-09-15T00:00:00Z","timestamp":1663200000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Syst Sci Complex"],"published-print":{"date-parts":[[2023,2]]},"DOI":"10.1007\/s11424-022-1326-y","type":"journal-article","created":{"date-parts":[[2022,9,17]],"date-time":"2022-09-17T17:02:32Z","timestamp":1663434152000},"page":"3-28","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Improve Robustness and Accuracy of Deep Neural Network with L2,\u221e Normalization"],"prefix":"10.1007","volume":"36","author":[{"given":"Lijia","family":"Yu","sequence":"first","affiliation":[]},{"given":"Xiao-Shan","family":"Gao","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,9,15]]},"reference":[{"issue":"7553","key":"1326_CR1","doi-asserted-by":"publisher","first-page":"436","DOI":"10.1038\/nature14539","volume":"521","author":"Y LeCun","year":"2015","unstructured":"LeCun Y, Bengio Y, and Hinton G, Deep learning, Nature, 2015, 521(7553): 436\u2013444.","journal-title":"Nature"},{"key":"1326_CR2","doi-asserted-by":"publisher","DOI":"10.1155\/2018\/7068349","volume-title":"Comput. Intel. and Neurosc.","author":"A Voulodimos","year":"2018","unstructured":"Voulodimos A, Doulamis N, Doulamis A, et al., Deep learning for computer vision: A brief review, Comput. Intel. and Neurosc., 2018, DOI: https:\/\/doi.org\/10.1155\/2018\/7068349."},{"key":"1326_CR3","first-page":"5","volume-title":"Tutorial Abstracts of ACL\u20192012","author":"R Socher","year":"2012","unstructured":"Socher R, Bengio Y, and Manning C D, Deep Learning for NLP (without magic), Tutorial Abstracts of ACL\u20192012, 2012, 5."},{"issue":"6","key":"1326_CR4","doi-asserted-by":"publisher","first-page":"861","DOI":"10.1016\/S0893-6080(05)80131-5","volume":"6","author":"M Leshno","year":"1993","unstructured":"Leshno M, Lin V Y, Pinkus A, et al., Multilayer feedforward networks with a nonpolynomial activation function can approximate any function, Neural Networks, 1993, 6(6): 861\u2013867.","journal-title":"Neural Networks"},{"key":"1326_CR5","volume-title":"Deep Learning","author":"I Goodfellow","year":"2016","unstructured":"Goodfellow I, Bengio Y, and Courville A, Deep Learning, MIT Press, Cambridge, 2016."},{"key":"1326_CR6","volume-title":"Variational dropout sparsifies deep neural networks","author":"D Molchanov","year":"2017","unstructured":"Molchanov D, Ashukha A, and Vetrov D, Variational dropout sparsifies deep neural networks, arXiv: 1701.05369, 2017."},{"key":"1326_CR7","first-page":"1929","volume":"15","author":"N Srivastava","year":"2014","unstructured":"Srivastava N, Hinton G E, Krizhevsky A, et al., Dropout: A simple way to prevent neural networks from overfitting, Journal of Machine Learning Research, 2014, 15: 1929\u20131958.","journal-title":"Journal of Machine Learning Research"},{"key":"1326_CR8","first-page":"III-1058","volume":"28","author":"L Wan","year":"2013","unstructured":"Wan L, Zeiler M, Zhang S, et al., Regularization of neural networks using DropConnect, ICML\u201913, 2013, 28: III-1058\u2013III-1066.","journal-title":"ICML\u201913"},{"key":"1326_CR9","volume-title":"Batch normalization: Accelerating deep network training by reducing internal covariate shift","author":"S Ioffe","year":"2015","unstructured":"Ioffe S and Szegedy C, Batch normalization: Accelerating deep network training by reducing internal covariate shift, arXiv: 1502.03167, 2015."},{"key":"1326_CR10","volume-title":"NIPS\u20192014","author":"G Mont\u00fafar","year":"2014","unstructured":"Mont\u00fafar G, Pascanu R, Cho K, et al., On the number of linear regions of deep neural networks, NIPS\u20192014, 2014."},{"issue":"6","key":"1326_CR11","doi-asserted-by":"publisher","first-page":"894","DOI":"10.1109\/JPROC.2020.2989782","volume":"108","author":"X Y Zhang","year":"2020","unstructured":"Zhang X Y, Liu C L, and Suen C Y, Towards robust pattern recognition: A review, Proc. of the IEEE, 2020, 108(6): 894\u2013922.","journal-title":"Proc. of the IEEE"},{"key":"1326_CR12","first-page":"4480","volume-title":"CVPR\u201916","author":"S Zheng","year":"2016","unstructured":"Zheng S, Song Y, Leung T, et al., Improving the robustness of deep neural networks via stability training, CVPR\u201916, 2016, 4480\u20134488."},{"key":"1326_CR13","doi-asserted-by":"publisher","first-page":"487","DOI":"10.1016\/j.patcog.2011.07.009","volume":"45","author":"D Meng","year":"2012","unstructured":"Meng D, Zhao Q, and Xu Z, Improve robustness of sparse PCA by L\n1-norm maximization, Pattern Recognition, 2012, 45: 487\u2013497.","journal-title":"Pattern Recognition"},{"key":"1326_CR14","volume-title":"Distilling the knowledge in a neural network","author":"G Hinton","year":"2015","unstructured":"Hinton G, Vinyals O, and Dean J, Distilling the knowledge in a neural network, arXiv: 1503.02531, 2015."},{"key":"1326_CR15","volume-title":"Robust and information-theoretically safe bias classifier against adversarial attacks","author":"L Yu","year":"2021","unstructured":"Yu L and Gao X S, Robust and information-theoretically safe bias classifier against adversarial attacks, arXiv: 2111.04404, 2021."},{"key":"1326_CR16","volume-title":"Adversarial parameter attack on deep neural networks","author":"L Yu","year":"2022","unstructured":"Yu L, Wang Y, and Gao X S, Adversarial parameter attack on deep neural networks, arXiv: 2203.10502, 2022."},{"key":"1326_CR17","volume-title":"Towards deep learning models resistant to adversarial attacks","author":"A Madry","year":"2017","unstructured":"Madry A, Makelov A, Schmidt L, et al., Towards deep learning models resistant to adversarial attacks, arXiv: 1706.06083, 2017."},{"key":"1326_CR18","first-page":"11418","volume-title":"CVPR\u20192019","author":"W Lin","year":"2019","unstructured":"Lin W, Yang Z, Chen X, et al., Robustness verification of classification deep neural networks via linear programming, CVPR\u20192019, 2019, 11418\u201311427."},{"key":"1326_CR19","doi-asserted-by":"publisher","unstructured":"Carlini N and Wagner D, Towards evaluating the robustness of neural networks, IEEE Symposium on Security and Privacy, DOI: https:\/\/doi.org\/10.1109\/SP.2017.49.","DOI":"10.1109\/SP.2017.49"},{"key":"1326_CR20","first-page":"1376","volume-title":"COLT\u201915","author":"B Neyshabur","year":"2015","unstructured":"Neyshabur B, Tomioka R, and Srebro N, Norm-based capacity control in neural networks, COLT\u201915, 2015, 1376\u20131401."},{"key":"1326_CR21","first-page":"1397","volume":"31","author":"M Wen","year":"2021","unstructured":"Wen M, Xu Y, Zheng Y, et al., Sparse deep neural networks using L\n1,\u221e-weight normalization, Statistica Sinica, 2021, 31: 1397\u20131414.","journal-title":"Statistica Sinica"},{"key":"1326_CR22","volume-title":"Recent advances in understanding adversarial robustness of deep neural networks","author":"T Bai","year":"2020","unstructured":"Bai T, Luo J, and Zhao J, Recent advances in understanding adversarial robustness of deep neural networks, ArXiv: 2011.01539, 2020."},{"key":"1326_CR23","volume-title":"Methods of Algebraic Geometry, Volume I","author":"W V D Hodge","year":"1968","unstructured":"Hodge W V D and Pedoe D, Methods of Algebraic Geometry, Volume I. Cambridge University Press, Cambridge, 1968."},{"key":"1326_CR24","first-page":"2196","volume-title":"International Conference on Machine Learning","author":"F Croce","year":"2020","unstructured":"Croce F and Hein M, Minimally distorted adversarial examples with a fast adaptive boundary attack\/\/ International Conference on Machine Learning, PMLR, 2020, 2196\u20132205."},{"issue":"1","key":"1326_CR25","doi-asserted-by":"publisher","first-page":"11","DOI":"10.3390\/computers10010011","volume":"10","author":"L Vaccaro","year":"2021","unstructured":"Vaccaro L, Sansonetti G, and Micarelli A, An empirical review of automated machine learning, Computers, 2021, 10(1): 11.","journal-title":"Computers"}],"container-title":["Journal of Systems Science and Complexity"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11424-022-1326-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11424-022-1326-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11424-022-1326-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,1]],"date-time":"2023-03-01T16:14:46Z","timestamp":1677687286000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11424-022-1326-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,9,15]]},"references-count":25,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2023,2]]}},"alternative-id":["1326"],"URL":"https:\/\/doi.org\/10.1007\/s11424-022-1326-y","relation":{},"ISSN":["1009-6124","1559-7067"],"issn-type":[{"value":"1009-6124","type":"print"},{"value":"1559-7067","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,9,15]]},"assertion":[{"value":"30 August 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 June 2022","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 September 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}