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廖宁毅;王舒凡;向、李瑶;叶南阳;邵、朔;楚、彭志

通过稀疏性实现对抗性鲁棒性。 （英语） Zbl 07510325号

机器。学习。 111，第2期，685-711（2022）.
摘要：众所周知，网络修剪可以生成紧凑的模型，而不会导致精度下降。然而，剪枝过程如何影响网络的健壮性以及背后的工作机制仍未解决。在这项工作中，我们从理论上证明了网络权重的稀疏性与模型鲁棒性密切相关。通过对多种对抗性剪枝方法、图像分类模型和数据集的实验，我们发现权重稀疏性并不会损害网络的鲁棒性，但会提高网络剪枝的鲁棒性。基于这些发现，我们提出了一种新的对抗性训练方法，称为逆权值继承，该方法通过从小网络继承权值，在大网络上施加稀疏的权值分布，从而提高了大网络的鲁棒性。

MSC公司：

68T05型 人工智能中的学习和自适应系统

关键词：

对抗学习;神经网络剪枝;稳健性;稀疏

软件：

ThiNet公司;深度愚人
PDF格式BibTeX公司 XML格式引用
\textit{N.Liao}等人，马赫。学习。111，编号2，685--711（2022；Zbl 07510325）
全文： 内政部 arXiv公司

参考文献：

[1] Alzantot，M.、Sharma，Y.、Elgohary，A.、Ho，B.J.、Srivastava，M.和；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；Chang，K.W.（2018）。生成自然语言对手示例。摘自：《2018年自然语言处理实证方法会议记录》，计算语言学协会，第2890-2896页。
[2] Arora，S.、Ge，R.、Neyshabur，B.和；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；张毅（2018）。通过压缩方法，深度网具有更强的泛化边界。摘自：第35届机器学习国际会议，第1卷，第390-418页。
[3] Balda，E.R.，Behboodi，A.，Koep，N.和；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；Mathar，R.（2019年）。通过基于稀疏性的压缩实现神经网络的对抗风险边界。摘自：第23届国际人工智能与统计会议，第108卷，第3816-3825页。
[4] Bartoldson，B.R.、Morcos，A.S.、Barbu，A.和；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；Erlebacher，G.（2020年）。神经网络修剪中的泛化稳定性权衡。第33届神经信息处理系统进展。
[5] Bastani，O.，Ioannou，Y.，Lampropoulos，L.，Vytiniotis，D.，Nori，A.，&amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；克里米尼西，A.（2016）。带约束的神经网络鲁棒性度量。摘自：《神经信息处理系统的进展》，第2613-2621页。
[6] Cosentino，J.、Zaiter，F.、Pei，D.和；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；Zhu，J.（2019）。搜索稀疏、鲁棒的神经网络。在：第33届神经信息处理系统会议，NeurIPS 2019。
[7] Dhillon，G.S.、Azizzadenesheli，K.、Lipton，Z.C.、Bernstein，J.、Kossaifi，J.和Khanna，A；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；Anandkumar，A.（2018年）。稳健对抗防御的随机激活剪枝。arXiv预打印arXiv:180301442。
[8] Dinh，T.、Wang，B.、Bertozzi，A.L.和；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；Osher，S.J.（2020）。稀疏性满足健壮性：feynman-kac形式主义原理健壮深度神经网络的通道修剪。arXiv预打印arXiv:200300631。
[9] Fawzi，A.、Moosavi-Dezfouli，S.M.和；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；Frossard，P.（2016）。分类器的鲁棒性：从对抗性噪声到随机噪声。摘自：第29届神经信息处理系统进展，第1632-1640页。
[10] Fawzi，A.，Fawzi.，O.，&amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；Frossard，P.（2018）。分类器对对抗扰动的鲁棒性分析。机器学习，107（3），481-508·Zbl 1462.62383号
[11] Frankle，J.和；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；Carbin，M.（2019年）。彩票假设：寻找稀疏、可训练的神经网络。参加：2019年5月6日至9日在美国洛杉矶新奥尔良举行的第七届国际学习代表大会。
[12] Goldblum，M.、Fowl，L.、Feizi，S.和；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；Goldstein，T.（2020年）。对抗性强蒸馏。参加：第三十四届AAAI人工智能会议。
[13] I.J.Goodfellow、J.Shlens和；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；Szegedy，C.（2015）。解释和利用对抗性示例。在：2015年5月7日至9日，美国加利福尼亚州圣地亚哥，ICLR 2015，第三届学习表征国际会议，会议记录。
[14] 桂S.、王H.、余C.、杨H.、王Z.和；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；Liu，J.（2019）。具有对抗鲁棒性的模型压缩：统一优化框架。收录：《神经信息处理系统进展》，第1283-1294页。
[15] Guo，M.，Yang，Y.，Xu，R.，Liu，Z.，&amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；Lin，D.（2020年）。当nas满足健壮性时：寻找对抗对抗性攻击的健壮架构。摘自：IEEE/CVF计算机视觉和模式识别会议（CVPR），第631-640页。
[16] Guo，Y.、Zhang，C.、Zhanng，C.和；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；Chen，Y.（2018）。具有改进的对抗鲁棒性的稀疏dnn。摘自：《神经信息处理系统的进展》，第242-251页。
[17] Han，S.、Pool，J.、Tran，J.和；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；Dally，W.（2015）。学习有效神经网络的权重和连接。《神经信息处理系统的进展》，第1135-1143页。
[18] Han，S.，Mao，H.和；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；Dally，W.J.（2016）。深度压缩：通过剪枝、训练量化和哈夫曼编码压缩深度神经网络。2016年5月2日至4日，波多黎各圣胡安，第四届国际学习代表大会，ICLR 2016，会议记录。
[19] 哈西比，B.，&；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；Stork，D.G.（1993年）。网络修剪的二阶导数：最佳脑外科医生。摘自：《神经信息处理系统的进展》，第164-171页。
[20] He，K.，Zhang，X.，Ren，S.和；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；Sun，J.（2016）。用于图像识别的深度残差学习。摘自：2016年IEEE计算机视觉和模式识别会议，CVPR 2016，美国内华达州拉斯维加斯，2016年6月27日至30日，第770-778页。
[21] Hein，M.和；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；Andriushchenko，M.（2017）。形式上保证分类器对对抗性操作的鲁棒性。摘自：《神经信息处理系统进展》，第2266-2276页。
[22] Huang，G.，Liu，Z.，van der Maaten，L.和；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；Weinberger，K.Q.（2017）。紧密连接的卷积网络。2017年7月21日至26日，美国夏威夷州火奴鲁鲁市，2017年IEEE计算机视觉和模式识别会议，CVPR 2017，第2261-2269页。
[23] Keskar，N.S.、Nocedal，J.、Tang，P.T.P.、Mudigere，D.和；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；Smelyanskiy，M.（2017年）。关于深度学习的大范围训练：泛化差距和显著极小值。参加：第五届国际学习代表大会。
[24] Kurakin，A.，Goodfellow，I.J.和；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；Bengio，S.（2017）。大规模的对抗性机器学习。2017年4月24日至26日，法国土伦，第五届国际学习代表大会，2017年ICLR，会议记录。
[25] Lang，J.（ed）（2018）《第二十七届国际人工智能联合会议论文集》，2018年7月13日至19日，瑞典斯德哥尔摩，IJCAI.org。
[26] LeCun，Y.、Denker，J.S.和；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；Solla，S.A.（1990年）。最佳脑损伤。摘自：神经信息处理系统进展，第598-605页。
[27] Li，B.、Wang，S.、Jia，Y.、Lu，Y.、Zhong，Z.、Carin，L.和；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；Jana，S.（2020年）。对抗性训练的实用彩票假设。arXiv预打印arXiv:200305733。
[28] Li，H.，Kadav，A.，Durdanovic，I.，Samet，H.和；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；Graf，H.P.（2017）。修剪过滤器以实现高效转换。2017年4月24日至26日，法国土伦，第五届国际学习代表大会，2017年ICLR，会议记录。
[29] Liu，Z.，Li，J.，Shen，Z.、Huang，G.、Yan，S.和；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；Zhang，C.（2017）。通过网络精简学习有效的卷积网络。在：IEEE国际计算机视觉会议，ICCV 2017，意大利威尼斯，2017年10月22日至29日，第2755-2763页。
[30] Liu，Z.、Sun，M.、Zhou，T.、Huang，G.和；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；Darrell，T.（2019）。重新思考网络修剪的价值。参加：2019年5月6日至9日在美国洛杉矶新奥尔良举行的第七届国际学习代表大会。
[31] Luo，J.H.、Wu，J.和；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；Lin，W.（2017）。Thinet：用于深度神经网络压缩的过滤器级剪枝方法。参见：2017年10月22日至29日在意大利威尼斯举行的IEEE国际计算机视觉会议，ICCV 2017，第5068-5076页。
[32] Madaan，D.、Shin，J.和；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；Hwang，S.J.（2019）。具有潜在脆弱性抑制的对抗性神经修剪。arXiv电子打印。
[33] Madry，A.、Makelov，A.、Schmidt，L.、Tsipras，D.和；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；Vladu，A.（2018）。面向抗对抗性攻击的深度学习模型。参加：2018年4月30日至5月3日在加拿大不列颠哥伦比亚省温哥华举行的第六届国际学习代表大会，会议记录。
[34] Miyato，T.、Dai，A.M.和；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；古德费罗，I.（2017）。半监督文本分类的对抗训练方法。参加：第五届国际学习代表大会。
[35] Moosavi-Dezfuli，S.M.、Fawzi，A.和；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；Frossard，P.（2016）。深度愚弄：一种简单而准确的愚弄深度神经网络的方法。摘自：IEEE计算机视觉和模式识别会议记录，第2574-2582页。
[36] Morcos，A.S.、Yu，H.、Paganini，M.和；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；田毅（2019）。一张彩票可以赢得所有彩票：在数据集和优化器中推广彩票初始化。In:32神经信息处理系统进展。
[37] Petzka，H.、Kamp，M.、Adilova，L.、Boley，M.和；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；Sminchisescu，C.（2020年）。插值体制中的相对平坦性和推广。arXiv电子打印。
[38] Rakin，A.S.，He，Z.，Yang，L.，Wang，Y.，Wang；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；Fan，D.（2019）。鲁棒稀疏正则化：同时优化神经网络的鲁棒性和紧凑性。arXiv预打印arXiv:190513074。
[39] Salman，H.、Yang，G.、Zhang，H.，Hsieh，C.J.和；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；Zhang，P.（2019）。用于神经网络紧鲁棒性验证的凸松弛障碍。摘自：《神经信息处理系统进展》，第9832-9842页。
[40] Sehwag，V.、Wang，S.、Mittal，P.和；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；Jana，S.（2019年）。面向紧凑和稳健的深层神经网络。arXiv电子打印。
[41] Simonyan，K.，&；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；Zisserman，A.（2015）。用于大规模图像识别的深度卷积网络。2015年5月7日至9日，美国加利福尼亚州圣地亚哥，第三届国际学习代表大会，ICLR 2015，会议记录。
[42] Wang，B.，Shi，Z.，&amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；Osher，S.（2019）。通过feynman-kac形式重新定义系综，以提高自然和稳健的精确度。摘自：《神经信息处理系统进展》，第1655-1665页。
[43] Wang，L.，Ding，G.W.，Huang，R.，Cao，Y.，&amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；Lui，Y.C.（2018）。剪枝神经网络的对抗鲁棒性。参加：第六届学习代表国际会议研讨会。
[44] Wen，W.，Wu，C.，Wang，Y.，Chen，Y；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；Li，H.（2016）。深度神经网络中的结构化稀疏性学习。摘自：神经信息处理系统进展，第2074-2082页。
[45] 徐，H。；Mannor，S.，《鲁棒性和泛化》，机器学习，86，3，391-423（2012）·Zbl 1242.68259号 ·doi:10.1007/s10994-011-5268-1
[46] Yang，Y.，Zhang，G.，Xu，Z.，&amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；Katabi，D.（2019）。Me-net：通过矩阵估计实现有效的对抗鲁棒性。摘自：第36届机器学习国际会议记录，2019年6月9日至15日，美国加利福尼亚州长滩，第7025-7034页。
[47] Ye，J.，Lu，X.，Lin，Z.，&amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；Wang，J.Z.（2018）。重新思考卷积层通道剪枝中的小无范数信息假设。参加：学习代表国际会议。
[48] Ye，S.，Xu，K.，Liu，S.、Cheng，H.、Lambrechts，J.H.、Zhang，H.，Zhou，A.、Ma，K.、Wang，Y.和amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；Lin，X.（2019）。对抗性稳健性与模型压缩，或两者兼而有之？参加：计算机视觉国际会议。
[49] Zhang，H.，Yu，Y.，Jiao，J.，Xing，E.P.，Ghaoui，L.E.和；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；Jordan，M.I.（2019）。在理论上权衡稳健性和准确性。摘自：第36届国际机器学习会议记录，2019年6月9日至15日，美国加利福尼亚州长滩，ICML 2019，第7472-7482页。
[50] Zhang，T.和；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；朱忠（2019）。解释经过对手训练的卷积神经网络。摘自：第36届机器学习国际会议记录，2019年6月9日至15日，美国加利福尼亚州长滩，第7502-7511页。
[51] Zhao，Y.、Shumailov，I.、Mullins，R.和；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；amp；Anderson，R.（2018）。压缩或不压缩：了解对抗性攻击和神经网络压缩之间的相互作用。arXiv预打印arXiv:181000208。
此参考列表基于出版商或数字数学图书馆提供的信息。其项与zbMATH标识符进行启发式匹配，可能包含数据转换错误。在某些情况下，zbMATH Open的数据对这些数据进行了补充/增强。这试图尽可能准确地反映原始论文中列出的参考文献，而不要求完整或完全匹配。