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We show the sup-norm convergence of deep neural network estimators with a novel adversarial training scheme.
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Robert M De Jong · 2002
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Shuanglin Zhang, Man-Yu Wong, and Zhongguo Zheng · 2002
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Evarist Giné, Vladimir Koltchinskii, and Lyudmila Sakhanenko · 2004
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Evarist Giné and Richard Nickl · 2011
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Minimax theory of image reconstruction
Aleksandr Petrovich Korostelev and Alexandre B Tsybakov · 2012
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On the estimation of smooth densities by strict probability densities at optimal rates in sup-norm
Evarist Giné and Hailin Sang · 2013
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Ismaël Castillo · 2014
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Ian J Goodfellow, Jonathon Shlens, and Christian Szegedy · 2014
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Alexandre Belloni, Victor Chernozhukov, Denis Chetverikov, and Kengo Kato · 2015
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Optimal uniform convergence rates and asymptotic normality for series estimators under weak dependence and weak conditions
Xiaohong Chen and Timothy M Christensen · 2015
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Marc Hoffmann, Judith Rousseau, and Johannes Schmidt-Hieber · 2015
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Deep residual learning for image recognition
Vc classes are adversarially robustly learnable, but only improperly
Omar Montasser, Steve Hanneke, and Nathan Srebro · 2019
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Deep relu network approximation of functions on a manifold
Johannes Schmidt-Hieber · 2019
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Improving adversarial robustness requires revisiting misclassified examples
Yisen Wang, Difan Zou, Jinfeng Yi, James Bailey, Xingjun Ma, and Quanquan Gu · 2019
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Rademacher complexity for adversarially robust generalization
Dong Yin, Ramchandran Kannan, and Peter Bartlett · 2019
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Adversarially robust generalization just requires more unlabeled data
Runtian Zhai, Tianle Cai, Di He, Chen Dan, Kun He, John Hopcroft, and Liwei Wang · 2019
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Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun · 2016
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Adversarial machine learning at scale
Alexey Kurakin, Ian Goodfellow, and Samy Bengio · 2016
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Distillation as a defense to adversarial perturbations against deep neural networks
Nicolas Papernot, Patrick McDaniel, Xi Wu, Somesh Jha, and Ananthram Swami · 2016
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Supremum norm posterior contraction and credible sets for nonparametric multivariate regression
William Weimin Yoo and Subhashis Ghosal · 2016
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Nearly-tight vc-dimension bounds for piecewise linear neural networks
Nick Harvey, Christopher Liaw, and Abbas Mehrabian · 2017
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Imagenet classification with deep convolutional neural networks
Alex Krizhevsky, Ilya Sutskever, and Geoffrey E Hinton · 2017
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The expressive power of neural networks: A view from the width
Zhou Lu, Hongming Pu, Feicheng Wang, Zhiqiang Hu, and Liwei Wang · 2017
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Theoretically principled trade-off between robustness and accuracy
Hongyang Zhang, Yaodong Yu, Jiantao Jiao, Eric Xing, Laurent El Ghaoui, and Michael Jordan · 2019
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Precise tradeoffs in adversarial training for linear regression
Adel Javanmard, Mahdi Soltanolkotabi, and Hamed Hassani · 2020
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Adaptive approximation and generalization of deep neural network with intrinsic dimensionality
Ryumei Nakada and Masaaki Imaizumi · 2020
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Adversarial training is a form of data-dependent operator norm regularization
Kevin Roth, Yannic Kilcher, and Thomas Hofmann · 2020
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Nonparametric regression using deep neural networks with relu activation function
Johannes Schmidt-Hieber · 2020
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Deep neural networks for estimation and inference
Max H Farrell, Tengyuan Liang, and Sanjog Misra · 2021
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Mathematical foundations of infinite-dimensional statistical models
Evarist Giné and Richard Nickl · 2021
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Deep nonparametric regression on approximately low-dimensional manifolds
Yuling Jiao, Guohao Shen, Yuanyuan Lin, and Jian Huang · 2021
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On the rate of convergence of fully connected deep neural network regression estimates
Michael Kohler and Sophie Langer · 2021
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Deep network approximation for smooth functions
Jianfeng Lu, Zuowei Shen, Haizhao Yang, and Shijun Zhang · 2021
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Fundamental tradeoffs in distributionally adversarial training
Mohammad Mehrabi, Adel Javanmard, Ryan A Rossi, Anup Rao, and Tung Mai · 2021
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Deep quantile regression: Mitigating the curse of dimensionality through composition
Guohao Shen, Yuling Jiao, Yuanyuan Lin, Joel L. Horowitz, and Jian Huang · 2021
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Robust nonparametric regression with deep neural networks
Guohao Shen, Yuling Jiao, Yuanyuan Lin, and Jian Huang · 2021
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Deep learning is adaptive to intrinsic dimensionality of model smoothness in anisotropic besov space
Taiji Suzuki and Atsushi Nitanda · 2021
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Estimation error analysis of deep learning on the regression problem on the variable exponent besov space
Kazuma Tsuji and Taiji Suzuki · 2021
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On the convergence and robustness of adversarial training
Yisen Wang, Xingjun Ma, James Bailey, Jinfeng Yi, Bowen Zhou, and Quanquan Gu · 2021
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Hamed Hassani and Adel Javanmard · 2022
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Advantage of deep neural networks for estimating functions with singularity on hypersurfaces
Masaaki Imaizumi and Kenji Fukumizu · 2022
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Overparameterized linear regression under adversarial attacks
Antônio H Ribeiro and Thomas B Schön · 2022
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Local convergence rates of the least squares estimator with applications to transfer learning
Johannes Schmidt-Hieber and Petr Zamolodtchikov · 2022
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