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We introduce Parseval networks, a form of deep neural networks in which the Lipschitz constant of linear, convolutional and aggregation layers is constrained to be smaller than 1.
A finite algorithm for finding the projection of a point onto the canonical simplex of? n
Michelot, Christian · 1986
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An algorithm for a singly constrained class of quadratic programs subject to upper and lower bounds
Pardalos, Panos M and Kovoor, Naina · 1990
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Improving generalization performance using double backpropagation
Drucker, Harris and Le Cun, Yann · 1992
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Independent component analysis: algorithms and applications
Hyvärinen, Aapo and Oja, Erkki · 2000
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Fast monte carlo algorithms for matrices i: Approximating matrix multiplication
Drineas, Petros, Kannan, Ravi, and Mahoney, Michael W · 2006
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Random projection trees and low dimensional manifolds
Dasgupta, Sanjoy and Freund, Yoav · 2008
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Efficient projections onto the l 1-ball for learning in high dimensions
Duchi, John, Shalev-Shwartz, Shai, Singer, Yoram, and Chandra, Tushar · 2008
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An introduction to frames
Kovačević, Jelena and Chebira, Amina · 2008
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Optimization algorithms on matrix manifolds
Absil, P-A, Mahony, Robert, and Sepulchre, Rodolphe · 2009
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Learning multiple layers of features from tiny images, 2009
Krizhevsky, Alex · 2009
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Randomized algorithms for matrices and data
Mahoney, Michael W et al · 2011
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Robustness and generalization
Xu, Huan and Mannor, Shie · 2012
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Lin, Min, Chen, Qiang, and Yan, Shuicheng · 2013
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Exploiting linear structure within convolutional networks for efficient evaluation
Denton, Emily L, Zaremba, Wojciech, Bruna, Joan, LeCun, Yann, and Fergus, Rob · 2014
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Intriguing properties of neural networks
Szegedy, Christian, Zaremba, Wojciech, Sutskever, Ilya, Bruna, Joan, Erhan, Dumitru, Goodfellow, Ian, and Fergus, Rob · 2014
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Deep speech 2: End-to-end speech recognition in english and mandarin
Amodei, Dario, Anubhai, Rishita, Battenberg, Eric, Case, Carl, Casper, Jared, Catanzaro, Bryan, Chen, Jingdong, Chrzanowski, Mike, Coates, Adam, Diamos, Greg, et al · 2015
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Deep neural networks are easily fooled: High confidence predictions for unrecognizable images
Nguyen, Anh, Yosinski, Jason, and Clune, Jeff · 2015
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Shaham, Uri, Yamada, Yutaro, and Negahban, Sahand · 2015
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Fast projection onto the simplex and the \ \backslash pmb { \{ l } \} _ \ \backslash mathbf { \{ 1 } \} ball
Condat, Laurent · 2016
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Robustness of classifiers: from adversarial to random noise
Fawzi, Alhussein, Moosavi-Dezfooli, Seyed-Mohsen, and Frossard, Pascal · 2016
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Deep residual learning for image recognition
He, Kaiming, Zhang, Xiangyu, Ren, Shaoqing, and Sun, Jian · 2016
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Fawzi, Alhussein, Fawzi, Omar, and Frossard, Pascal · 2015
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Explaining and harnessing adversarial examples
Goodfellow, Ian J, Shlens, Jonathon, and Szegedy, Christian · 2015
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Towards deep neural network architectures robust to adversarial examples
Gu, Shixiang and Rigazio, Luca · 2015
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Distributional smoothing with virtual adversarial training
Miyato, Takeru, Maeda, Shin-ichi, Koyama, Masanori, Nakae, Ken, and Ishii, Shin · 2015
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Deepfool: a simple and accurate method to fool deep neural networks
Moosavi-Dezfooli, Seyed-Mohsen, Fawzi, Alhussein, and Frossard, Pascal · 2015
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Densely connected convolutional networks
Huang, Gao, Liu, Zhuang, Weinberger, Kilian Q, and van der Maaten, Laurens
Cited in the paper.
Deep networks with stochastic depth
Huang, Gao, Sun, Yu, Liu, Zhuang, Sedra, Daniel, and Weinberger, Kilian Q
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Kurakin, Alexey, Goodfellow, Ian, and Bengio, Samy · 2016
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Delving into transferable adversarial examples and black-box attacks
Liu, Yanpei, Chen, Xinyun, Liu, Chang, and Song, Dawn · 2016
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Distillation as a defense to adversarial perturbations against deep neural networks
Papernot, Nicolas, McDaniel, Patrick, Wu, Xi, Jha, Somesh, and Swami, Ananthram · 2016
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Weight normalization: A simple reparameterization to accelerate training of deep neural networks
Salimans, Tim and Kingma, Diederik P · 2016
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Zagoruyko, Sergey and Komodakis, Nikos · 2016
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