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Several recent results provide theoretical insights into the phenomena of adversarial examples.
On the uniform convergence of relative frequencies of events to their probabilities
Vladimir N Vapnik and A Ya Chervonenkis · 1971
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Regression shrinkage and selection via the lasso
Robert Tibshirani · 1996
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Optimally sparse representation in general (nonorthogonal) dictionaries via ℓ 1 \ell_{1} minimization
David L Donoho and Michael Elad · 2003
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Improved sparse approximation over quasiincoherent dictionaries
Joel A Tropp, Anna C Gilbert, Sambavi Muthukrishnan, and Martin J Strauss · 2003
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On the importance of small coordinate projections
Shahar Mendelson and Petra Philips · 2004
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Just relax: Convex programming methods for identifying sparse signals in noise
Joel A Tropp · 2006
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Sparse representation for color image restoration
Julien Mairal, Michael Elad, and Guillermo Sapiro · 2007
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Unsupervised learning of invariant feature hierarchies with applications to object recognition
Marc’Aurelio Ranzato, Fu Jie Huang, Y-Lan Boureau, and Yann LeCun · 2007
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Discriminative learned dictionaries for local image analysis
Julien Mairal, Francis Bach, Jean Ponce, Guillermo Sapiro, and Andrew Zisserman · 2008
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A fast iterative shrinkage-thresholding algorithm for linear inverse problems
Amir Beck and Marc Teboulle · 2009
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Sparse and redundant representations: from theory to applications in signal and image processing
Michael Elad · 2010
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Fast inference in sparse coding algorithms with applications to object recognition
Koray Kavukcuoglu, Marc’Aurelio Ranzato, and Yann LeCun · 2010
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Sparse representation for computer vision and pattern recognition
John Wright, Yi Ma, Julien Mairal, Guillermo Sapiro, Thomas S Huang, and Shuicheng Yan · 2010
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Deconvolutional networks
Matthew D Zeiler, Dilip Krishnan, Graham W Taylor, and Rob Fergus · 2010
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The importance of encoding versus training with sparse coding and vector quantization
Adam Coates and Andrew Y Ng · 2011
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Unsupervised learning of sparse features for scalable audio classification
Mikael Henaff, Kevin Jarrett, Koray Kavukcuoglu, and Yann LeCun · 2011
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Task-driven dictionary learning
Julien Mairal, Francis Bach, and Jean Ponce · 2011
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Evasion attacks against machine learning at test time
Battista Biggio, Igino Corona, Davide Maiorca, Blaine Nelson, Nedim Srndić, Pavel Laskov, Giorgio Giacinto, and Fabio Roli · 2013
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Robust sparse regression under adversarial corruption
Yudong Chen, Constantine Caramanis, and Shie Mannor · 2013
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Sparsity-based generalization bounds for predictive sparse coding
Nishant Mehta and Alexander Gray · 2013
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Intriguing properties of neural networks
Christian Szegedy, Wojciech Zaremba, Ilya Sutskever, Joan Bruna, Dumitru Erhan, Ian Goodfellow, and Rob Fergus · 2013
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The lasso problem and uniqueness
Ryan J Tibshirani et al · 2013
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Explaining and harnessing adversarial examples
Ian J Goodfellow, Jonathon Shlens, and Christian Szegedy · 2014
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Towards deep neural network architectures robust to adversarial examples
Shixiang Gu and Luca Rigazio · 2014
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Projective dictionary pair learning for pattern classification
Shuhang Gu, Lei Zhang, Wangmeng Zuo, and Xiangchu Feng · 2014
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Adam: A method for stochastic optimization
Diederik P Kingma and Jimmy Ba · 2014
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Sample complexity of dictionary learning and other matrix factorizations
Rémi Gribonval, Rodolphe Jenatton, Francis Bach, Martin Kleinsteuber, and Matthias Seibert · 2015
Cited alongside, same era.
On security and sparsity of linear classifiers for adversarial settings
Ambra Demontis, Paolo Russu, Battista Biggio, Giorgio Fumera, and Fabio Roli · 2016
Cited alongside, same era.
Adversarially robust generalization requires more data
Ludwig Schmidt, Shibani Santurkar, Dimitris Tsipras, Kunal Talwar, and Aleksander Madry · 2018
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Are adversarial examples inevitable?
Ali Shafahi, W Ronny Huang, Christoph Studer, Soheil Feizi, and Tom Goldstein · 2018
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Robustness may be at odds with accuracy
Dimitris Tsipras, Shibani Santurkar, Logan Engstrom, Alexander Turner, and Aleksander Madry · 2018
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Rademacher complexity for adversarially robust generalization
Dong Yin, Kannan Ramchandran, and Peter Bartlett · 2018
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Multi-layer sparse coding: the holistic way
Aviad Aberdam, Jeremias Sulam, and Michael Elad · 2019
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Thomas Moreau and Joan Bruna · 2016
Cited alongside, same era.
Maximal sparsity with deep networks?
Bo Xin, Yizhou Wang, Wen Gao, David Wipf, and Baoyuan Wang · 2016
Cited alongside, same era.
Adversarial examples are not easily detected: Bypassing ten detection methods
Nicholas Carlini and David Wagner · 2017
Cited alongside, same era.
Parseval networks: Improving robustness to adversarial examples
Moustapha Cisse, Piotr Bojanowski, Edouard Grave, Yann Dauphin, and Nicolas Usunier · 2017
Cited alongside, same era.
A mathematical introduction to compressive sensing
Simon Foucart and Holger Rauhut · 2017
Cited alongside, same era.
Towards deep learning models resistant to adversarial attacks
Aleksander Madry, Aleksandar Makelov, Ludwig Schmidt, Dimitris Tsipras, and Adrian Vladu · 2017
Cited alongside, same era.
On detecting adversarial perturbations
Jan Hendrik Metzen, Tim Genewein, Volker Fischer, and Bastian Bischoff · 2017
Cited alongside, same era.
Adversarial risk bounds for neural networks through sparsity based compression
Emilio Rafael Balda, Arash Behboodi, Niklas Koep, and Rudolf Mathar · 2019
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Convergence and margin of adversarial training on separable data
Zachary Charles, Shashank Rajput, Stephen Wright, and Dimitris Papailiopoulos · 2019
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Certified adversarial robustness via randomized smoothing
Jeremy M Cohen, Elan Rosenfeld, and J Zico Kolter · 2019
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https://www.darpa.mil/news-events/2019-02-06 , 2019
DARPA · 2019
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Adversarial examples are not bugs, they are features
Andrew Ilyas, Shibani Santurkar, Dimitris Tsipras, Logan Engstrom, Brandon Tran, and Aleksander Madry · 2019
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Inductive bias of gradient descent based adversarial training on separable data
Yan Li, Ethan X Fang, Huan Xu, and Tuo Zhao · 2019
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Adversarial noise attacks of deep learning architectures: Stability analysis via sparse-modeled signals
Yaniv Romano, Aviad Aberdam, Jeremias Sulam, and Michael Elad · 2019
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Sample Complexity of Representation Learning for Sparse and Related Data Models
Matthias Seibert · 2019
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On multi-layer basis pursuit, efficient algorithms and convolutional neural networks
Jeremias Sulam, Aviad Aberdam, Amir Beck, and Michael Elad · 2019
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Deep residual auto-encoders for expectation maximization-based dictionary learning
Bahareh Tolooshams, Sourav Dey, and Demba Ba · 2019
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Theoretical analysis of adversarial learning: A minimax approach
Zhuozhuo Tu, Jingwei Zhang, and Dacheng Tao · 2019
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Ada-lista: Learned solvers adaptive to varying models
Aviad Aberdam, Alona Golts, and Michael Elad · 2020
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Fast convex pruning of deep neural networks
Alireza Aghasi, Afshin Abdi, and Justin Romberg · 2020
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Feature purification: How adversarial training performs robust deep learning
Zeyuan Allen-Zhu and Yuanzhi Li · 2020
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Dataless model selection with the deep frame potential
Calvin Murdock and Simon Lucey · 2020
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Black-box smoothing: A provable defense for pretrained classifiers
Hadi Salman, Mingjie Sun, Greg Yang, Ashish Kapoor, and J Zico Kolter · 2020
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On adaptive attacks to adversarial example defenses
Florian Tramer, Nicholas Carlini, Wieland Brendel, and Aleksander Madry · 2020
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