A law of robustness for two-layers neural networks

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Eric B Baum · 1988

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George Cybenko · 1989

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Multilayer feedforward networks with a nonpolynomial activation function can approximate any function

Moshe Leshno, Vladimir Ya Lin, Allan Pinkus, and Shimon Schocken · 1993

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Arkadi Nemirovski · 2004

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Roman Vershynin · 2012

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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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Explaining and harnessing adversarial examples

Ian Goodfellow, Jonathon Shlens, and Christian Szegedy · 2015

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Batch normalization: Accelerating deep network training by reducing internal covariate shift

Sergey Ioffe and Christian Szegedy · 2015

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Adam: A method for stochastic optimization

Diederik P Kingma and Jimmy Ba · 2015

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Random version of dvoretzky’s theorem in lpn

Grigoris Paouris, Petros Valettas, and Joel Zinn · 2017

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Nuclear norm of higher-order tensors

Shmuel Friedland and Lek-Heng Lim · 2018

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Adversarially robust generalization requires more data

Ludwig Schmidt, Shibani Santurkar, Dimitris Tsipras, Kunal Talwar, and Aleksander Madry · 2018

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Adversarial examples from computational constraints

Sébastien Bubeck, Yin Tat Lee, Eric Price, and Ilya Razenshteyn · 2019

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Computational limitations in robust classification and win-win results

Akshay Degwekar, Preetum Nakkiran, and Vinod Vaikuntanathan · 2019

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Adversarial training can hurt generalization

Aditi Raghunathan, Sang Michael Xie, Fanny Yang, John C Duchi, and Percy Liang · 2019

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Small relu networks are powerful memorizers: a tight analysis of memorization capacity

Chulhee Yun, Suvrit Sra, and Ali Jadbabaie · 2019

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Feature purification: How adversarial training performs robust deep learning