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2019

Adversarial Robustness May Be at Odds With Simplicity

Nakkiran, Preetum

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Current techniques in machine learning are so far are unable to learn classifiers that are robust to adversarial perturbations.

However, they are able to learn non-robust classifiers with very high accuracy, even in the presence of random perturbations.
Towards explaining this gap, we highlight the hypothesis that $\textit{robust classification may require more complex classifiers (i.e.
more capacity) than standard classification.}$ In this note, we show that this hypothesis is indeed possible, by giving several theoretical examples of classification tasks and sets of "simple" classifiers for which: (1) There exists a simple classifier with high standard accuracy, and also high accuracy under random $\ell_\infty$ noise.

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Christian Szegedy, Wojciech Zaremba, Ilya Sutskever, Joan Bruna, Dumitru Erhan, Ian Goodfellow, and Rob Fergus · 2013
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Aleksander Madry, Aleksandar Makelov, Ludwig Schmidt, Dimitris Tsipras, and Adrian Vladu · 2017
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Obfuscated gradients give a false sense of security: Circumventing defenses to adversarial examples
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Anish Athalye, Nicholas Carlini, and David Wagner · 2018
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