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We show a hardness result for random smoothing to achieve certified adversarial robustness against attacks in the $\ell_p$ ball of radius $\epsilon$ when $p>2$.
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Semidefinite relaxations for certifying robustness to adversarial examples
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Xiao Yang, Fangyun Wei, Hongyang Zhang, Xiang Ming, and Jun Zhu · 2019
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Hongyang Zhang, Yaodong Yu, Jiantao Jiao, Eric P Xing, Laurent El Ghaoui, and Michael I Jordan · 2019
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