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The impressive performance of deep neural networks (DNNs) has immensely strengthened the line of research that aims at theoretically analyzing their effectiveness. This has incited research on the reaction of DNNs to noisy input, namely developing adversarial input attacks and strategies that lead to robust DNNs to these attacks. To that end, in this paper, we derive exact analytic expressions for the first and second moments (mean and variance) of a small piecewise linear (PL) network (Affine, ReLU, Affine) subject to Gaussian input. In particular, we generalize the second-moment expression of Bibi et al. to arbitrary input Gaussian distributions, dropping the zero-mean assumption. We show that the new variance expression can be efficiently approximated leading to much tighter variance estimates as compared to the preliminary results of Bibi et al. Moreover, we experimentally show that these expressions are tight under simple linearizations of deeper PL-DNNs, where we investigate the effect of the linearization sensitivity on the accuracy of the moment estimates. Lastly, we show that the derived expressions can be used to construct sparse and smooth Gaussian adversarial attacks (targeted and non-targeted) that tend to lead to perceptually feasible input attacks.
This paper introduces stochastic sparse adversarial attacks (SSAA), simple, fast and purely noise-based targeted and untargeted $L_0$ attacks of neural network classifiers (NNC). SSAA are devised by exploiting a simple small-time expansion idea widel
Robustness against image perturbations bounded by a $ell_p$ ball have been well-studied in recent literature. Perturbations in the real-world, however, rarely exhibit the pixel independence that $ell_p$ threat models assume. A recently proposed Wasse
Certifiers for neural networks have made great progress towards provable robustness guarantees against evasion attacks using adversarial examples. However, introducing certifiers into deep learning systems also opens up new attack vectors, which need
We investigate how an adversary can optimally use its query budget for targeted evasion attacks against deep neural networks in a black-box setting. We formalize the problem setting and systematically evaluate what benefits the adversary can gain by
Deep neural networks (DNNs) have demonstrated impressive performance on many challenging machine learning tasks. However, DNNs are vulnerable to adversarial inputs generated by adding maliciously crafted perturbations to the benign inputs. As a growi