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    Network Moments: Extensions and Sparse-Smooth Attacks

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    Type
    Preprint
    Authors
    Alfadly, Modar cc
    Bibi, Adel cc
    Botero, Emilio
    Al-Subaihi, Salman
    Ghanem, Bernard cc
    KAUST Department
    Computer Science Program
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Electrical Engineering
    Electrical Engineering Program
    VCC Analytics Research Group
    Date
    2020-06-21
    Permanent link to this record
    http://hdl.handle.net/10754/663903
    
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    Abstract
    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.
    Publisher
    arXiv
    arXiv
    2006.11776
    Additional Links
    https://arxiv.org/pdf/2006.11776
    Collections
    Preprints; Computer Science Program; Electrical and Computer Engineering Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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