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    ANCER: Anisotropic Certification via Sample-wise Volume Maximization

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    Type
    Preprint
    Authors
    Eiras, Francisco
    Alfarra, Motasem
    Kumar, M. Pawan
    Torr, Philip H. S.
    Dokania, Puneet K.
    Ghanem, Bernard cc
    Bibi, Adel
    KAUST Department
    Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division
    Electrical and Computer Engineering
    Electrical and Computer Engineering Program
    VCC Analytics Research Group
    Date
    2021-07-09
    Permanent link to this record
    http://hdl.handle.net/10754/670194
    
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    Abstract
    Randomized smoothing has recently emerged as an effective tool that enables certification of deep neural network classifiers at scale. All prior art on randomized smoothing has focused on isotropic $\ell_p$ certification, which has the advantage of yielding certificates that can be easily compared among isotropic methods via $\ell_p$-norm radius. However, isotropic certification limits the region that can be certified around an input to worst-case adversaries, \ie it cannot reason about other "close", potentially large, constant prediction safe regions. To alleviate this issue, (i) we theoretically extend the isotropic randomized smoothing $\ell_1$ and $\ell_2$ certificates to their generalized anisotropic counterparts following a simplified analysis. Moreover, (ii) we propose evaluation metrics allowing for the comparison of general certificates - a certificate is superior to another if it certifies a superset region - with the quantification of each certificate through the volume of the certified region. We introduce ANCER, a practical framework for obtaining anisotropic certificates for a given test set sample via volume maximization. Our empirical results demonstrate that ANCER achieves state-of-the-art $\ell_1$ and $\ell_2$ certified accuracy on both CIFAR-10 and ImageNet at multiple radii, while certifying substantially larger regions in terms of volume, thus highlighting the benefits of moving away from isotropic analysis. Code used in our experiments is available in https://github.com/MotasemAlfarra/ANCER.
    Publisher
    arXiv
    arXiv
    2107.04570
    Additional Links
    https://arxiv.org/pdf/2107.04570.pdf
    Collections
    Preprints; Electrical and Computer Engineering Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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