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    Expected Tight Bounds for Robust Deep Neural Network Training

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    Type
    Preprint
    Authors
    Al-Subaihi, Salman
    Bibi, Adel cc
    Alfadly, Modar cc
    Ghanem, Bernard cc
    Hamdi, Abdullah cc
    KAUST Department
    Electrical Engineering Program
    Computer Science Program
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Date
    2019-05-28
    Permanent link to this record
    http://hdl.handle.net/10754/660655
    
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    Abstract
    Training Deep Neural Networks (DNNs) that are robust to norm bounded adversarial attacks remains an elusive problem. While verification based methods are generally too expensive to robustly train large networks, it was demonstrated in Gowal et al that bounded input intervals can be inexpensively propagated per layer through large networks. This interval bound propagation (IBP) approach led to high robustness and was the first to be employed on large networks. However, due to the very loose nature of the IBP bounds, particularly for large networks, the required training procedure is complex and involved. In this paper, we closely examine the bounds of a block of layers composed of an affine layer followed by a ReLU nonlinearity followed by another affine layer. To this end, we propose expected bounds, true bounds in expectation, that are provably tighter than IBP bounds in expectation. We then extend this result to deeper networks through blockwise propagation and show that we can achieve orders of magnitudes tighter bounds compared to IBP. With such tight bounds, we demonstrate that a simple standard training procedure can achieve the best robustness-accuracy trade-off across several architectures on both MNIST and CIFAR10.
    Sponsors
    This work was supported by the King Abdullah University of Science and Technology (KAUST) Office of Sponsored Research.
    Publisher
    arXiv
    arXiv
    1905.12418
    Additional Links
    https://arxiv.org/pdf/1905.12418
    Collections
    Preprints; Computer Science Program; Electrical Engineering Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

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