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    Deep Layers as Stochastic Solvers

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    Name:
    deep_layers_as_stochastic_solvers.pdf
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    PDF
    Description:
    Conference Paper
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    Type
    Conference Paper
    Authors
    Bibi, Adel cc
    Ghanem, Bernard cc
    Koltun, Vladlen
    Ranftl, Rene
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Electrical Engineering
    Electrical Engineering Program
    VCC Analytics Research Group
    Date
    2019-02-23
    Submitted Date
    2018-09-18
    Permanent link to this record
    http://hdl.handle.net/10754/662270
    
    Metadata
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    Abstract
    We provide a novel perspective on the forward pass through a block of layers in a deep network. In particular, we show that a forward pass through a standard dropout layer followed by a linear layer and a non-linear activation is equivalent to optimizing a convex objective with a single iteration of a τ-nice Proximal Stochastic Gradient method. We further show that replacing standard Bernoulli dropout with additive dropout is equivalent to optimizing the same convex objective with a variance-reduced proximal method. By expressing both fully-connected and convolutional layers as special cases of a high-order tensor product, we unify the underlying convex optimization problem in the tensor setting and derive a formula for the Lipschitz constant L used to determine the optimal step size of the above proximal methods. We conduct experiments with standard convolutional networks applied to the CIFAR-10 and CIFAR-100 datasets and show that replacing a block of layers with multiple iterations of the corresponding solver, with step size set via L, consistently improves classification accuracy.
    Sponsors
    This work was partially supported by the King Abdullah University of Science and Technology (KAUST) Office of Sponsored Research.
    Publisher
    OpenReview.net
    Conference/Event name
    International Conference on Learning Representations
    Additional Links
    https://openreview.net/forum?id=ryxxCiRqYX
    Collections
    Conference Papers; Electrical Engineering Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

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