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    Channel-Directed Gradients for Optimization of Convolutional Neural Networks

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    Type
    Preprint
    Authors
    Alzahrani, Majed A. cc
    Zhu, Peihao
    Wonka, Peter cc
    Sundaramoorthi, Ganesh cc
    KAUST Department
    Applied Mathematics & Computational Sci
    Applied Mathematics and Computational Science Program
    Computational Vision Lab
    Computer Science
    Computer Science Program
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Electrical Engineering Program
    Visual Computing Center (VCC)
    Date
    2020-08-25
    Permanent link to this record
    http://hdl.handle.net/10754/665108
    
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    Abstract
    We introduce optimization methods for convolutional neural networks that can be used to improve existing gradient-based optimization in terms of generalization error. The method requires only simple processing of existing stochastic gradients, can be used in conjunction with any optimizer, and has only a linear overhead (in the number of parameters) compared to computation of the stochastic gradient. The method works by computing the gradient of the loss function with respect to output-channel directed re-weighted L2 or Sobolev metrics, which has the effect of smoothing components of the gradient across a certain direction of the parameter tensor. We show that defining the gradients along the output channel direction leads to a performance boost, while other directions can be detrimental. We present the continuum theory of such gradients, its discretization, and application to deep networks. Experiments on benchmark datasets, several networks and baseline optimizers show that optimizers can be improved in generalization error by simply computing the stochastic gradient with respect to output-channel directed metrics.
    Publisher
    arXiv
    arXiv
    2008.10766
    Additional Links
    https://arxiv.org/pdf/2008.10766
    Collections
    Preprints; Applied Mathematics and Computational Science Program; Computer Science Program; Electrical Engineering Program; Visual Computing Center (VCC); Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

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