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Learning a deep convolutional neural network via tensor decomposition | OUP Journals & Magazine | IEEE Xplore

Learning a deep convolutional neural network via tensor decomposition

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Abstract:

In this paper, we study the problem of learning the weights of a deep convolutional neural network. We consider a network where convolutions are carried out over non-over...Show More

Abstract:

In this paper, we study the problem of learning the weights of a deep convolutional neural network. We consider a network where convolutions are carried out over non-overlapping patches. We develop an algorithm for simultaneously learning all the kernels from the training data. Our approach dubbed deep tensor decomposition (DeepTD) is based on a low-rank tensor decomposition. We theoretically investigate DeepTD under a realizable model for the training data where the inputs are chosen i.i.d. from a Gaussian distribution and the labels are generated according to planted convolutional kernels. We show that DeepTD is sample efficient and provably works as soon as the sample size exceeds the total number of convolutional weights in the network.
Published in: Information and Inference: A Journal of the IMA ( Volume: 10, Issue: 3, February 2021)
Page(s): 1031 - 1071
Date of Publication: February 2021

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