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Deep CNN Sparse Coding Analysis

Abstract: 

Deep Convolutional Sparse Coding (D-CSC) is a framework reminiscent
of deep convolutional neural nets (DCNN), but by omitting the learning of the
dictionaries one can more transparently analyse the role of the
activation function and its ability to recover activation paths
through the layers. Papyan, Romano, and Elad conducted an analysis of
such an architecture \cite{2016arXiv160708194P}, demonstrated the
relationship with DCNNs and proved conditions under which a D-CSC is
guaranteed to recover activation paths. A technical innovation of
their work highlights that one can view the efficacy of the ReLU nonlinear activation
function of a DCNN through a new variant of the tensor's sparsity,
referred to as stripe-sparsity.Using this they
proved that representations with an activation density proportional to the
ambient dimension of the data are recoverable. We extend their uniform guarantees
to a modified model and prove that with high
probability the true activation is typically possible to recover
for a greater density of activations per layer. Our extension
follows from incorporating the prior work on one step thresholding by
Schnass and Vandergheynst into the appropriately
modified architecture of Papyan et al.

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Paper Details

Authors:
Michael Murray, Jared Tanner
Submitted On:
31 May 2018 - 12:05pm
Short Link:
Type:
Poster
Event:
Presenter's Name:
Michael Murray
Document Year:
2018
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Deep CNN Sparse Coding Analysis.pdf

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[1] Michael Murray, Jared Tanner, "Deep CNN Sparse Coding Analysis", IEEE SigPort, 2018. [Online]. Available: http://sigport.org/3225. Accessed: Dec. 10, 2018.
@article{3225-18,
url = {http://sigport.org/3225},
author = {Michael Murray; Jared Tanner },
publisher = {IEEE SigPort},
title = {Deep CNN Sparse Coding Analysis},
year = {2018} }
TY - EJOUR
T1 - Deep CNN Sparse Coding Analysis
AU - Michael Murray; Jared Tanner
PY - 2018
PB - IEEE SigPort
UR - http://sigport.org/3225
ER -
Michael Murray, Jared Tanner. (2018). Deep CNN Sparse Coding Analysis. IEEE SigPort. http://sigport.org/3225
Michael Murray, Jared Tanner, 2018. Deep CNN Sparse Coding Analysis. Available at: http://sigport.org/3225.
Michael Murray, Jared Tanner. (2018). "Deep CNN Sparse Coding Analysis." Web.
1. Michael Murray, Jared Tanner. Deep CNN Sparse Coding Analysis [Internet]. IEEE SigPort; 2018. Available from : http://sigport.org/3225