We describe the class of convexified convolutional neural networks (CCNNs),
which capture the parameter sharing of convolutional neural networks in a
convex manner. By representing the nonlinear convolutional filters as vectors
in a reproducing kernel Hilbert space, the CNN parameters can be represented as
a low-rank matrix, which can be relaxed to obtain a convex optimization
problem. For learning two-layer convolutional neural networks, we prove that
the generalization error obtained by a convexified CNN converges to that of the
best possible CNN. For learning deeper networks, we train CCNNs in a layer-wise
manner. Empirically, CCNNs achieve performance competitive with CNNs trained by
backpropagation, SVMs, fully-connected neural networks, stacked denoising
auto-encoders, and other baseline methods.
%0 Journal Article
%1 zhang2016convexified
%A Zhang, Yuchen
%A Liang, Percy
%A Wainwright, Martin J.
%D 2016
%K deep-learning learning optimization readings theory
%T Convexified Convolutional Neural Networks
%U http://arxiv.org/abs/1609.01000
%X We describe the class of convexified convolutional neural networks (CCNNs),
which capture the parameter sharing of convolutional neural networks in a
convex manner. By representing the nonlinear convolutional filters as vectors
in a reproducing kernel Hilbert space, the CNN parameters can be represented as
a low-rank matrix, which can be relaxed to obtain a convex optimization
problem. For learning two-layer convolutional neural networks, we prove that
the generalization error obtained by a convexified CNN converges to that of the
best possible CNN. For learning deeper networks, we train CCNNs in a layer-wise
manner. Empirically, CCNNs achieve performance competitive with CNNs trained by
backpropagation, SVMs, fully-connected neural networks, stacked denoising
auto-encoders, and other baseline methods.
@article{zhang2016convexified,
abstract = {We describe the class of convexified convolutional neural networks (CCNNs),
which capture the parameter sharing of convolutional neural networks in a
convex manner. By representing the nonlinear convolutional filters as vectors
in a reproducing kernel Hilbert space, the CNN parameters can be represented as
a low-rank matrix, which can be relaxed to obtain a convex optimization
problem. For learning two-layer convolutional neural networks, we prove that
the generalization error obtained by a convexified CNN converges to that of the
best possible CNN. For learning deeper networks, we train CCNNs in a layer-wise
manner. Empirically, CCNNs achieve performance competitive with CNNs trained by
backpropagation, SVMs, fully-connected neural networks, stacked denoising
auto-encoders, and other baseline methods.},
added-at = {2019-11-01T15:37:53.000+0100},
author = {Zhang, Yuchen and Liang, Percy and Wainwright, Martin J.},
biburl = {https://www.bibsonomy.org/bibtex/258b4bddbcc45fdb901efab99ad133109/kirk86},
description = {[1609.01000] Convexified Convolutional Neural Networks},
interhash = {49ec3fad9fdbcedfbd5a1c9daea9f1df},
intrahash = {58b4bddbcc45fdb901efab99ad133109},
keywords = {deep-learning learning optimization readings theory},
note = {cite arxiv:1609.01000Comment: 29 pages},
timestamp = {2019-11-01T15:37:53.000+0100},
title = {Convexified Convolutional Neural Networks},
url = {http://arxiv.org/abs/1609.01000},
year = 2016
}