ShuffleNet is a state-of-the-art light weight convolutional neural
network architecture. Its basic operations include group, channelwise
convolution and channel shuffling. However, channel shuffling
is manually designed on empirical grounds. Mathematically, shuffling
is a multiplication by a permutation matrix. In this paper, we
propose to automate channel shuffling by learning permutation
matrices in network training. We introduce an exact Lipschitz continuous
non-convex penalty so that it can be incorporated in the
stochastic gradient descent to approximate permutation at high
precision. Exact permutations are obtained by simple rounding at
the end of training and are used in inference. The resulting network,
referred to as AutoShuffleNet, achieved improved classification accuracies
on data from CIFAR-10, CIFAR-100 and ImageNet while
preserving the inference costs of ShuffleNet. In addition, we found
experimentally that the standard convex relaxation of permutation
matrices into stochastic matrices leads to poor performance. We
prove theoretically the exactness (error bounds) in recovering permutation
matrices when our penalty function is zero (very small).
We present examples of permutation optimization through graph
matching and two-layer neural network models where the loss
functions are calculated in closed analytical form. In the examples,
convex relaxation failed to capture permutations whereas our
penalty succeeded.
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Convex Optimization for Shallow Neural Networks
We consider non-convex training of shallow neural networks and introduce a convex relaxation approach with theoretical guarantees. For the single neuron case, we prove that the relaxation preserves the location of the global minimum under a planted model assumption. Therefore, a globally optimal solution can be efficiently found via a gradient method. We show that gradient descent applied on the relaxation always outperforms gradient descent on the original non-convex loss with no additional computational cost. We then characterize this relaxation as a regularizer and further introduce extensions to multineuron single hidden layer networks.
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- Award ID(s):
- 1838179
- NSF-PAR ID:
- 10128378
- Date Published:
- Journal Name:
- 2019 57th Annual Allerton Conference on Communication, Control, and Computing (Allerton)
- Page Range / eLocation ID:
- 79 to 83
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/ALLERTON.2019.8919769
