Title: AutoShuffleNet: Learning Permutation Matrices via an Exact Lipschitz Continuous Penalty in Deep Convolutional Neural Networks,
Abstract: ShuffleNet is a state-of-the-art light weight convolutional neural network
architecture. Its basic operations include group, channel-wise convolution and
channel shuffling. However, channel shuffling is manually designed empirically.
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 CIFAR-10 and ImageNet data sets. 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.