We characterize the singular values of the linear transformation associated with a standard 2D multi-channel convolutional layer, enabling their efficient computation. This characterization also leads to an algorithm for projecting a convolutional layer onto an operator-norm ball. We show that this is an effective regularizer; for example, it improves the test error of a deep residual network using batch normalization on CIFAR-10 from 6.2\% to 5.3\%.
@article{arxiv.1805.10408,
title = {The Singular Values of Convolutional Layers},
author = {Hanie Sedghi and Vineet Gupta and Philip M. Long},
journal= {arXiv preprint arXiv:1805.10408},
year = {2019}
}