Data dependent frequency sensitivity of convolutional neural networks

Charles Godfrey, Elise Bishoff, Myles McKay, Davis Brown, Grayson Jorgenson, Henry Kvinge, Eleanor Byler

Keywords: deep learning, convolutional neural networks, sparsity, matrix factorization, robustness

TL;DR: We show with theory and experiments that the observed sensitivity of convolutional neural networks (CNNs) to low frequency perturbations of input images is a consequence of the frequency distribution of natural images.

Abstract: It is widely acknowledged that trained convolutional neural networks (CNNs) have different levels of sensitivity to signals of different frequency. In particular, a number of empirical studies have documented CNNs sensitivity to low-frequency signals. In this work we show with theory and experiments that this observed sensitivity is a consequence of the frequency distribution of natural images, which is known to have most of its power concentrated in low-to-mid frequencies. Our theoretical analysis relies on representations of the layers of a CNN in frequency space, an idea that has previously been used to accelerate computations and study implicit bias of network training algorithms, but to the best of our knowledge has not been applied in the domain of model robustness.

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