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.

翻译：众所周知，训练后的卷积神经网络(CNN)对不同频率信号的敏感度存在显著差异。特别地，大量实证研究记录了CNN对低频信号的敏感性。本研究通过理论与实验表明，这种观测到的敏感性源于自然图像的频率分布特性，该分布的主要能量集中在低频至中频区间。我们的理论分析基于CNN各层在频率空间中的表示，这一思想先前已被用于加速计算和研究网络训练算法的隐式偏差，但据我们所知，尚未应用于模型鲁棒性领域。