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：人们普遍承认,经过培训的进化神经网络对不同频率信号的敏感度不同,特别是,一些经验性研究记录了CNN对低频信号的敏感度,在这项工作中,我们用理论和实验表明,观察到的这种敏感度是自然图像频率分布的结果,据知自然图像大部分的能量集中在中低频频率。我们的理论分析依赖于CNN在频率空间的层次的描述,这一想法过去曾被用来加速计算和研究网络培训算法的隐含偏差,但据我们所知,在模型稳健性领域没有应用到我们的知识。