Deep CNNs are known to exhibit the following peculiarity: on the one hand
they generalize extremely well to a test set, while on the other hand they are
extremely sensitive to so-called adversarial perturbations. The extreme
sensitivity of high performance CNNs to adversarial examples casts serious
doubt that these networks are learning high level abstractions in the dataset.
We are concerned with the following question: How can a deep CNN that does not
learn any high level semantics of the dataset manage to generalize so well? The
goal of this article is to measure the tendency of CNNs to learn surface
statistical regularities of the dataset. To this end, we use Fourier filtering
to construct datasets which share the exact same high level abstractions but
exhibit qualitatively different surface statistical regularities. For the SVHN
and CIFAR-10 datasets, we present two Fourier filtered variants: a low
frequency variant and a randomly filtered variant. Each of the Fourier
filtering schemes is tuned to preserve the recognizability of the objects. Our
main finding is that CNNs exhibit a tendency to latch onto the Fourier image
statistics of the training dataset, sometimes exhibiting up to a 28%
generalization gap across the various test sets. Moreover, we observe that
significantly increasing the depth of a network has a very marginal impact on
closing the aforementioned generalization gap. Thus we provide quantitative
evidence supporting the hypothesis that deep CNNs tend to learn surface
statistical regularities in the dataset rather than higher-level abstract
concepts.

本研究使用 Fourier 滤波技术构建数据集，并发现深度 CNN 倾向于抓取训练集的 Fourier 图像统计数据，导致出现高泛化差距，从而支持深层 CNN 更倾向于学习数据集的表面统计规律而非高层次的抽象概念。