Benford's law: what does it say on adversarial images?
This research provides a basis for developing new adversarial example detection methods for CNNs that do not require modifying the classifier or using raw high-dimensional pixel features.
This paper investigates statistical differences between natural and adversarial images, finding that for a class of adversarial attacks, the distribution of the leading digit of pixels in adversarial images deviates from Benford's law after a specific image transformation. The study shows a direct correlation between attack strength and the degree of deviation from Benford's law.
Convolutional neural networks (CNNs) are fragile to small perturbations in the input images. These networks are thus prone to malicious attacks that perturb the inputs to force a misclassification. Such slightly manipulated images aimed at deceiving the classifier are known as adversarial images. In this work, we investigate statistical differences between natural images and adversarial ones. More precisely, we show that employing a proper image transformation and for a class of adversarial attacks, the distribution of the leading digit of the pixels in adversarial images deviates from Benford's law. The stronger the attack, the more distant the resulting distribution is from Benford's law. Our analysis provides a detailed investigation of this new approach that can serve as a basis for alternative adversarial example detection methods that do not need to modify the original CNN classifier neither work on the raw high-dimensional pixels as features to defend against attacks.