  Adversarial examples have been well known as a serious threat to deep neural
networks (DNNs). In this work, we study the detection of adversarial examples,
based on the assumption that the output and internal responses of one DNN model
for both adversarial and benign examples follow the generalized Gaussian
distribution (GGD), but with different parameters (i.e., shape factor, mean,
and variance). GGD is a general distribution family to cover many popular
distributions (e.g., Laplacian, Gaussian, or uniform). It is more likely to
approximate the intrinsic distributions of internal responses than any specific
distribution. Besides, since the shape factor is more robust to different
databases rather than the other two parameters, we propose to construct
discriminative features via the shape factor for adversarial detection,
employing the magnitude of Benford-Fourier coefficients (MBF), which can be
easily estimated using responses. Finally, a support vector machine is trained
as the adversarial detector through leveraging the MBF features. Extensive
experiments in terms of image classification demonstrate that the proposed
detector is much more effective and robust on detecting adversarial examples of
different crafting methods and different sources, compared to state-of-the-art
adversarial detection methods.
