title: Effective and Robust Detection of Adversarial Examples via Benford-Fourier Coefficients
abstract: Adversarial examples have been well known as a serious threat to deep neural
  networks (DNNs). To ensure successful and safe operations of DNNs on realworld tasks, 
  it is urgent to equip DNNs with effective defense strategies. 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. Through the
  Kolmogorov-Smirnov (KS) test, we empirically verify that: 1) the posterior vectors 
  of both adversarial and benign examples follow GGD; 2) the extracted MBF features 
  of adversarial and benign examples follow different distributions. 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, in contrast to state-of-the-art 
  adversarial detection methods.
authors: Chengcheng Ma Baoyuan Wu Shibiao Xu Yanbo Fan Yong Zhang Xiaopeng Zhang Zhifeng Li
hIndex: Zhifeng Li 34