  Although deep convolutional neural networks (CNNs) have demonstrated
remarkable performance on multiple computer vision tasks, researches on
adversarial learning have shown that deep models are vulnerable to adversarial
examples, which are crafted by adding visually imperceptible perturbations to
the input images. Most of the existing adversarial attack methods only create a
single adversarial example for the input, which just gives a glimpse of the
underlying data manifold of adversarial examples. An attractive solution is to
explore the solution space of the adversarial examples and generate a diverse
bunch of them, which could potentially improve the robustness of real-world
systems and help prevent severe security threats and vulnerabilities. In this
paper, we present an effective method, called Hamiltonian Monte Carlo with
Accumulated Momentum (HMCAM), aiming to generate a sequence of adversarial
examples. To improve the efficiency of HMC, we propose a new regime to
automatically control the length of trajectories, which allows the algorithm to
move with adaptive step sizes along the search direction at different
positions. Moreover, we revisit the reason for high computational cost of
adversarial training under the view of MCMC and design a new generative method
called Contrastive Adversarial Training (CAT), which approaches equilibrium
distribution of adversarial examples with only few iterations by building from
small modifications of the standard Contrastive Divergence (CD) and achieve a
trade-off between efficiency and accuracy. Both quantitative and qualitative
analysis on several natural image datasets and practical systems have confirmed
the superiority of the proposed algorithm.
