  Adversarial examples of deep neural networks are receiving ever increasing
attention because they help in understanding and reducing the sensitivity to
their input. This is natural given the increasing applications of deep neural
networks in our everyday lives. When white-box attacks are almost always
successful, it is typically only the distortion of the perturbations that
matters in their evaluation.
  In this work, we argue that speed is important as well, especially when
considering that fast attacks are required by adversarial training. Given more
time, iterative methods can always find better solutions. We investigate this
speed-distortion trade-off in some depth and introduce a new attack called
boundary projection (BP) that improves upon existing methods by a large margin.
Our key idea is that the classification boundary is a manifold in the image
space: we therefore quickly reach the boundary and then optimize distortion on
this manifold.
