Classifiers such as deep neural networks have been shown to be vulnerable against adversarial perturbations on problems with high-dimensional input space. While adversarial training improves the robustness of classifiers against such adversarial perturbations, it leaves classifiers sensitive to them on a non-negligible fraction of the inputs. We argue that there are two different kinds of adversarial perturbations: shared perturbations which fool a classifier on many inputs and singular perturbations which only fool the classifier on a small fraction of the data. We find that adversarial training increases the robustness of classifiers against shared perturbations. Moreover, it is particularly effective in removing universal perturbations, which can be seen as an extreme form of shared perturbations. Unfortunately, adversarial training does not consistently increase the robustness against singular perturbations on unseen inputs. However, we find that adversarial training decreases robustness of the remaining perturbations against image transformations such as changes to contrast and brightness or  Gaussian blurring. It thus makes successful attacks on the classifier in the physical world less likely. Finally, we show that even singular perturbations can be easily detected and must thus exhibit generalizable patterns even though the perturbations are specific for certain inputs.
We empirically show that adversarial training is effective for removing universal perturbations, makes adversarial examples less robust to image transformations, and leaves them detectable for a detection approach. Analyses adversarial training and its effect on universal adversarial examples as well as standard (basic iteration) adversarial examples and how adversarial training affects detection.  The authors show that adversarial training is effective in protecting against "shared" adversarial perturbation, in particular against universal perturbation, but less effective to protect against singular perturbations.