  The problem of adversarial examples has shown that modern Neural Network (NN)
models could be rather fragile. Among the more established techniques to solve
the problem, one is to require the model to be {\it $\epsilon$-adversarially
robust} (AR); that is, to require the model not to change predicted labels when
any given input examples are perturbed within a certain range. However, it is
observed that such methods would lead to standard performance degradation,
i.e., the degradation on natural examples. In this work, we study the
degradation through the regularization perspective. We identify quantities from
generalization analysis of NNs; with the identified quantities we empirically
find that AR is achieved by regularizing/biasing NNs towards less confident
solutions by making the changes in the feature space (induced by changes in the
instance space) of most layers smoother uniformly in all directions; so to a
certain extent, it prevents sudden change in prediction w.r.t. perturbations.
However, the end result of such smoothing concentrates samples around decision
boundaries, resulting in less confident solutions, and leads to worse standard
performance. Our studies suggest that one might consider ways that build AR
into NNs in a gentler way to avoid the problematic regularization.
