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

Towards Understanding the Regularization of Adversarial Robustness on Neural Networks