Before revision:  We reveal that the Lipschitz continuity depends on the types of constraints of adversarial attacks in the binary linear classification . Specifically, under the L2 constraints, the adversarial loss is smooth except at zero. We extend the analysis to general cases and prove local smoothness in several cases. Our analysis reveals that the constraint of adversarial examples is a cause of the non-smoothness of adversarial loss .
After revision:  We reveal that the Lipschitz continuity depends on the types of constraints of adversarial attacks in the binary linear classification . Specifically, the L_\infty constraint can cause non-smoothness of adversarial loss .