Before revision:  We reveal that the Lipschitz continuity depends on the types of constraints of adversarial attacks in this case . Specifically, under the L2 constraints, the adversarial loss is smooth except at zero  .
After revision:  We reveal that the Lipschitz continuity depends on the types of constraints of adversarial attacks in this case . 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. Moreover, we reveal the relation between the flatness of the loss function with respect to input data and the smoothness of the adversarial loss with respect to parameters. Our analysis implies that if we flatten the loss function with respect to input data, the smoothness of adversarial loss tends to decrease .