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Recent works have shown that the input domain of any machine learningclassifier is bound to contain adversarial examples. Thus we can no longer hopeto immune classifiers against adversarial examples and instead can only aim toachieve the following two defense goals: 1) making adversarial examples harderto find, or 2) weakening their adversarial nature by pushing them further awayfrom correctly classified data points. Most if not all the previously suggesteddefense mechanisms attend to just one of those two goals, and as such, could bebypassed by adaptive attacks that take the defense mechanism intoconsideration. In this work we suggest a novel defense mechanism thatsimultaneously addresses both defense goals: We flatten the gradients of theloss surface, making adversarial examples harder to find, using a novelstochastic regularization term that explicitly decreases the sensitivity ofindividual neurons to small input perturbations. In addition, we push thedecision boundary away from correctly classified inputs by leveraging Jacobianregularization. We present a solid theoretical basis and an empirical testingof our suggested approach, demonstrate its superiority over previouslysuggested defense mechanisms, and show that it is effective against a widerange of adaptive attacks.

Adversarial robustness via stochastic regularization of neural activation sensitivity