Image classifiers based on deep neural networks suffer from harassment caused by adversarial examples. Two defects exist in black-box iterative attacks that generate adversarial examples by incrementally adjusting the noise-adding direction for each step. On the one hand, existing iterative attacks add noises monotonically along the direction of gradient ascent, resulting in a lack of diversity and adaptability of the generated iterative trajectories. On the other hand, it is trivial to perform adversarial attack by adding excessive noises, but currently there is no refinement mechanism to squeeze redundant noises. In this work, we propose Curls & Whey black-box attack to fix the above two defects. During Curls iteration, by combining gradient ascent and descent, we curl' up iterative trajectories to integrate more diversity and transferability into adversarial examples. Curls iteration also alleviates the diminishing marginal effect in existing iterative attacks. The Whey optimization further squeezes the whey' of noises by exploiting the robustness of adversarial perturbation. Extensive experiments on Imagenet and Tiny-Imagenet demonstrate that our approach achieves impressive decrease on noise magnitude in l2 norm. Curls & Whey attack also shows promising transferability against ensemble models as well as adversarially trained models. In addition, we extend our attack to the targeted misclassification, effectively reducing the difficulty of targeted attacks under black-box condition.
MI-FGSM @cite_8 introduced a momentum term to make the adjustment of the noise-adding direction smoother, but the impact of diminishing marginal effect on iteration number still exists:
@cite_8
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Deep neural networks are vulnerable to adversarial examples, which poses security concerns on these algorithms due to the potentially severe consequences. Adversarial attacks serve as an important surrogate to evaluate the robustness of deep learning models before they are deployed. However, most of existing adversarial attacks can only fool a black-box model with a low success rate. To address this issue, we propose a broad class of momentum-based iterative algorithms to boost adversarial attacks. By integrating the momentum term into the iterative process for attacks, our methods can stabilize update directions and escape from poor local maxima during the iterations, resulting in more transferable adversarial examples. To further improve the success rates for black-box attacks, we apply momentum iterative algorithms to an ensemble of models, and show that the adversarially trained models with a strong defense ability are also vulnerable to our black-box attacks. We hope that the proposed methods will serve as a benchmark for evaluating the robustness of various deep models and defense methods. With this method, we won the first places in NIPS 2017 Non-targeted Adversarial Attack and Targeted Adversarial Attack competitions.