Although great progress has been made on adversarial attacks for deep neural networks (DNNs), their transferability is still unsatisfactory, especially for targeted attacks. There are two problems behind that have been long overlooked: 1) the conventional setting of $T$ iterations with the step size of $epsilon/T$ to comply with the $epsilon$-constraint. In this case, most of the pixels are allowed to add very small noise, much less than $epsilon$; and 2) usually manipulating pixel-wise noise. However, features of a pixel extracted by DNNs are influenced by its surrounding regions, and different DNNs generally focus on different discriminative regions in recognition. To tackle these issues, our previous work proposes a patch-wise iterative method (PIM) aimed at crafting adversarial examples with high transferability. Specifically, we introduce an amplification factor to the step size in each iteration, and one pixels overall gradient overflowing the $epsilon$-constraint is properly assigned to its surrounding regions by a project kernel. But targeted attacks aim to push the adversarial examples into the territory of a specific class, and the amplification factor may lead to underfitting. Thus, we introduce the temperature and propose a patch-wise++ iterative method (PIM++) to further improve transferability without significantly sacrificing the performance of the white-box attack. Our method can be generally integrated to any gradient-based attack methods. Compared with the current state-of-the-art attack methods, we significantly improve the success rate by 33.1% for defense models and 31.4% for normally trained models on average.
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