Adversarial examples can deceive a deep neural network (DNN) by significantly altering its response with imperceptible perturbations, which poses new potential vulnerabilities as the growing ubiquity of DNNs. However, most of the existing adversarial examples cannot maintain the malicious functionality if we apply an affine transformation on the resultant examples, which is an important measurement to the robustness of adversarial attacks for the practical risks. To address this issue, we propose an affine-invariant adversarial attack which can consistently construct adversarial examples robust over a distribution of affine transformation. To further improve the efficiency, we propose to disentangle the affine transformation into rotations, translations, magnifications, and reformulate the transformation in polar space. Afterwards, we construct an affine-invariant gradient estimator by convolving the gradient at the original image with derived kernels, which can be integrated with any gradient-based attack methods. Extensive experiments on the ImageNet demonstrate that our method can consistently produce more robust adversarial examples under significant affine transformations, and as a byproduct, improve the transferability of adversarial examples compared with the alternative state-of-the-art methods.
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