Going Far Boosts Attack Transferability, but Do Not Do It

Sizhe Chen, Qinghua Tao, Zhixing Ye, Xiaolin Huang

Abstract: Deep neural networks could be fooled by adversarial examples with trivial differences to original samples. To keep the difference imperceptible in human eyes, researchers bound the adversarial perturbations by the $\ell_\infty$ norm, which is now commonly served as the standard to align the strength of different attacks for a fair comparison. However, we propose that using the $\ell_\infty$ norm alone is not sufficient in measuring the attack strength, because even with a fixed $\ell_\infty$ distance, the $\ell_2$ distance also greatly affects the attack transferability between models. Through the discovery, we reach more in-depth understandings towards the attack mechanism, i.e., several existing methods attack black-box models better partly because they craft perturbations with 70% to 130% larger $\ell_2$ distances. Since larger perturbations naturally lead to better transferability, we thereby advocate that the strength of attacks should be simultaneously measured by both the $\ell_\infty$ and $\ell_2$ norm. Our proposal is firmly supported by extensive experiments on ImageNet dataset from 7 attacks, 4 white-box models, and 9 black-box models.