Investigating Top-$k$ White-Box and Transferable Black-box Attack

Existing works have identified the limitation of top-$1$ attack success rate (ASR) as a metric to evaluate the attack strength but exclusively investigated it in the white-box setting, while our work extends it to a more practical black-box setting: transferable attack. It is widely reported that stronger I-FGSM transfers worse than simple FGSM, leading to a popular belief that transferability is at odds with the white-box attack strength. Our work challenges this belief with empirical finding that stronger attack actually transfers better for the general top-$k$ ASR indicated by the interest class rank (ICR) after attack. For increasing the attack strength, with an intuitive interpretation of the logit gradient from the geometric perspective, we identify that the weakness of the commonly used losses lie in prioritizing the speed to fool the network instead of maximizing its strength. To this end, we propose a new normalized CE loss that guides the logit to be updated in the direction of implicitly maximizing its rank distance from the ground-truth class. Extensive results in various settings have verified that our proposed new loss is simple yet effective for top-$k$ attack. Code is available at: \url{https://bit.ly/3uCiomP}