# Measuring the Transferability of $\\ell\_\\infty$ Attacks by the $\\ell\_2$ Norm Source: [Measuring the Transferability of $\\ell\_\\infty$ Attacks by the $\\ell\_2$ Norm]() Collection index: [llms.txt]() Data updated: 2025-10-26T01:03:50.423Z Authors: Sizhe Chen, Qinghua Tao, Zhixing Ye, Xiaolin Huang Published: 2021-02-20T13:19:31.000Z ## 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. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. ## Original sources and implementation [Original paper]() [PDF]()