Abstract: The generation of adversarial samples can be due to an optimization problem aimed at maximizing the objective functions of models.Currently,the strategies to solve the induced problems primarily rely on sign-gradient or sign-momentum methods.However,these approaches sacrifice critical gradient and momentum direction information,often leading to convergence issues and then resulting in instability of adversarial attacks.Inspired by the convergence analysis of AMSGrad,this paper proposes a momentum method with monotonical coordinate-wise step-size(MCS-MI) based on MI-FGSM,which enforces monotonically decreasing coordinate-wise step-sizes.For general convex cases,MCS-MI is proved to attain an optimal convergence rate of O(1/T),where T is the number of iterations.Furthermore,the strategy of enforcing monotonic coordinate-wise step-sizes is a general and efficient technique that can be integrated with existing momentum-based attack algorithms.Experimental comparisons with eight state-of-the-art adversarial attack methods on benchmark datasets demonstrate that the proposed approach not only exhibits superior stability but also significantly improves attack success rates,achieving maximum increases of 12.3% on CNN models and 5.9% on ViTs(Vision Transformers) respectively.

Key words: Machine learning, Adversarial attacks, Momentum, Sign-gradient, Convergence