Abstract: Deep neural networks exhibit significant vulnerability in the face of adversarial examples and are prone to attacks.The construction of adversarial examples can be abstracted as an optimization problem that maximizes the objective function.How-ever,gradient-based iterative methods often face convergence challenges when dealing with such optimization problems.These methods primarily rely on the gradient sign for iterative updates,neglecting the magnitude and direction information of the gra-dient,which can lead to algorithm instability.Studies have shown that the I-FGSM adversarial attack algorithm originates from the stochastic projection subgradient method in the field of optimization.Literature has indicated that in optimization problems,using linear interpolation methods to replace stochastic projection subgradient methods can achieve superior performance.Based on this,this paper proposes a novel linear interpolation-based adversarial attack method,which applies the interpolation strategy to adversarial attacks and replaces the traditional sign gradient with the actual gradient.Theoretically,the proposed linear interpolation adversarial attack algorithm is proved can achieve the optimal individual convergence rate in general convex optimization pro-blems,thereby overcoming the convergence difficulties of sign gradient-based algorithms.Experimental results confirm that the linear interpolation method,as a universal and efficient strategy,when combined with gradient-based adversarial attack methods,can form new attack algorithms.Compared to the original algorithms,these new algorithms significantly increase the success rate of attacks while maintaining the imperceptibility of adversarial examples and exhibit high stability during the iterative process.

Key words: Linear interpolation, Adversarial attack, Gradient sign, Convergence, stability