Sparse and Imperceptible Adversarial Attack via a Homotopy Algorithm
This work addresses the vulnerability of deep neural networks to adversarial attacks, which is a critical security concern for AI systems, but it is incremental as it builds on existing sparse and imperceptible attack methods.
The paper tackles the challenge of generating sparse and imperceptible adversarial attacks on deep neural networks by proposing a homotopy algorithm that jointly optimizes sparsity and perturbation bounds, resulting in significantly fewer perturbations, such as reductions of 42.91% on CIFAR-10 and 75.03% on ImageNet, while maintaining 100% attack success rates.
Sparse adversarial attacks can fool deep neural networks (DNNs) by only perturbing a few pixels (regularized by l_0 norm). Recent efforts combine it with another l_infty imperceptible on the perturbation magnitudes. The resultant sparse and imperceptible attacks are practically relevant, and indicate an even higher vulnerability of DNNs that we usually imagined. However, such attacks are more challenging to generate due to the optimization difficulty by coupling the l_0 regularizer and box constraints with a non-convex objective. In this paper, we address this challenge by proposing a homotopy algorithm, to jointly tackle the sparsity and the perturbation bound in one unified framework. Each iteration, the main step of our algorithm is to optimize an l_0-regularized adversarial loss, by leveraging the nonmonotone Accelerated Proximal Gradient Method (nmAPG) for nonconvex programming; it is followed by an l_0 change control step, and an optional post-attack step designed to escape bad local minima. We also extend the algorithm to handling the structural sparsity regularizer. We extensively examine the effectiveness of our proposed homotopy attack for both targeted and non-targeted attack scenarios, on CIFAR-10 and ImageNet datasets. Compared to state-of-the-art methods, our homotopy attack leads to significantly fewer perturbations, e.g., reducing 42.91% on CIFAR-10 and 75.03% on ImageNet (average case, targeted attack), at similar maximal perturbation magnitudes, when still achieving 100% attack success rates. Our codes are available at: https://github.com/VITA-Group/SparseADV_Homotopy.