IWA: Integrated Gradient based White-box Attacks for Fooling Deep Neural Networks

The widespread application of deep neural network (DNN) techniques is being challenged by adversarial examples, the legitimate input added with imperceptible and well-designed perturbations that can fool DNNs easily in the DNN testing/deploying stage. Previous adversarial example generation algorithms for adversarial white-box attacks used Jacobian gradient information to add perturbations. This information is too imprecise and inexplicit, which will cause unnecessary perturbations when generating adversarial examples. This paper aims to address this issue. We first propose to apply a more informative and distilled gradient information, namely integrated gradient, to generate adversarial examples. To further make the perturbations more imperceptible, we propose to employ the restriction combination of $L_0$ and $L_1/L_2$ secondly, which can restrict the total perturbations and perturbation points simultaneously. Meanwhile, to address the non-differentiable problem of $L_1$, we explore a proximal operation of $L_1$ thirdly. Based on these three works, we propose two Integrated gradient based White-box Adversarial example generation algorithms (IWA): IFPA and IUA. IFPA is suitable for situations where there are a determined number of points to be perturbed. IUA is suitable for situations where no perturbation point number is preset in order to obtain more adversarial examples. We verify the effectiveness of the proposed algorithms on both structured and unstructured datasets, and we compare them with five baseline generation algorithms. The results show that our proposed algorithms do craft adversarial examples with more imperceptible perturbations and satisfactory crafting rate. $L_2$ restriction is more suitable for unstructured dataset and $L_1$ restriction performs better in structured dataset.