Probabilistic Jacobian-based Saliency Maps Attacks

Neural network classifiers (NNC) are known to be vulnerable to malicious adversarial perturbations of inputs including those modifying a small fraction of the input features named sparse or $L_0$ attacks. Effective and fast $L_0$ attacks are practical to thwart NNC and improve their robustness. In particular, the Jacobian-based Saliency Map Attack (JSMA) is a fast, widely used method to fool NNC. In this paper, we introduce new variants of JSMA that can be used for targeted and non-targeted misclassification of NNC. Our attacks are derived by crucially penalising saliency maps of JSMA by the output probabilities and the input features of the NNC. We propose Weighted JSMA (WJSMA) and Taylor JSMA (TJSMA) and demonstrate, through a variety of white-box and black-box experiments on three different datasets (MNIST, CIFAR-10 and GTSRB), that they are significantly faster and more efficient than JSMA as well as its known non-targeted versions. Experiments also demonstrate, in some cases, very competitive results of our attacks in comparison with Carlini-Wagner (CW) $L_0$ attack. Our attacks are, however, significantly much faster than CW $L_0$ (for example more than 50 hundred times faster measuring the average execution time on CIFAR-10). Therefore, they provide good trade-offs between JSMA and CW for $L_0$ real-time adversarial testing on datasets as the previous ones. Codes are publicly available through the link https://github.com/probabilistic-jsmas/probabilistic-jsmas.