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Deep Neural Networks(DNN) have excessively advanced the field of computervision by achieving state of the art performance in various vision tasks. Theseresults are not limited to the field of vision but can also be seen in speechrecognition and machine translation tasks. Recently, DNNs are found to poorlyfail when tested with samples that are crafted by making imperceptible changesto the original input images. This causes a gap between the validation andadversarial performance of a DNN. An effective and generalizable robustnessmetric for evaluating the performance of DNN on these adversarial inputs isstill missing from the literature. In this paper, we propose Noise SensitivityScore (NSS), a metric that quantifies the performance of a DNN on a specificinput under different forms of fix-directional attacks. An insightfulmathematical explanation is provided for deeply understanding the proposedmetric. By leveraging the NSS, we also proposed a skewness based datasetrobustness metric for evaluating a DNN's adversarial performance on a givendataset. Extensive experiments using widely used state of the art architecturesalong with popular classification datasets, such as MNIST, CIFAR-10, CIFAR-100,and ImageNet, are used to validate the effectiveness and generalization of ourproposed metrics. Instead of simply measuring a DNN's adversarial robustness inthe input domain, as previous works, the proposed NSS is built on top ofinsightful mathematical understanding of the adversarial attack and gives amore explicit explanation of the robustness.

An Explainable Adversarial Robustness Metric for Deep Learning Neural Networks