Despite the significant advances in deep learning over the past decade, a major challenge that limits the wide-spread adoption of deep learning has been their fragility to adversarial attacks. This sensitivity to making erroneous predictions in the presence of adversarially perturbed data makes deep neural networks difficult to adopt for certain real-world, mission-critical applications. While much of the research focus has revolved around adversarial example creation and adversarial hardening, the area of performance measures for assessing adversarial robustness is not well explored. Motivated by this, this study presents the concept of residual error, a new performance measure for not only assessing the adversarial robustness of a deep neural network at the individual sample level, but also can be used to differentiate between adversarial and non-adversarial examples to facilitate for adversarial example detection. Furthermore, we introduce a hybrid model for approximating the residual error in a tractable manner. Experimental results using the case of image classification demonstrates the effectiveness and efficacy of the proposed residual error metric for assessing several well-known deep neural network architectures. These results thus illustrate that the proposed measure could be a useful tool for not only assessing the robustness of deep neural networks used in mission-critical scenarios, but also in the design of adversarially robust models.
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