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There exists a vast number of adversarial attacks and defences for machinelearning algorithms of various types which makes assessing the robustness ofalgorithms a daunting task. To make matters worse, there is an intrinsic biasin these adversarial algorithms. Here, we organise the problems faced: a) ModelDependence, b) Insufficient Evaluation, c) False Adversarial Samples, and d)Perturbation Dependent Results). Based on this, we propose a model agnosticdual quality assessment method, together with the concept of robustness levelsto tackle them. We validate the dual quality assessment on state-of-the-artneural networks (WideResNet, ResNet, AllConv, DenseNet, NIN, LeNet and CapsNet)as well as adversarial defences for image classification problem. We furthershow that current networks and defences are vulnerable at all levels ofrobustness. The proposed robustness assessment reveals that depending on themetric used (i.e., $L_0$ or $L_\infty$), the robustness may vary significantly.Hence, the duality should be taken into account for a correct evaluation.Moreover, a mathematical derivation, as well as a counter-example, suggest that$L_1$ and $L_2$ metrics alone are not sufficient to avoid spurious adversarialsamples. Interestingly, the threshold attack of the proposed assessment is anovel $L_\infty$ black-box adversarial method which requires even lessperturbation than the One-Pixel Attack (only $12\%$ of One-Pixel Attack'samount of perturbation) to achieve similar results.  Code is available at http://bit.ly/DualQualityAssessment.

Adversarial Robustness Assessment: Why both $L_0$ and $L_\infty$ Attacks Are Necessary