Deep Learning has enabled significant progress towards more accurate predictions and is increasingly integrated into our everyday lives in real-world applications; this is true especially for Convolutional Neural Networks (CNNs) in the field of image analysis. Nevertheless, it has been shown that Deep Learning is vulnerable against well-crafted, small perturbations to the input, i.e., adversarial examples. Defending against such attacks is therefore crucial to ensure the proper functioning of these models—especially when autonomous decisions are taken in safety-critical applications, such as autonomous vehicles. In this work, shallow machine learning models, such as Logistic Regression and Support Vector Machine, are utilised as surrogates of a CNN based on the assumption that they would be differently affected by the minute modifications crafted for CNNs. We develop three detection strategies for adversarial examples by analysing differences in the prediction of the surrogate and the CNN model: namely, deviation in (i) the prediction, (ii) the distance of the predictions, and (iii) the confidence of the predictions. We consider three different feature spaces: raw images, extracted features, and the activations of the CNN model. Our evaluation shows that our methods achieve state-of-the-art performance compared to other approaches, such as Feature Squeezing, MagNet, PixelDefend, and Subset Scanning, on the MNIST, Fashion-MNIST, and CIFAR-10 datasets while being robust in the sense that they do not entirely fail against selected single attacks. Further, we evaluate our defence against an adaptive attacker in a grey-box setting.
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