Gradient-based adversarial attacks on deep neural networks pose a serious threat, since they can be deployed by adding imperceptible perturbations to the test data of any network, and the risk they introduce cannot be assessed through the network's original training performance. Denoising and dimensionality reduction are two distinct methods that have been independently investigated to combat such attacks. While denoising offers the ability to tailor the defense to the specific nature of the attack, dimensionality reduction offers the advantage of potentially removing previously unseen perturbations, along with reducing the training time of the network being defended. We propose strategies to combine the advantages of these two defense mechanisms. First, we propose the cascaded defense, which involves denoising followed by dimensionality reduction. To reduce the training time of the defense for a small trade-off in performance, we propose the hidden layer defense, which involves feeding the output of the encoder of a denoising autoencoder into the network. Further, we discuss how adaptive attacks against these defenses could become significantly weak when an alternative defense is used, or when no defense is used. In this light, we propose a new metric to evaluate a defense which measures the sensitivity of the adaptive attack to modifications in the defense. Finally, we present a guideline for building an ordered repertoire of defenses, a.k.a. a defense infrastructure, that adjusts to limited computational resources in presence of uncertainty about the attack strategy.

Deep learning has shown impressive performance on challenging perceptual tasks and has been widely used in software to provide intelligent services. However, researchers found deep neural networks vulnerable to adversarial examples. Since then, many methods are proposed to defend against adversaries in inputs, but they are either attack-dependent or shown to be ineffective with new attacks. And most of existing techniques have complicated structures or mechanisms that cause prohibitively high overhead or latency, impractical to apply on real software. We propose DAFAR, a feedback framework that allows deep learning models to detect/purify adversarial examples in high effectiveness and universality, with low area and time overhead. DAFAR has a simple structure, containing a victim model, a plug-in feedback network, and a detector. The key idea is to import the high-level features from the victim model's feature extraction layers into the feedback network to reconstruct the input. This data stream forms a feedback autoencoder. For strong attacks, it transforms the imperceptible attack on the victim model into the obvious reconstruction-error attack on the feedback autoencoder directly, which is much easier to detect; for weak attacks, the reformation process destroys the structure of adversarial examples. Experiments are conducted on MNIST and CIFAR-10 data-sets, showing that DAFAR is effective against popular and arguably most advanced attacks without losing performance on legitimate samples, with high effectiveness and universality across attack methods and parameters.