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Deep Neural Networks (DNNs) have recently been shown to be vulnerable againstadversarial examples, which are carefully crafted instances that can misleadDNNs to make errors during prediction. To better understand such attacks, acharacterization is needed of the properties of regions (the so-called'adversarial subspaces') in which adversarial examples lie. We tackle thischallenge by characterizing the dimensional properties of adversarial regions,via the use of Local Intrinsic Dimensionality (LID). LID assesses thespace-filling capability of the region surrounding a reference example, basedon the distance distribution of the example to its neighbors. We first provideexplanations about how adversarial perturbation can affect the LIDcharacteristic of adversarial regions, and then show empirically that LIDcharacteristics can facilitate the distinction of adversarial examplesgenerated using state-of-the-art attacks. As a proof-of-concept, we show that apotential application of LID is to distinguish adversarial examples, and thepreliminary results show that it can outperform several state-of-the-artdetection measures by large margins for five attack strategies considered inthis paper across three benchmark datasets. Our analysis of the LIDcharacteristic for adversarial regions not only motivates new directions ofeffective adversarial defense, but also opens up more challenges for developingnew attacks to better understand the vulnerabilities of DNNs.

Characterizing Adversarial Subspaces Using Local Intrinsic Dimensionality