Deep neural networks (DNNs) can easily be cheated by some imperceptible but purposeful noise added to images, and erroneously classify them. Previous defensive work mostly focused on retraining the models or detecting the noise, but has either shown limited success rates or been attacked by new adversarial examples. Instead of focusing on adversarial images or the interior of DNN models, we observed that adversarial examples generated by different algorithms can be identified based on the output of DNNs (logits). Logit can serve as an exterior feature to train detectors. Then, we propose HOLMES (Hierarchically Organized Light-weight Multiple dEtector System) to reinforce DNNs by detecting potential adversarial examples to minimize the threats they may bring in practical. HOLMES is able to distinguish \textit{unseen} adversarial examples from multiple attacks with high accuracy and low false positive rates than single detector systems even in an adaptive model. To ensure the diversity and randomness of detectors in HOLMES, we use two methods: training dedicated detectors for each label and training detectors with top-k logits. Our effective and inexpensive strategies neither modify original DNN models nor require its internal parameters. HOLMES is not only compatible with all kinds of learning models (even only with external APIs), but also complementary to other defenses to achieve higher detection rates (may also fully protect the system against various adversarial examples).

In recent years, Deep Reinforcement Learning (DRL) has become a popular paradigm in machine learning due to its successful applications to real-world and complex systems. However, even the state-of-the-art DRL models have been shown to suffer from reliability concerns -- for example, their susceptibility to adversarial inputs, i.e., small and abundant input perturbations that can fool the models into making unpredictable and potentially dangerous decisions. This drawback limits the deployment of DRL systems in safety-critical contexts, where even a small error cannot be tolerated. In this work, we present a comprehensive analysis of the characterization of adversarial inputs, through the lens of formal verification. Specifically, we introduce a novel metric, the Adversarial Rate, to classify models based on their susceptibility to such perturbations, and present a set of tools and algorithms for its computation. Our analysis empirically demonstrates how adversarial inputs can affect the safety of a given DRL system with respect to such perturbations. Moreover, we analyze the behavior of these configurations to suggest several useful practices and guidelines to help mitigate the vulnerability of trained DRL networks.