Time series adversarial attacks: an investigation of smooth perturbations and defense approaches

Adversarial attacks represent a threat to every deep neural network. They are particularly effective if they can perturb a given model while remaining undetectable. They have been initially introduced for image classifiers, and are well studied for this task. For time series, few attacks have yet been proposed. Most that have are adaptations of attacks previously proposed for image classifiers. Although these attacks are effective, they generate perturbations containing clearly discernible patterns such as sawtooth and spikes. Adversarial patterns are not perceptible on images, but the attacks proposed to date are readily perceptible in the case of time series. In order to generate stealthier adversarial attacks for time series, we propose a new attack that produces smoother perturbations. We introduced a function to measure the smoothness for time series. Using it, we find that smooth perturbations are harder to detect both visually, by the naked eye and by deep learning models. We also show two ways of protection against adversarial attacks: the first one by detecting the attacks using a deep model; the second one by using adversarial training to improve the robustness of a model against a specific attack, thus making it less vulnerable.