  In this work we present a formal theoretical framework for assessing and
analyzing two classes of malevolent action towards generic Artificial
Intelligence (AI) systems. Our results apply to general multi-class classifiers
that map from an input space into a decision space, including artificial neural
networks used in deep learning applications. Two classes of attacks are
considered. The first class involves adversarial examples and concerns the
introduction of small perturbations of the input data that cause
misclassification. The second class, introduced here for the first time and
named stealth attacks, involves small perturbations to the AI system itself.
Here the perturbed system produces whatever output is desired by the attacker
on a specific small data set, perhaps even a single input, but performs as
normal on a validation set (which is unknown to the attacker). We show that in
both cases, i.e., in the case of an attack based on adversarial examples and in
the case of a stealth attack, the dimensionality of the AI's decision-making
space is a major contributor to the AI's susceptibility. For attacks based on
adversarial examples, a second crucial parameter is the absence of local
concentrations in the data probability distribution, a property known as
Smeared Absolute Continuity. According to our findings, robustness to
adversarial examples requires either (a) the data distributions in the AI's
feature space to have concentrated probability density functions or (b) the
dimensionality of the AI's decision variables to be sufficiently small. We also
show how to construct stealth attacks on high-dimensional AI systems that are
hard to spot unless the validation set is made exponentially large.
