  Recent advances in machine learning (ML) algorithms, especially deep neural
networks (DNNs), have demonstrated remarkable success (sometimes exceeding
human-level performance) on several tasks, including face and speech
recognition. However, ML algorithms are vulnerable to \emph{adversarial
attacks}, such test-time, training-time, and backdoor attacks. In test-time
attacks an adversary crafts adversarial examples, which are specially crafted
perturbations imperceptible to humans which, when added to an input example,
force a machine learning model to misclassify the given input example.
Adversarial examples are a concern when deploying ML algorithms in critical
contexts, such as information security and autonomous driving. Researchers have
responded with a plethora of defenses. One promising defense is
\emph{randomized smoothing} in which a classifier's prediction is smoothed by
adding random noise to the input example we wish to classify. In this paper, we
theoretically and empirically explore randomized smoothing. We investigate the
effect of randomized smoothing on the feasible hypotheses space, and show that
for some noise levels the set of hypotheses which are feasible shrinks due to
smoothing, giving one reason why the natural accuracy drops after smoothing. To
perform our analysis, we introduce a model for randomized smoothing which
abstracts away specifics, such as the exact distribution of the noise. We
complement our theoretical results with extensive experiments.
