  Despite their unprecedented performance in various domains, utilization of
Deep Neural Networks (DNNs) in safety-critical environments is severely limited
in the presence of even small adversarial perturbations. The present work
develops a randomized approach to detecting such perturbations based on minimum
uncertainty metrics that rely on sampling at the hidden layers during the DNN
inference stage. Inspired by Bayesian approaches to uncertainty estimation, the
sampling probabilities are designed for effective detection of the
adversarially corrupted inputs. Being modular, the novel detector of
adversaries can be conveniently employed by any pre-trained DNN at no extra
training overhead. Selecting which units to sample per hidden layer entails
quantifying the amount of DNN output uncertainty, where the overall uncertainty
is expressed in terms of its layer-wise components - what also promotes
scalability. Sampling probabilities are then sought by minimizing uncertainty
measures layer-by-layer, leading to a novel convex optimization problem that
admits an exact solver with superlinear convergence rate. By simplifying the
objective function, low-complexity approximate solvers are also developed. In
addition to valuable insights, these approximations link the novel approach
with state-of-the-art randomized adversarial detectors. The effectiveness of
the novel detectors in the context of competing alternatives is highlighted
through extensive tests for various types of adversarial attacks with variable
levels of strength.
