  The use of neural networks in safety-critical systems requires safe and
robust models, due to the existence of adversarial attacks. Knowing the minimal
adversarial perturbation of any input x, or, equivalently, knowing the distance
of x from the classification boundary, allows evaluating the classification
robustness, providing certifiable predictions. Unfortunately, state-of-the-art
techniques for computing such a distance are computationally expensive and
hence not suited for online applications. This work proposes a novel family of
classifiers, namely Signed Distance Classifiers (SDCs), that, from a
theoretical perspective, directly output the exact distance of x from the
classification boundary, rather than a probability score (e.g., SoftMax). SDCs
represent a family of robust-by-design classifiers. To practically address the
theoretical requirements of a SDC, a novel network architecture named
Unitary-Gradient Neural Network is presented. Experimental results show that
the proposed architecture approximates a signed distance classifier, hence
allowing an online certifiable classification of x at the cost of a single
inference.
