  Deep neural networks are vulnerable to adversarial attacks, which can fool
them by adding minuscule perturbations to the input images. The robustness of
existing defenses suffers greatly under white-box attack settings, where an
adversary has full knowledge about the network and can iterate several times to
find strong perturbations. We observe that the main reason for the existence of
such perturbations is the close proximity of different class samples in the
learned feature space. This allows model decisions to be totally changed by
adding an imperceptible perturbation in the inputs. To counter this, we propose
to class-wise disentangle the intermediate feature representations of deep
networks. Specifically, we force the features for each class to lie inside a
convex polytope that is maximally separated from the polytopes of other
classes. In this manner, the network is forced to learn distinct and distant
decision regions for each class. We observe that this simple constraint on the
features greatly enhances the robustness of learned models, even against the
strongest white-box attacks, without degrading the classification performance
on clean images. We report extensive evaluations in both black-box and
white-box attack scenarios and show significant gains in comparison to
state-of-the art defenses.
