Fooling the Big Picture in Classification Tasks.

Minimally perturbed adversarial examples were shown to drastically reduce the performance of one-stage classifiers while being imperceptible. This paper investigates the susceptibility of hierarchical classifiers, which use fine and coarse level output categories, to adversarial attacks. We formulate a program that encodes minimax constraints to induce misclassification of the coarse class of a hierarchical classifier (e.g., changing the prediction of a 'monkey' to a 'vehicle' instead of some 'animal'). Subsequently, we develop solutions based on convex relaxations of said program. An algorithm is obtained using the alternating direction method of multipliers with competitive performance in comparison with state-of-the-art solvers. We show the ability of our approach to fool the coarse classification through a set of measures such as the relative loss in coarse classification accuracy and imperceptibility factors. In comparison with perturbations generated for one-stage classifiers, we show that fooling a classifier about the 'big picture' requires higher perturbation levels which results in lower imperceptibility. We also examine the impact of different label groupings on the performance of the proposed attacks. Supplementary Information: The online version contains supplementary material available at 10.1007/s00034-022-02226-w.