JMA: a General Algorithm to Craft Nearly Optimal Targeted Adversarial Example

Most of the approaches proposed so far to craft targeted adversarial examples against Deep Learning classifiers are highly suboptimal and typically rely on increasing the likelihood of the target class, thus implicitly focusing on one-hot encoding settings. In this paper, a more general, theoretically sound, targeted attack is proposed, which resorts to the minimization of a Jacobian-induced Mahalanobis distance term, taking into account the effort (in the input space) required to move the latent space representation of the input sample in a given direction. The minimization is solved by exploiting the Wolfe duality theorem, reducing the problem to the solution of a Non-Negative Least Square (NNLS) problem. The proposed algorithm (referred to as JMA) provides an optimal solution to a linearised version of the adversarial example problem originally introduced by Szegedy et al. The results of the experiments confirm the generality of the proposed attack which is proven to be effective under a wide variety of output encoding schemes. Noticeably, JMA is also effective in a multi-label classification scenario, being capable to induce a targeted modification of up to half the labels in complex multi-label classification scenarios, a capability that is out of reach of all the attacks proposed so far. As a further advantage, JMA requires very few iterations, thus resulting more efficient than existing methods.