Can Kanbak, Seyed-Mohsen Moosavi-Dezfooli, Pascal Frossard. Geometric Robustness of Deep Networks: Analysis and Improvement. CVPR, 2018.

Kanbak et al. propose ManiFool, a method to determine a network’s invariance to transformations by iteratively finding adversarial transformations. In particular, given a class of transformations to consider, ManiFool iteratively alternates two steps. First, a gradient step is taken in order to move into an adversarial direction; then, the obtained perturbation/direction is projected back to the space of allowed transformations. While the details are slightly more involved, I found that this approach is similar to the general projected gradient ascent approach to finding adversarial examples. By finding worst-case transformations for a set of test samples, Kanbak et al. Are able to quantify the invariance of a network against specific transformations. Furthermore, they show that adversarial fine-tuning using the found adversarial transformations allows to boost invariance, while only incurring a small loss in general accuracy. Examples of the found adversarial transformations are shown in Figure 1.

Figure 1: The proposed attack method allows to consider different classes of transformations as shown in these examples.

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