  Deep convolutional neural networks have been shown to be vulnerable to
arbitrary geometric transformations. However, there is no systematic method to
measure the invariance properties of deep networks to such transformations. We
propose ManiFool as a simple yet scalable algorithm to measure the invariance
of deep networks. In particular, our algorithm measures the robustness of deep
networks to geometric transformations in a worst-case regime as they can be
problematic for sensitive applications. Our extensive experimental results show
that ManiFool can be used to measure the invariance of fairly complex networks
on high dimensional datasets and these values can be used for analyzing the
reasons for it. Furthermore, we build on Manifool to propose a new adversarial
training scheme and we show its effectiveness on improving the invariance
properties of deep neural networks.
