  Convolutional Neural Networks (CNNs) define an exceptionally powerful class
of models for image classification, but the theoretical background and the
understanding of how invariances to certain transformations are learned is
limited. In a large scale screening with images modified by different affine
and nonaffine transformations of varying magnitude, we analyzed the behavior of
the CNN architectures AlexNet and ResNet. If the magnitude of different
transformations does not exceed a class- and transformation dependent
threshold, both architectures show invariant behavior. In this work we
furthermore introduce a new learnable module, the Invariant Transformer Net,
which enables us to learn differentiable parameters for a set of affine
transformations. This allows us to extract the space of transformations to
which the CNN is invariant and its class prediction robust.
