  Data augmentation has led to substantial improvements in the performance and
generalization of deep models, and remain a highly adaptable method to evolving
model architectures and varying amounts of data---in particular, extremely
scarce amounts of available training data. In this paper, we present a novel
method of applying Mobius transformations to augment input images during
training. Mobius transformations are bijective conformal maps that generalize
image translation to operate over complex inversion in pixel space. As a
result, Mobius transformations can operate on the sample level and preserve
data labels. We show that the inclusion of Mobius transformations during
training enables improved generalization over prior sample-level data
augmentation techniques such as cutout and standard crop-and-flip
transformations, most notably in low data regimes.
