  Second- and higher-order statistics of data points have played an important
role in advancing the state of the art on several computer vision problems such
as the fine-grained image and scene recognition. However, these statistics need
to be passed via an appropriate pooling scheme to obtain the best performance.
Power Normalizations are non-linear activation units which enjoy
probability-inspired derivations and can be applied in CNNs. In this paper, we
propose a similarity learning network leveraging second-order information and
Power Normalizations. To this end, we propose several formulations capturing
second-order statistics and derive a sigmoid-like Power Normalizing function to
demonstrate its interpretability. Our model is trained end-to-end to learn the
similarity between the support set and query images for the problem of one- and
few-shot learning. The evaluations on Omniglot, miniImagenet and Open MIC
datasets demonstrate that this network obtains state-of-the-art results on
several few-shot learning protocols.
