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.
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