# Power Normalizing Second-order Similarity Network for Few-shot Learning

arXiv: https://arxiv.org/abs/1811.04167 · HTML: https://mlsanity.com/paper/1811.04167/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Nov 2018.

## Built on by (most cited first, 13 of 13)

- [Joint Distribution Matters: Deep Brownian Distance Covariance for Few-Shot Classification](https://mlsanity.com/paper/2204.04567/) (2022)
- [Few-Shot Object Detection: A Comprehensive Survey](https://mlsanity.com/paper/2112.11699/) (2021)
- [Temporal-Viewpoint Transportation Plan for Skeletal Few-shot Action Recognition](https://mlsanity.com/paper/2210.16820/) (2022)
- [Meta-Learning for Multi-Label Few-Shot Classification](https://mlsanity.com/paper/2110.13494/) (2021)
- [NDPNet: A novel non-linear data projection network for few-shot fine-grained image classification](https://mlsanity.com/paper/2106.06988/) (2021)
- [Multi-level Second-order Few-shot Learning](https://mlsanity.com/paper/2201.05916/) (2022)
- [3D Skeleton-based Few-shot Action Recognition with JEANIE is not so Na"ive](https://mlsanity.com/paper/2112.12668/) (2021)
- [Time-rEversed diffusioN tEnsor Transformer: A new TENET of Few-Shot Object Detection](https://mlsanity.com/paper/2210.16897/) (2022)
- [Meet JEANIE: a Similarity Measure for 3D Skeleton Sequences via Temporal-Viewpoint Alignment](https://mlsanity.com/paper/2402.04599/) (2024)
- [Robust Saliency-Aware Distillation for Few-shot Fine-grained Visual Recognition](https://mlsanity.com/paper/2305.07180/) (2023)
- [Simple Dialogue System with AUDITED](https://mlsanity.com/paper/2110.11881/) (2021)
- [An Adaptive Plug-and-Play Network for Few-Shot Learning](https://mlsanity.com/paper/2302.09326/) (2023)
- [Not All Instances Contribute Equally: Instance-adaptive Class Representation Learning for Few-Shot Visual Recognition](https://mlsanity.com/paper/2209.03034/) (2022)

## Abstract (arXiv)

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.