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.

本研究提出了一种利用二阶信息和功率归一化的相似性学习网络，用于解决一种和少量样本学习问题，并在 Omniglot，miniImagenet 和 Open MIC 数据集上获得了最优结果。

二阶相似度规范化弱监督学习的网络

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

Convolutional Neural Networks (CNNs) have been successfully applied to many
computer vision tasks, such as image classification. By performing linear
combinations and element-wise nonlinear operations, these networks can be
thought of as extracting solely first-order information from an input image. In
the past, however, second-order statistics computed from handcrafted features,
e.g., covariances, have proven highly effective in diverse recognition tasks.
In this paper, we introduce a novel class of CNNs that exploit second-order
statistics. To this end, we design a series of new layers that (i) extract a
covariance matrix from convolutional activations, (ii) compute a parametric,
second-order transformation of a matrix, and (iii) perform a parametric
vectorization of a matrix. These operations can be assembled to form a
Covariance Descriptor Unit (CDU), which replaces the fully-connected layers of
standard CNNs. Our experiments demonstrate the benefits of our new
architecture, which outperform the first-order CNNs, while relying on up to 90%
fewer parameters.

本文提出一种新颖的卷积神经网络（CNN）类，它利用二阶统计量，可以形成协方差描述符单元（CDU），可以替代标准 CNN 的全连接层，并在参数少至 90％的情况下优于一阶 CNN。

二阶卷积神经网络

Second-order Convolutional Neural Networks

This paper addresses the problem of channel estimation in multi-cell
interference-limited cellular networks. We consider systems employing multiple
antennas and are interested in both the finite and large-scale antenna number
regimes (so-called "massive MIMO"). Such systems deal with the multi-cell
interference by way of per-cell beamforming applied at each base station.
Channel estimation in such networks, which is known to be hampered by the pilot
contamination effect, constitute a major bottleneck for overall performance. We
present a novel approach which tackles this problem by enabling a low-rate
coordination between cells during the channel estimation phase itself. The
coordination makes use of the additional second-order statistical information
about the user channels, which are shown to offer a powerful way of
discriminating across interfering users with even strongly correlated pilot
sequences. Importantly, we demonstrate analytically that in the
large-number-of-antennas regime, the pilot contamination effect is made to
vanish completely under certain conditions on the channel covariance. Gains
over the conventional channel estimation framework are confirmed by our
simulations for even small antenna array sizes.

本文提出了一种采用多个天线设计的系统，在多个蜂窝网络中通过每个基站应用针对每个蜂窝的波束成形来处理多蜂窝干扰，并在信道估计阶段自身实现低速率协调，从而使用用户信道的二阶统计信息降低信道污染效应，得到较传统方法更好的性能，并证明在最大的 MIMO 体制下这种方法有效。