Since their first applications, Convolutional Neural Networks (CNNs) have
solved problems that have advanced the state-of-the-art in several domains.
CNNs represent information using real numbers. Despite encouraging results,
theoretical analysis shows that representations such as hyper-complex numbers
can achieve richer representational capacities than real numbers, and that
Hamilton products can capture intrinsic interchannel relationships. Moreover,
in the last few years, experimental research has shown that Quaternion-Valued
CNNs (QCNNs) can achieve similar performance with fewer parameters than their
real-valued counterparts. This paper condenses research in the development of
QCNNs from its very beginnings. We propose a conceptual organization of current
trends and analyze the main building blocks used in the design of QCNN models.
Based on this conceptual organization, we propose future directions of
research.

本文介绍了关于四元数卷积神经网络 (QCNNs) 的发展、目前的趋势和在设计 QCNN 模型中使用的主要模块，并提出了未来的研究方向。

四元数卷积神经网络：当前进展与未来方向

Quaternion Convolutional Neural Networks: Current Advances and Future  Directions

The field of deep learning has seen significant advancement in recent years.
However, much of the existing work has been focused on real-valued numbers.
Recent work has shown that a deep learning system using the complex numbers can
be deeper for a fixed parameter budget compared to its real-valued counterpart.
In this work, we explore the benefits of generalizing one step further into the
hyper-complex numbers, quaternions specifically, and provide the architecture
components needed to build deep quaternion networks. We develop the theoretical
basis by reviewing quaternion convolutions, developing a novel quaternion
weight initialization scheme, and developing novel algorithms for quaternion
batch-normalization. These pieces are tested in a classification model by
end-to-end training on the CIFAR-10 and CIFAR-100 data sets and a segmentation
model by end-to-end training on the KITTI Road Segmentation data set. These
quaternion networks show improved convergence compared to real-valued and
complex-valued networks, especially on the segmentation task, while having
fewer parameters

本文介绍了如何使用四元数构建深度网络，通过在 CIFAR-10 和 CIFAR-100 数据集上进行端到端训练以及在 KITTI Road Segmentation 数据集上进行端到端训练，我们证明了四元数网络比实数网络和复数网络具有更好的收敛性能，在分割任务中表现尤为突出。