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.

翻译：自首次应用以来，卷积神经网络（CNN）已在多个领域推动了前沿技术的发展。传统CNN使用实数进行信息表示。尽管取得了令人鼓舞的成果，理论分析表明，超复数等表示形式比实数具有更丰富的表征能力，且汉密尔顿乘积能够捕捉通道间的固有相互关系。此外，近年来的实验研究显示，四元数值卷积神经网络（QCNN）能以更少的参数达到与实数对应模型相当的性能。本文系统梳理了QCNN从诞生至今的研究发展历程，提出了当前研究趋势的概念化组织框架，并分析了QCNN模型设计中使用的核心构建模块。基于这一概念框架，我们提出了未来的研究方向。