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

This paper proposes Quaternion Collaborative Filtering (QCF), a novel
representation learning method for recommendation. Our proposed QCF relies on
and exploits computation with Quaternion algebra, benefiting from the
expressiveness and rich representation learning capability of Hamilton
products. Quaternion representations, based on hypercomplex numbers, enable
rich inter-latent dependencies between imaginary components. This encourages
intricate relations to be captured when learning user-item interactions,
serving as a strong inductive bias as compared with the real-space inner
product. All in all, we conduct extensive experiments on six real-world
datasets, demonstrating the effectiveness of Quaternion algebra in recommender
systems. The results exhibit that QCF outperforms a wide spectrum of strong
neural baselines on all datasets. Ablative experiments confirm the
effectiveness of Hamilton-based composition over multi-embedding composition in
real space.

该研究提出了四元协作过滤（QCF）算法，其基于四元数代数计算，利用 Hamilton 积的表达能力和强大的表示学习能力来帮助学习用户 - 物品之间的交互。作者在六个真实数据集上进行了广泛的实验比对，证明 QCF 在推荐系统中的有效性并优于许多强基线神经网络方法。