Hypercomplex numbers, such as quaternions and octonions, have recently gained attention because of their advantageous properties over real numbers, e.g., in the development of parameter-efficient neural networks. For instance, the 16-component sedenion has the capacity to reduce the number of network parameters by a factor of 16. Moreover, hypercomplex neural networks offer advantages in the processing of spatiotemporal data as they are able to represent variable temporal data divisions through the hypercomplex components. Similarly, they support multimodal learning, with each component representing an individual modality. In this article, the key components of deep learning in the hypercomplex domain are introduced, encompassing concatenation, activation functions, convolution, and batch normalization. The use of the backpropagation algorithm for training hypercomplex networks is discussed in the context of hypercomplex algebra. These concepts are brought together in the design of a ResNet backbone using hypercomplex convolution, which is integrated within a U-Net configuration and applied in weather and traffic forecasting problems. The results demonstrate the superior performance of hypercomplex networks compared to their real-valued counterparts, given a fixed parameter budget, highlighting their potential in spatiotemporal data processing.

中文翻译：

---

用于时空数据处理的深层超复杂网络：参数效率和卓越性能[超复杂信号和图像处理]


超复数（例如四元数和八元数）最近因其优于实数的特性而受到关注，例如在参数高效神经网络的开发中。例如，16 分量 Sedenion 能够将网络参数的数量减少 16 倍。此外，超复杂神经网络在处理时空数据方面具有优势，因为它们能够通过超复杂神经网络表示可变的时间数据划分。成分。同样，它们支持多模式学习，每个组件代表一种单独的模式。在本文中，介绍了超复杂领域深度学习的关键组成部分，包括串联、激活函数、卷积和批量归一化。在超复杂代数的背景下讨论了使用反向传播算法来训练超复杂网络。这些概念在使用超复杂卷积的 ResNet 主干设计中得到了融合，该主干被集成到 U-Net 配置中并应用于天气和交通预测问题。结果证明，在给定固定参数预算的情况下，超复杂网络与其实值网络相比具有优越的性能，突显了它们在时空数据处理方面的潜力。