Hypercomplex algebras have recently been gaining prominence in the field of
deep learning owing to the advantages of their division algebras over real
vector spaces and their superior results when dealing with multidimensional
signals in real-world 3D and 4D paradigms. This paper provides a foundational
framework that serves as a roadmap for understanding why hypercomplex deep
learning methods are so successful and how their potential can be exploited.
Such a theoretical framework is described in terms of inductive bias, i.e., a
collection of assumptions, properties, and constraints that are built into
training algorithms to guide their learning process toward more efficient and
accurate solutions. We show that it is possible to derive specific inductive
biases in the hypercomplex domains, which extend complex numbers to encompass
diverse numbers and data structures. These biases prove effective in managing
the distinctive properties of these domains, as well as the complex structures
of multidimensional and multimodal signals. This novel perspective for
hypercomplex deep learning promises to both demystify this class of methods and
clarify their potential, under a unifying framework, and in this way promotes
hypercomplex models as viable alternatives to traditional real-valued deep
learning for multidimensional signal processing.

为了更高效和准确地解决多维信号处理问题，本文提供了一个基础框架来解释超复深度学习方法成功的原因以及如何充分利用其潜力，并以归纳偏差的理论框架来描述。这一新颖的超复深度学习视角将有助于使这一类方法更为清晰与易懂，并将其作为传统实数深度学习的替代选择推广至多维信号处理。