A Comprehensive Analysis of Quaternion Deep Neural Networks: Architectures, Applications, Challenges, and Future Scope

Quaternions are extensively used in several fields including physics, applied mathematics, computer graphics, and control systems because of their notable and unique characteristics. Embedding quaternions into deep neural networks has attracted significant attention to neurocomputing researchers in recent years. Quaternion’s algebra helps to reconstruct neural networks in the quaternionic domain. This paper comprehensively reviewed and analyzed the recent advancements in quaternion deep neural networks (QDNNs) and their practical applications. Several architectures integrating quaternions in deep neural networks such as quaternion convolutional neural networks, quaternion recurrent neural networks, quaternion self-attention networks, hypercomplex convolutional neural networks, quaternion long-short term memory networks, quaternion residual networks, and quaternion variational autoencoders are thoroughly examined and reviewed with applications. It is observed that they have outperformed conventional real-valued neural networks. This study also discusses the main discoveries and possible advanced mechanisms of QDNN for future research. The open challenges and future scopes of QDNNs are also addressed, which provides the right direction of work in this field. This review may help researchers interested in architectural advancements and their practical applications.