Neural Network Inversion for Multilayer Quaternion Neural Networks

Recently, solutions to inverse problems have been required in various engineering fields. The neural network inversion method has been studied as one of the neural network-based solutions. On the other hand, the extension of the neural network to a higher-dimensional domain, e.g., complex-value or quaternion, has been proposed, and a number of higher-dimensional neural network models have been proposed. Using the quaternion, we have the advantage of expressing 3D (three-dimensional) object attitudes easily. In the quaternion domain, we can define inverse problems where the cause and the result are expressed by the quaternion. In this paper, we extend the neural network inversion method to the quaternion domain. Further, we provide the results of the computer experiments to demonstrate the process and effectiveness of our method.