Generalization ability of the three-dimensional back-propagation network

The 3D vector version of the back-propagation algorithm (3DV-BP) is a natural extension of the complex-valued version of the back-propagation algorithm (Complex-BP). The Complex-BP can be applied to multilayered neural networks whose weights, threshold values, input and output signals are all complex numbers, and the 3DV-BP can be applied to multilayered neural networks whose threshold values, input and output signals are all 3D real valued vectors, and whose weights are all 3D orthogonal matrices. It has already been reported that an inherent property of the Complex-BP is its ability to learn 2D motion. This paper shows in computational experiments that the 3DV-BP has the ability to learn 3D motion, which corresponds to the ability of the Complex-BP to learn 2D motion