A sufficient condition for decision boundaries in neural networks with complex numbered weights to intersect orthogonally

This paper presents some results of an analysis on the decision boundaries of complex valued neural networks. The main results may be summarized as follows. (a) Weight parameters of a complex valued neuron have a restriction which is concerned with two-dimensional motion. (b) The decision boundary of a complex valued neuron consists of two hypersurfaces which intersect orthogonally, and divides a decision region into four equal sections. The decision boundary of a three-layered complex valued neural network has this as a basic structure, and its two hypersurfaces intersect orthogonally if net inputs to each hidden neuron are all sufficiently large