New complex-valued activation functions

Abstract

We present a new type of activation functions for a complex-valued neural net-work (CVNN). A proposed activation function is constructed such that it fixesa given ellipse. We obtain an application to a complex-valued Hopfield neuralnetwork (CVHNN) using a special form of the introduced complex functionsas an activation function. Considering the interesting geometric propertiesof the plane curve ellipse such as focusing property, we emphasize that theseproperties may have possible applications in various neural networks.