Approximation of neural network operators based on the Joukowski transformation

Abstract

The properties of activation functions profoundly affect the approximation performance of neural networks. It is always one of the most important tasks to find proper activation functions in approximation by neural networks for some specific purpose. In this paper, we introduce a new activation function which is generated by the Joukowski transformation, and construct some new neural network operators activated by the new activation function. We show that the new neural network operators can be used to approximate the continuous functions on some compact sets. In fact, we give the approximation rate by using the modulus of continuity of the objective function (see Theorem 1). Finally, we provide some specific numerical examples to verify the fitting effects of the neural network operators with different parameters for continuous functions.