Monotone Approximation by Quadratic Neural Network of Functions in Lp Spaces for p

Hawraa Abbas  Almurieb; Eman Samir Bhaya

doi:10.24996/ijs.2020.61.4.20

Authors

Hawraa Abbas Almurieb Department of Mathematics, College of Education for Pure Sciences, University of Babylon, Hillah, Iraq
Eman Samir Bhaya Department of Mathematics, College of Education for Pure Sciences, University of Babylon, Hillah, Iraq

DOI:

https://doi.org/10.24996/ijs.2020.61.4.20

Keywords:

Essential approximation, monotone approximation, modulus of smoothness, activation function, neural network

Abstract

Some researchers are interested in using the flexible and applicable properties of quadratic functions as activation functions for FNNs. We study the essential approximation rate of any Lebesgue-integrable monotone function by a neural network of quadratic activation functions. The simultaneous degree of essential approximation is also studied. Both estimates are proved to be within the second order of modulus of smoothness.