Convolutional Neural Networks Approximation in Quasi-Orlicz Spaces on Sphers

Abstract

It is necessary to study the theoretical bases of an approximation deep convolutional neural networks,  because of its interesting developments in vital domains. The approximation abilities of deep-convolution neural  networks produced by downsampling operators in quasi- Orlicz spaces have been studied, since this space is wider and more important than other spaces. In this paper, we define quasi-Orlicz norm on spherical spaces. In addition, modulus of smoothness is also studied in terms of quasi-Orlicz norm. Finally, Function approximation theorems are studied by using convolution neural networks with