Nearly Exponential Neural Networks Approximation in Lp Spaces

Abstract

In different applications, we can widely use the neural network approximation. They are being applied to solve many problems in computer science, engineering, physics, etc. The reason for successful application of neural network approximation is the neural network ability to approximate arbitrary function. In the last 30 years, many papers have been published showing that we can approximate any continuous function defined on a compact subset of the Euclidean spaces of dimensions greater than 1, uniformly using a neural network with one hidden layer. Here we prove that any real function in L_P (C) defined on a compact and convex subset of can be approximated by a sigmoidal neural network with one hidden layer, that we call nearly exponential approximation.