Global Universality of the Two-Layer Neural Network with the -Rectified Linear Unit

Abstract

This paper concerns the universality of the two-layer neural network with the -rectified linear unit activation function with with a suitable norm without any restriction on the shape of the domain in the real line. This type of result is called global universality, which extends the previous result for by the present authors. This paper covers -sigmoidal functions as an application of the fundamental result on -rectified linear unit functions.