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

This paper concerns the universality of the two-layer neural network with the k -rectified linear unit activation function with k = 1 , 2 , ... 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 k = 1 by the present authors. This paper covers k -sigmoidal functions as an application of the fundamental result on k -rectified linear unit functions. [ABSTRACT FROM AUTHOR]