English

Global universality of the two-layer neural network with the $k$-rectified linear unit

Functional Analysis 2022-12-29 v1

Abstract

This paper concerns the universality of the two-layer neural network with the kk-rectified linear unit activation function with k=1,2,k=1,2,\ldots with a suitable norm without any restriction on the shape of the domain. This type of result is called global universality, which extends the previous result for k=1k=1 by the present authors. This paper covers kk-sigmoidal functions as an application of the fundamental result on kk-rectified linear unit functions.

Keywords

Cite

@article{arxiv.2212.13713,
  title  = {Global universality of the two-layer neural network with the $k$-rectified linear unit},
  author = {N. Hatano and M. Ikeda and I. Ishikawa and Y. Sawano},
  journal= {arXiv preprint arXiv:2212.13713},
  year   = {2022}
}