A Global Universality of Two-Layer Neural Networks with ReLU Activations-Reference-Cited by-同舟云学术

A Global Universality of Two-Layer Neural Networks with ReLU Activations

Published:2021-09-17 Issue: Volume:2021 Page:1-3
ISSN:2314-8888
Container-title:Journal of Function Spaces
language:en
Short-container-title:Journal of Function Spaces

Author:

Hatano Naoya¹²³^ORCID,Ikeda Masahiro¹²,Ishikawa Isao²⁴,Sawano Yoshihiro¹²³^ORCID

Affiliation:

1. Department of Mathematics, Faculty of Science and Technology, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan

2. Center for Advanced Intelligence Project, Riken, Japan

3. Department of Mathematics, Chuo University, 1-13-27, Kasuga, Bunkyo-ku, Tokyo 112-8551, Japan

4. Center for Data Science, Ehime University, 3 Bunkyo-cho, Matsuyama, Ehime 790-8577, Japan

Abstract

In the present study, we investigate a universality of neural networks, which concerns a density of the set of two-layer neural networks in function spaces. There are many works that handle the convergence over compact sets. In the present paper, we consider a global convergence by introducing a norm suitably, so that our results will be uniform over any compact set.

Funder

Japan Society for the Promotion of Science

Publisher

Hindawi Limited

Subject

Analysis

Link

http://downloads.hindawi.com/journals/jfs/2021/6637220.pdf

Reference8 articles.

1. Universal Function Approximation by Deep Neural Nets with Bounded Width and ReLU Activations

2. Approximation theory of the MLP model in neural networks

3. Approximation by superpositions of a sigmoidal function