Heaviside function as an activation function-Reference-Cited by-同舟云学术

Heaviside function as an activation function

Published:2022-10-26 Issue:0 Volume:0 Page:
ISSN:1425-6908
Container-title:Journal of Applied Analysis
language:en
Short-container-title:

Author:

Hatano Naoya¹,Ikeda Masahiro²,Ishikawa Isao³,Sawano Yoshihiro¹

Affiliation:

1. Department of Mathematics, Faculty of Science and Technology, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522; and Center for Advanced Intelligence Project, RIKEN ; and Department of Mathematics , Chuo University , 1-13-27, Kasuga , Bunkyo-ku , Tokyo 112-8551 , Japan

2. Center for Advanced Intelligence Project , RIKEN , Nihonbashi 1-chome Mitsui Building, 15th floor, 1-4-1 Nihonbashi, Chuo-ku Tokyo 103-0027; and Department of Mathematics, Faculty of Science and Technology, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522 , Japan

3. Center for Advanced Intelligence Project, RIKEN, Tokyo ; and Center for Data Science , Ehime University , 3 Bunkyo-cho, Matsuyama , Ehime 790-8577 , Japan

Abstract

Abstract The uniform closure of the neural networks with Heaviside activation is specified.

Funder

Japan Society for the Promotion of Science

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Computational Theory and Mathematics,Statistics, Probability and Uncertainty,Mathematical Physics

Link

https://www.degruyter.com/document/doi/10.1515/jaa-2022-2012/pdf

Reference6 articles.

1. G. Cybenko, Approximation by superpositions of a sigmoidal function, Math. Control Signals Systems 2 (1989), no. 4, 303–314.

2. B. Hanin, Universal function approximation by deep neural nets with bounded width and ReLU activations, Mathematics 7 (2019), no. 10, Paper No. 992.

3. N. Hatano, M. Ikeda, M. Ishikawa and Y. Sawano, A global universality of two-layer neural networks with ReLU activations, J. Funct. Spaces 2021 (2021), Article ID 6637220.

4. P. Kainen, V. Kůrková and A. Vogt, Best approximation by Heaviside perceptron networks, Neural Networks 13 (2000), no. 7, 695–697.

5. A. Pinkus, Approximation theory of the MLP model in neural networks, Acta Numer. 8 (1999), 143–195.