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 previo...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2024-01-01
|
| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2024/3262798 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832548347068547072 |
|---|---|
| author | Naoya Hatano Masahiro Ikeda Isao Ishikawa Yoshihiro Sawano |
| author_facet | Naoya Hatano Masahiro Ikeda Isao Ishikawa Yoshihiro Sawano |
| author_sort | Naoya Hatano |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-b4c0a42b583e47c7b7be1e9a51cf7ddc |
| institution | Kabale University |
| issn | 2314-8888 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-b4c0a42b583e47c7b7be1e9a51cf7ddc2025-02-03T06:14:52ZengWileyJournal of Function Spaces2314-88882024-01-01202410.1155/2024/3262798Global Universality of the Two-Layer Neural Network with the k-Rectified Linear UnitNaoya Hatano0Masahiro Ikeda1Isao Ishikawa2Yoshihiro Sawano3Department of MathematicsDepartment of MathematicsCenter for Advanced Intelligence ProjectDepartment of MathematicsThis 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.http://dx.doi.org/10.1155/2024/3262798 |
| spellingShingle | Naoya Hatano Masahiro Ikeda Isao Ishikawa Yoshihiro Sawano Global Universality of the Two-Layer Neural Network with the k-Rectified Linear Unit Journal of Function Spaces |
| title | Global Universality of the Two-Layer Neural Network with the k-Rectified Linear Unit |
| title_full | Global Universality of the Two-Layer Neural Network with the k-Rectified Linear Unit |
| title_fullStr | Global Universality of the Two-Layer Neural Network with the k-Rectified Linear Unit |
| title_full_unstemmed | Global Universality of the Two-Layer Neural Network with the k-Rectified Linear Unit |
| title_short | Global Universality of the Two-Layer Neural Network with the k-Rectified Linear Unit |
| title_sort | global universality of the two layer neural network with the k rectified linear unit |
| url | http://dx.doi.org/10.1155/2024/3262798 |
| work_keys_str_mv | AT naoyahatano globaluniversalityofthetwolayerneuralnetworkwiththekrectifiedlinearunit AT masahiroikeda globaluniversalityofthetwolayerneuralnetworkwiththekrectifiedlinearunit AT isaoishikawa globaluniversalityofthetwolayerneuralnetworkwiththekrectifiedlinearunit AT yoshihirosawano globaluniversalityofthetwolayerneuralnetworkwiththekrectifiedlinearunit |