Neural network with unbounded activation functions is universal approximator

This paper presents an investigation of the approximation property of neural networks with unbounded activation functions, such as the rectified linear unit (ReLU), which is the new de-facto standard of deep learning. The ReLU network can be analyzed by the ridgelet transform with respect to Lizorki...

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Bibliographic Details
Published in:	Applied and computational harmonic analysis Vol. 43; no. 2; pp. 233 - 268
Main Authors:	Sonoda, Sho, Murata, Noboru
Format:	Journal Article
Language:	English
Published:	Elsevier Inc 01.09.2017
Subjects:	Admissibility condition Backprojection filter Bounded extension to [formula omitted] Integral representation Lizorkin distribution Neural network Radon transform Rectified linear unit (ReLU) Ridgelet transform Universal approximation Admissibility condition Universal approximation Radon transform Lizorkin distribution Neural network Bounded extension to L2 Integral representation Backprojection filter Rectified linear unit (ReLU) Ridgelet transform
ISSN:	1063-5203, 1096-603X
Online Access:	Get full text
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