Robustness of representations in multilayer feedforward neural networks

Diamond P. and Fomenko I.V. (1993) Robustness of representations in multilayer feedforward neural networks. Circuits, Systems, and Signal Processing, 12 2: 211-221. doi:10.1007/BF01189874


Author Diamond P.
Fomenko I.V.
Title Robustness of representations in multilayer feedforward neural networks
Journal name Circuits, Systems, and Signal Processing   Check publisher's open access policy
ISSN 0278-081X
Publication date 1993
Sub-type Article (original research)
DOI 10.1007/BF01189874
Volume 12
Issue 2
Start page 211
End page 221
Total pages 11
Publisher Birkhäuser-Verlag
Subject 2208 Electrical and Electronic Engineering
1711 Signal Processing
Abstract Recent research has shown that multilayer feedforward networks with sigmoidal activation functions are universal approximators, and that this holds for more general activations as well. The mathematical underpinning for these results has been various: Kolmogorov's resolution of Hilbert's thirteenth problem; the Stone-Weierstrass theorem; approximation of Fourier and Radon integral representations; and convergence of probability measures. This paper • Rigorously establishes the robustness of feedforward network realizations. • Uses a theorem of Wiener and ideas of translation invariant subspaces to provide conditions for universal approximations to L1 and L2 functions by networks, for quite general activation functions. The second result extends and simplifies some of the recent results of Stinchcombe and White, at least for the special cases of L1 and L2 functions.
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Unknown

Document type: Journal Article
Sub-type: Article (original research)
Collection: Scopus Import
 
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Created: Tue, 12 Jul 2016, 01:27:02 EST by System User