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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2021, Volume 61, Number 7, Pages 1172–1178
DOI: https://doi.org/10.31857/S0044466921070103 (Mi zvmmf11267) 		 
Computer science

Neural network with smooth activation functions and without bottlenecks is almost surely a Morse function

S. V. Kurochkin

National Research University Higher School of Economics, 109028, Moscow, Russia
DOI: https://doi.org/10.31857/S0044466921070103
Abstract: It is proved that a neural network with sigmoidal activation functions is a Morse function for almost all, with respect to the Lebesgue measure, sets of parameters (weights) in the case when the network architecture has no bottlenecks, i.e., layers with fewer neurons than in the adjacent layers. It is shown by examples that the requirement for no bottlenecks is essential.
Key words: neural network, Morse functions.
Funding agency Grant number
NTI
These results were obtained within the framework of a research project implemented at the Center for Big Data Storage and Analysis of Lomonosov Moscow State University.
Received: 15.12.2019
Revised: 15.12.2019
Accepted: 15.09.2020
English version:
Computational Mathematics and Mathematical Physics, 2021, Volume 61, Issue 7, Pages 1162–1168
DOI: https://doi.org/10.1134/S0965542521070101
Bibliographic databases:
Document Type: Article
UDC: 519.87
Language: Russian
Citation: S. V. Kurochkin, “Neural network with smooth activation functions and without bottlenecks is almost surely a Morse function”, Zh. Vychisl. Mat. Mat. Fiz., 61:7 (2021), 1172–1178; Comput. Math. Math. Phys., 61:7 (2021), 1162–1168
Citation in format AMSBIB
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\paper Neural network with smooth activation functions and without bottlenecks is almost surely a Morse function
\jour Zh. Vychisl. Mat. Mat. Fiz.
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\vol 61
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\pages 1172--1178
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