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Intelligent systems. Theory and applications, 2022, Volume 26, Issue 2, Pages 145–165 (Mi ista409)  

Part 3. Mathematical models

On the expressibility of piecewise constant functions in the space of piecewise parallel

A. D. Otroschenko

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
References:
Abstract: For a finite system of piecewise parallel functions implemented by schemes of linear elements and Heaviside functions, the criterion for the expressiveness of piecewise constant functions is obtained, supplemented by all single linear functions. Thus, the criterion of expressiveness of the binary classifier implemented by the McCulloch-Pitts neural scheme is obtained.
Keywords: Piecewise constant function, piecewise parallel function, completeness problem, expressibility problem, McCulloch-Pitts neural circuits.
Document Type: Article
Language: Russian
Citation: A. D. Otroschenko, “On the expressibility of piecewise constant functions in the space of piecewise parallel”, Intelligent systems. Theory and applications, 26:2 (2022), 145–165
Citation in format AMSBIB
\Bibitem{Otr22}
\by A.~D.~Otroschenko
\paper On the expressibility of piecewise constant functions in the space of piecewise parallel
\jour Intelligent systems. Theory and applications
\yr 2022
\vol 26
\issue 2
\pages 145--165
\mathnet{http://mi.mathnet.ru/ista409}
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