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JOURNALS // Intelligent systems. Theory and applications // Archive

Intelligent systems. Theory and applications, 2021 Volume 25, Issue 3, Pages 137–156 (Mi ista317)

Part 2. Special Issues in Intellectual Systems Theory

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

A. D. Otroschenko

Lomonosov Moscow State University

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.



© Steklov Math. Inst. of RAS, 2024