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Intelligent systems. Theory and applications, 2022, Volume 26, Issue 2, Pages 145–165
(Mi ista409)
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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
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.
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
Linking options:
https://www.mathnet.ru/eng/ista409 https://www.mathnet.ru/eng/ista/v26/i2/p145
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