A Criterion of Expressibility of CPL Functions in Generalized Bases

In the paper, circuits obtained by superpositions over bases consisting of arbitrary subsets of piecewise-linear functions are studied, and criteria for the expressibility of an arbitrary continuous piecewise-linear function over such bases is proved. Estimates of the linear complexity and nonlinear dependence of the resulting circuits are given.

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Publication Details

Journal
Moscow University Mathematics Bulletin
Published
2025-04-01
DOI
https://doi.org/10.3103/s0027132225700354
Primary Topic
Control Systems and Identification
Type
article
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article

A Criterion of Expressibility of CPL Functions in Generalized Bases

V. G. Shishlyakov
Moscow University Mathematics Bulletin
Control Systems and Identification
article

A Criterion of Expressibility of CPL Functions in Generalized Bases

V. G. Shishlyakov
article en

Abstract

In the paper, circuits obtained by superpositions over bases consisting of arbitrary subsets of piecewise-linear functions are studied, and criteria for the expressibility of an arbitrary continuous piecewise-linear function over such bases is proved. Estimates of the linear complexity and nonlinear dependence of the resulting circuits are given.

Moscow University Mathematics BulletinVol. 80(2)
Lomonosov Moscow State University (RU)
Openalex Percentile: Top 80%
Control Systems and Identification
DOISourceOpenAlex
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A Criterion of Expressibility of CPL Functions in Generalized Bases — V. G. Shishlyakov · Moscow University Mathematics Bulletin (2025) | TGRS Research Map | TGRS