Approximative compactness of linear combinations of characteristic functions

DOI10.1016/j.jat.2020.105435zbMath1445.41020OpenAlexW3023494653MaRDI QIDQ783713

Andrew Vogt, Paul C. Kainen, Vera Kurková

Publication date: 4 August 2020

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jat.2020.105435

zbMATH Keywords

neural networksHausdorff metricHaar measuresymmetric difference metricapproximative compactnesscompact sets of characteristic (indicator) functions

Mathematics Subject Classification ID

Learning and adaptive systems in artificial intelligence (68T05) Neural networks for/in biological studies, artificial life and related topics (92B20) Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence (28A20) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65) Other problems of combinatorial convexity (52A37) Approximation by arbitrary linear expressions (41A45)

Related Items (4)

DENSITY RESULTS BY DEEP NEURAL NETWORK OPERATORS WITH INTEGER WEIGHTS ⋮ Quantitative estimates for neural network operators implied by the asymptotic behaviour of the sigmoidal activation functions ⋮ Nonclosedness of sets of neural networks in Sobolev spaces ⋮ Approximation error for neural network operators by an averaged modulus of smoothness

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