Quantitative estimates for neural network operators implied by the asymptotic behaviour of the sigmoidal activation functions

DOI10.1007/s00009-022-02138-8OpenAlexW4294571876WikidataQ114232203 ScholiaQ114232203MaRDI QIDQ2675943

Danilo Costarelli, Uğur Kadak, Lucian C. Coroianu

Publication date: 26 September 2022

Published in: Mediterranean Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00009-022-02138-8

zbMATH Keywords

uniform convergencesigmoidal functionsquantitative estimatesneural network operatorsReLU function

Mathematics Subject Classification ID

Approximation by rational functions (41A20) Rate of convergence, degree of approximation (41A25) Approximation by operators (in particular, by integral operators) (41A35)

Cites Work

• Unnamed Item
• Unnamed Item
• Approximation results for neural network operators activated by sigmoidal functions
• Multivariate neural network operators with sigmoidal activation functions
• Multivariate hyperbolic tangent neural network approximation
• Multivariate sigmoidal neural network approximation
• On sharpness of error bounds for univariate approximation by single hidden layer feedforward neural networks
• Approximative compactness of linear combinations of characteristic functions
• The approximation operators with sigmoidal functions
• Rate of convergence of some neural network operators to the unit-univariate case
• Saturation classes for MAX-product neural network operators activated by sigmoidal functions
• Approximation results in Orlicz spaces for sequences of Kantorovich MAX-product neural network operators
• Approximation with neural networks activated by ramp sigmoids
• The max-product generalized sampling operators: convergence and quantitative estimates
• Asymptotic expansion for neural network operators of the Kantorovich type and high order of approximation
• Approximation by exponential sampling type neural network operators
• Fractional type multivariate sampling operators
• Rates of approximation by neural network interpolation operators
• Modified neural network operators and their convergence properties with summability methods
• Convergence of a family of neural network operators of the Kantorovich type
• Error bounds for approximations with deep ReLU networks
• Universality of deep convolutional neural networks
• On the hexagonal Shepard method
• Intelligent systems II. Complete approximation by neural network operators
• Max-product neural network and quasi-interpolation operators activated by sigmoidal functions
• Quantitative estimates involving K-functionals for neural network-type operators
• Neural Approximations for Optimal Control and Decision
• Approximation by max-product sampling Kantorovich operators with generalized kernels
• Approximation by superpositions of a sigmoidal function

This page was built for publication: Quantitative estimates for neural network operators implied by the asymptotic behaviour of the sigmoidal activation functions