Approximation by neural networks with a bounded number of nodes at each level

DOI10.1016/S0021-9045(03)00078-9zbMath1019.41018OpenAlexW2036450593MaRDI QIDQ1395810

Gustaf Gripenberg

Publication date: 1 July 2003

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

Full work available at URL: https://doi.org/10.1016/s0021-9045(03)00078-9

zbMATH Keywords

densitymultilayerneural

Mathematics Subject Classification ID

Approximation by arbitrary nonlinear expressions; widths and entropy (41A46)

Related Items (17)

Approximation theorems for a family of multivariate neural network operators in Orlicz-type spaces ⋮ Approximation by max-product neural network operators of Kantorovich type ⋮ Max-product neural network and quasi-interpolation operators activated by sigmoidal functions ⋮ Neural network operators: constructive interpolation of multivariate functions ⋮ Probabilistic lower bounds for approximation by shallow perceptron networks ⋮ Saturation classes for MAX-product neural network operators activated by sigmoidal functions ⋮ Modified neural network operators and their convergence properties with summability methods ⋮ Pointwise and uniform approximation by multivariate neural network operators of the max-product type ⋮ Noncompact uniform universal approximation ⋮ Convergence results for a family of Kantorovich max-product neural network operators in a multivariate setting ⋮ Convergence for a family of neural network operators in Orlicz spaces ⋮ Predictive control of uncertain nonlinear parabolic PDE systems using a Galerkin/neural-network-based model ⋮ Approximation by sums of ridge functions with fixed directions ⋮ Approximation by neural networks with weights varying on a finite set of directions ⋮ Asymptotic expansion for neural network operators of the Kantorovich type and high order of approximation ⋮ Quantitative estimates involving K-functionals for neural network-type operators ⋮ Limitations of shallow nets approximation

Cites Work

• Unnamed Item
• Unnamed Item
• Approximation of continuous functions of several variables by an arbitrary nonlinear continuous function of one variable, linear functions, and their superpositions
• Uniform approximation by neural networks
• Lower bounds for approximation by MLP neural networks
• Error bounds for approximation with neural networks

This page was built for publication: Approximation by neural networks with a bounded number of nodes at each level