Approximation by neural networks with weights varying on a finite set of directions

DOI10.1016/j.jmaa.2011.11.037zbMath1348.41013OpenAlexW1988019790MaRDI QIDQ663685

Vugar E. Ismailov

Publication date: 27 February 2012

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2011.11.037

zbMATH Keywords

neural networkapproximationdensityorbitpathweightactivation functionMLP model

Mathematics Subject Classification ID

Learning and adaptive systems in artificial intelligence (68T05) Approximation by other special function classes (41A30)

Related Items (14)

Approximation by ridge functions and neural networks with a bounded number of neurons ⋮ Almost everywhere approximation capabilities of double Mellin approximate identity neural networks ⋮ Neural network interpolation operators activated by smooth ramp functions ⋮ On the approximation by single hidden layer feedforward neural networks with fixed weights ⋮ Approximation error of single hidden layer neural networks with fixed weights ⋮ Approximation by sums of ridge functions with fixed directions ⋮ Computing the Approximation Error for Neural Networks with Weights Varying on Fixed Directions ⋮ A Single Hidden Layer Feedforward Network with Only One Neuron in the Hidden Layer Can Approximate Any Univariate Function ⋮ On the approximation by neural networks with bounded number of neurons in hidden layers ⋮ Approximation Properties of Ridge Functions and Extreme Learning Machines ⋮ The universal approximation capabilities of double \(2\pi\)-periodic approximate identity neural networks ⋮ Unnamed Item ⋮ On the representation by bivariate ridge functions ⋮ Rates of approximation by neural network interpolation operators

Cites Work

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• Uniform approximation by neural networks
• Lower bounds for approximation by MLP neural networks
• Approximation by neural networks with a bounded number of nodes at each level
• When is \(f(x_1,x_1,\dots,x_n)= u_1(x_1)+ u_2(x_2)+\cdots+ u_n(x_n)\)?
• Some remarks on good sets
• Interpolation by Ridge functions
• On the representation by linear superpositions
• Approximation by neural networks and learning theory
• Théorie générale des fonctions moyenne-périodiques
• Sums of Subalgebras of C (X )
• Uniform approximation by real functions
• Approximation by superpositions of a sigmoidal function

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