Approximation by Ridge functions and neural networks with one hidden layer
From MaRDI portal
Publication:1198148
DOI10.1016/0021-9045(92)90081-XzbMath0768.41018OpenAlexW1983776716MaRDI QIDQ1198148
Publication date: 16 January 1993
Published in: Journal of Approximation Theory (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/0021-9045(92)90081-x
Interpolation in approximation theory (41A05) Approximation by other special function classes (41A30)
Related Items (63)
On Approximation by Neural Networks with Optimized Activation Functions and Fixed Weights ⋮ On the error of approximation by ridge functions with two fixed directions ⋮ Characterization of an extremal sum of ridge functions ⋮ Approximation by network operators with logistic activation functions ⋮ Interpolation and rates of convergence for a class of neural networks ⋮ Multivariate Jackson-type inequality for a new type neural network approximation ⋮ CONSTRUCTIVE ESTIMATION OF APPROXIMATION FOR TRIGONOMETRIC NEURAL NETWORKS ⋮ The estimate for approximation error of spherical neural networks ⋮ Approximation by ridge functions and neural networks with a bounded number of neurons ⋮ Approximation properties of a multilayered feedforward artificial neural network ⋮ Lower estimation of approximation rate for neural networks ⋮ The errors of approximation for feedforward neural networks in thelpmetric ⋮ Neural network interpolation operators activated by smooth ramp functions ⋮ Modeling a stochastic age-structured capital system with Poisson jumps using neural networks ⋮ Neural networks for optimal approximation of continuous functions in \(\mathbb R^d\) ⋮ Hyperbolic sigma-pi neural network operators for compactly supported continuous functions ⋮ Approximation by neural networks with sigmoidal functions ⋮ Standard representation and unified stability analysis for dynamic artificial neural network models ⋮ On the approximation by single hidden layer feedforward neural networks with fixed weights ⋮ A note on the applications of one primary function in deep neural networks ⋮ Neural network interpolation operators optimized by Lagrange polynomial ⋮ On the representation by linear superpositions ⋮ Neural network interpolation operators of multivariate functions ⋮ Analysis of convergence performance of neural networks ranking algorithm ⋮ The construction and approximation of feedforward neural network with hyperbolic tangent function ⋮ Approximation error of single hidden layer neural networks with fixed weights ⋮ Order of approximation for exponential sampling type neural network operators ⋮ Approximation by sums of ridge functions with fixed directions ⋮ Essential rate for approximation by spherical neural networks ⋮ The errors of simultaneous approximation of multivariate functions by neural networks ⋮ The ridge function representation of polynomials and an application to neural networks ⋮ Computing the Approximation Error for Neural Networks with Weights Varying on Fixed Directions ⋮ Approximation results for neural network operators activated by sigmoidal functions ⋮ A Single Hidden Layer Feedforward Network with Only One Neuron in the Hidden Layer Can Approximate Any Univariate Function ⋮ Multivariate neural network operators with sigmoidal activation functions ⋮ On the approximation by neural networks with bounded number of neurons in hidden layers ⋮ Approximation by neural networks with weights varying on a finite set of directions ⋮ Discrete directional Gabor frames ⋮ Neural networks for optimal approximation of continuous functions on the unit sphere ⋮ The fundamentality of sets of ridge functions ⋮ An approximation by neural networks with a fixed weight ⋮ Multivariate sigmoidal neural network approximation ⋮ Unnamed Item ⋮ The approximation operators with sigmoidal functions ⋮ A way of constructing translation network operators by Bernstein operators ⋮ Sigmoidal FFANN’s and the best approximation property ⋮ Neural Networks for Localized Approximation ⋮ New study on neural networks: the essential order of approximation ⋮ The essential order of approximation for nearly exponential type neural networks ⋮ Approximation by exponential sampling type neural network operators ⋮ CONSTRUCTIVE APPROXIMATION BY NEURAL NETWORKS WITH POSITIVE INTEGER WEIGHTS ⋮ Quantitative approximation by perturbed Kantorovich-Choquet neural network operators ⋮ Rates of approximation by neural network interpolation operators ⋮ Simultaneous \(\mathbf L^p\)-approximation order for neural networks ⋮ The construction and approximation of ReLU neural network operators ⋮ On the order of approximation by periodic neural networks based on scattered nodes ⋮ Approximation by perturbed neural network operators ⋮ Nonlinear Level Set Learning for Function Approximation on Sparse Data with Applications to Parametric Differential Equations ⋮ Stable recovery of entangled weights: towards robust identification of deep neural networks from minimal samples ⋮ Approximations by multivariate perturbed neural network operators ⋮ Extension of localised approximation by neural networks ⋮ On a problem of Hornik ⋮ Exponential ReLU DNN expression of holomorphic maps in high dimension
Cites Work
- The fundamentality of sets of ridge functions
- Moment problems and low rank Toeplitz approximations
- General Lagrange and Hermite interpolation in \(R^n\) with applications to finite element methods
- Learned classification of sonar targets using a massively parallel network
- Cardinal Interpolation by Multivariate Splines
- Experiments on neural net recognition of spoken and written text
- On a Class of Finite Elements Generated by Lagrange Interpolation
- Approximation by superpositions of a sigmoidal function
- Unnamed Item
This page was built for publication: Approximation by Ridge functions and neural networks with one hidden layer
