Journal ArticleDOI
Approximation by neural networks is not continuous
Reads0
Chats0
TLDR
In a Banach space X satisfying mild conditions, for its infinite, linearly independent subset G, there is no continuous best approximation map from X to the n-span, span n G.About:
This article is published in Neurocomputing.The article was published on 1999-11-01. It has received 44 citations till now. The article focuses on the topics: Subspace topology & Banach space.read more
Citations
More filters
Journal ArticleDOI
Approximation theory of the MLP model in neural networks
TL;DR: This survey discusses various approximation-theoretic problems that arise in the multilayer feedforward perceptron (MLP) model in neural networks.
Journal ArticleDOI
Error bounds for approximations with deep ReLU networks.
TL;DR: It is proved that deep ReLU networks more efficiently approximate smooth functions than shallow networks and adaptive depth-6 network architectures more efficient than the standard shallow architecture are described.
Posted Content
Error bounds for approximations with deep ReLU networks
TL;DR: In this paper, the expressive power of shallow and deep neural networks with piecewise linear activation functions was studied and upper and lower bounds for the network complexity in the setting of approximations in Sobolev spaces were established.
MonographDOI
Recurrent Neural Networks for Prediction
TL;DR: Within this text neural networks are considered as massively interconnected nonlinear adaptive filters.
Journal ArticleDOI
Comparison of worst case errors in linear and neural network approximation
Vera Kurkova,Marcello Sanguineti +1 more
TL;DR: A theoretical framework for describing sets of multivariable functions for which worst case errors in linear approximation are larger than those in approximation by neural networks is developed in the context of nonlinear approximation by fixed versus variable basis functions.
References
More filters
Book
Approximation of Functions
TL;DR: Possibility of approximating polynomials of best approximation with linear operators has been studied in the context of functions of one variable as mentioned in this paper, where the degree of approximation of differentiable functions has been shown to be a function of the complexity of the function.
Book
n-Widths in Approximation Theory
TL;DR: In this paper, Tchebycheff Systems and total positivity of n-widths are studied in the context of the Tchebyschka system, and the existence of optimal subspaces for dn.
Book
Best Approximation in Normed Linear Spaces by Elements of Linear Subspaces
TL;DR: In this paper, the authors propose an approximation of sous-espace lineaire de dimension finie, which is a lineaire lineaire of the dimension of the element d'ensemble.