Complexity estimates based on integral transforms induced by computational units

Authors:
Vra Krková
Affiliations:
-
Venue:
Neural Networks
Year:
2012

Citing 21
Cited 1

Eigenvalues and s-numbers

Eigenvalues and s-numbers
Representation of functions by superpositions of a step or sigmoid function and their applications to neural network theory

Neural Networks
Universal approximation using radial-basis-function networks

Neural Computation
Approximation and radial-basis-function networks

Neural Computation
Rate of approximation results motivated by robust neural network learning

COLT '93 Proceedings of the sixth annual conference on Computational learning theory
Approximation and learning of convex superpositions

Journal of Computer and System Sciences - Special issue: 26th annual ACM symposium on the theory of computing & STOC'94, May 23–25, 1994, and second annual Europe an conference on computational learning theory (EuroCOLT'95), March 13–15, 1995
Estimates of the number of hidden units and variation with respect to half-spaces

Neural Networks
Representations and rates of approximation of real-valued Boolean functions by neural networks

Neural Networks
Feedforward Neural Network Methodology

Feedforward Neural Network Methodology
On the tractability of multivariate integration and approximation by neural networks

Journal of Complexity
Error Estimates for Approximate Optimization by the Extended Ritz Method

SIAM Journal on Optimization
A Sobolev-type upper bound for rates of approximation by linear combinations of Heaviside plane waves

Journal of Approximation Theory
Minimization of error functionals over perceptron networks

Neural Computation
Complexity of Gaussian-radial-basis networks approximating smooth functions

Journal of Complexity
An integral upper bound for neural network approximation

Neural Computation
Model Complexity of Neural Networks and Integral Transforms

ICANN '09 Proceedings of the 19th International Conference on Artificial Neural Networks: Part I
Weighted quadrature formulas and approximation by zonal function networks on the sphere

Journal of Complexity
Comparison of worst case errors in linear and neural network approximation

IEEE Transactions on Information Theory
Geometric Upper Bounds on Rates of Variable-Basis Approximation

IEEE Transactions on Information Theory
Universal approximation bounds for superpositions of a sigmoidal function

IEEE Transactions on Information Theory
On the geometric convergence of neural approximations

IEEE Transactions on Neural Networks

Multivariate neural network operators with sigmoidal activation functions

Neural Networks

Quantified Score

Hi-index	0.00

Visualization

Abstract

Integral transforms with kernels corresponding to computational units are exploited to derive estimates of network complexity. The estimates are obtained by combining tools from nonlinear approximation theory and functional analysis together with representations of functions in the form of infinite neural networks. The results are applied to perceptron networks.