Approximation capability of layered neural networks with sigmoid units on two layers

Authors:
Yoshifusa Ito
Affiliations:
Toyohashi University of Technology, Toyohashi, Japan
Venue:
Neural Computation
Year:
1994

Citing 11
Cited 0

Multilayer feedforward networks are universal approximators

Neural Networks
On the approximate realization of continuous mappings by neural networks

Neural Networks
Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks

Neural Networks
Approximation capabilities of multilayer feedforward networks

Neural Networks
Representation of functions by superpositions of a step or sigmoid function and their applications to neural network theory

Neural Networks
Approximation of functions on a compact set by finite sums of a sigmoid function without scaling

Neural Networks
Original Contribution: Approximation of continuous functions on Rd by linear combinations of shifted rotations of a sigmoid function with and without scaling

Neural Networks
Kolmogorov's theorem and multilayer neural networks

Neural Networks
Differentiable approximation by means of the Radon transformation and its applications to neural networks

Journal of Computational and Applied Mathematics
Kolmogorov's theorem is relevant

Neural Computation
Representation properties of networks: Kolmogorov's theorem is irrelevant

Neural Computation

Quantified Score

Hi-index	0.00

Visualization

Abstract

Using only an elementary constructive method, we prove the universal approximation capability of three-layered feedforward neural networks that have sigmoid units on two layers. We regard the Heaviside function as a special case of sigmoid function and measure accuracy of approximation in either the supremum norm or in the Lp-norm. Given a continuous function defined on a unit hypercube and the required accuracy of approximation, we can estimate the numbers of necessary units on the respective sigmoid unit layers. In the case where the sigmoid function is the Heaviside function, our result improves the estimation of Kůrková (1992). If the accuracy of approximation is measured in the LP-norm, our estimation also improves that of Kůrková (1992), even when the sigmoid function is not the Heaviside function.