Abstract

A general approximation theorem is proved. It uniformly envelopes both the classical Stone theorem and approximation of functions of several variables by means of superpositions and linear combinations of functions of one variable. This theorem is interpreted as a statement on universal approximating possibilities ("approximating omnipotence") of arbitrary nonlinearity. For the neural networks, our result states that the function of neuron activation must be nonlinear, and nothing else

Meeting Name

1998 IEEE International Joint Conference on Neural Networks Proceedings, 1998. IEEE World Congress on Computational Intelligence

Department(s)

Electrical and Computer Engineering

Keywords and Phrases

Stone Theorem; Approximation Theory; Function Approximation; General Approximation Theorem; Mathematics Computing; Neural Nets; Neural Networks; Neuron Activation Function

Document Type

Article - Conference proceedings

Document Version

Final Version

File Type

text

Language(s)

English

Rights

© 1998 Institute of Electrical and Electronics Engineers (IEEE), All rights reserved.

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