# Universal Approximation Theorem for Interval Neural Networks

Universal Approximation Theorem for Interval Neural Networks One of the main computer-learning tools is an (artificial) neural network (NN); based on the values y (p) of a certain physical quantity y at several points x (p) =(x 1 (p) ,...,x n (p) ), the NN finds a dependence y = f(x1,...,x n ) that explains all known observations and predicts the value of y for other x = (x1,...,xn). The ability to describe an arbitrary dependence follows from the universal approximation theorem, according to which an arbitrary continuous function of a bounded set can be, within a given accuracy, approximated by an appropriate NN. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

# Universal Approximation Theorem for Interval Neural Networks

, Volume 4 (3) – Oct 14, 2004
5 pages

/lp/springer_journal/universal-approximation-theorem-for-interval-neural-networks-RvjD1SMLWe
Publisher
Subject
Mathematics; Numeric Computing; Approximations and Expansions; Computational Mathematics and Numerical Analysis; Mathematical Modeling and Industrial Mathematics
ISSN
1385-3139
eISSN
1573-1340
D.O.I.
10.1023/A:1009951412412
Publisher site
See Article on Publisher Site

### Abstract

One of the main computer-learning tools is an (artificial) neural network (NN); based on the values y (p) of a certain physical quantity y at several points x (p) =(x 1 (p) ,...,x n (p) ), the NN finds a dependence y = f(x1,...,x n ) that explains all known observations and predicts the value of y for other x = (x1,...,xn). The ability to describe an arbitrary dependence follows from the universal approximation theorem, according to which an arbitrary continuous function of a bounded set can be, within a given accuracy, approximated by an appropriate NN.

### Journal

Reliable ComputingSpringer Journals

Published: Oct 14, 2004

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