Existence and uniqueness results for neural network approximations
- 1 January 1995
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Neural Networks
- Vol. 6 (1) , 2-13
- https://doi.org/10.1109/72.363455
Abstract
Some approximation theoretic questions concerning a certain class of neural networks are considered. The networks considered are single input, single output, single hidden layer, feedforward neural networks with continuous sigmoidal activation functions, no input weights but with hidden layer thresholds and output layer weights. Specifically, questions of existence and uniqueness of best approximations on a closed interval of the real line under mean-square and uniform approximation error measures are studied. A by-product of this study is a reparametrization of the class of networks considered in terms of rational functions of a single variable. This rational reparametrization is used to apply the theory of Pade approximation to the class of networks considered. In addition, a question related to the number of local minima arising in gradient algorithms for learning is examined.Keywords
This publication has 16 references indexed in Scilit:
- Identification and rational L2 approximation A gradient algorithmAutomatica, 1991
- Maple V Language Reference ManualPublished by Springer Nature ,1991
- Analysis of gradient descent learning algorithms for multilayer feedforward neural networksIEEE Transactions on Circuits and Systems, 1991
- Networks and the best approximation propertyBiological Cybernetics, 1990
- On the approximate realization of continuous mappings by neural networksNeural Networks, 1989
- Multilayer feedforward networks are universal approximatorsNeural Networks, 1989
- On nonuniqueness in nonlinear L2-approximationJournal of Approximation Theory, 1987
- On the Remez algorithm for non-linear familiesNumerische Mathematik, 1970
- A generalization of the Padé approximantJournal of Mathematical Analysis and Applications, 1967
- Expansion of power series intoP-fractionsMathematische Zeitschrift, 1962