Geometric Interpretation of Nonlinear Approximation Capability for Feedforward Neural Networks.

Hu Bao-Gang 1 Xing Hong-Jie 2 Yang Yu-Jiu 2
1 LIAMA - Eco-informatics
2 LIAMA - Laboratoire Franco-Chinois d'Informatique, d'Automatique et de Mathématiques Appliquées
Abstract : This paper presents a preliminary study on the nonlinear approximation capability of feedforward neural networks (FNNs) via a geometric approach. Three simplest FNNs with at most four free parameters are defined and investigated. By approximations on one-dimensional functions, we observe that the Chebyshev-polynomials, Gaussian, and sigmoidal FNNs are ranked in order of providing more varieties of nonlinearities. If neglecting the compactness feature inherited by Gaussian neural networks, we consider that the Chebyshev-polynomial-based neural networks will be the best among three types of FNNs in an efficient use of free parameters. This work is supported by Natural Science of Foundation of China (#60275025, #60121302).
Type de document :
Communication dans un congrès
Advances in Neural Networks - ISNN 2004, International Symposium on Neural Networks, Aug 2004, Dalian / China, Springer, 3173 (3173), pp.7-13, 2004, Lecture Notes in Computer Science. 〈10.1007/b99834〉
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https://hal.inria.fr/inria-00122761
Contributeur : Chine Publications Liama <>
Soumis le : jeudi 4 janvier 2007 - 16:40:54
Dernière modification le : mardi 24 avril 2018 - 13:29:58

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Hu Bao-Gang, Xing Hong-Jie, Yang Yu-Jiu. Geometric Interpretation of Nonlinear Approximation Capability for Feedforward Neural Networks.. Advances in Neural Networks - ISNN 2004, International Symposium on Neural Networks, Aug 2004, Dalian / China, Springer, 3173 (3173), pp.7-13, 2004, Lecture Notes in Computer Science. 〈10.1007/b99834〉. 〈inria-00122761〉

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