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Geometric Interpretation of Nonlinear Approximation Capability for Feedforward Neural Networks.

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).
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https://hal.inria.fr/inria-00122761
Contributor : Chine Publications Liama <>
Submitted on : Thursday, January 4, 2007 - 4:40:54 PM
Last modification on : Thursday, June 4, 2020 - 6:55:49 AM

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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, China. pp.7-13, ⟨10.1007/b99834⟩. ⟨inria-00122761⟩

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