Universal approximation capability of EBF neural networks with arbitrary activation functions

Circuits, Systems, and Signal Processing

Volumn 15, Issue 5, 1996, Pages 671-683

  Tianping, Chen ^a   Hong, Hong ^b  

^a FUDAN UNIVERSITY   (China)

^b SUN MICROSYSTEMS   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; FUNCTION EVALUATION; PROBLEM SOLVING; THEOREM PROVING;

ACTIVATION FUNCTION; AFFINE BASIS FUNCTION; ELLIPTIC BASIS FUNCTION; GENERALIZED RADIAL BASIS FUNCTION;

NEURAL NETWORKS;

EID: 0029720180     PISSN: 0278081X     EISSN: None     Source Type: Journal    
DOI: 10.1007/bf01188988     Document Type: Article

References (15)

1. T. Chen and H. Chen, Approximation to continuous functionals by neural networks with application to dynamical systems, IEEE Trans. on Neural Networks, vol. 4, no. 6, pp. 910-918, 1993.
2. T. Chen and H. Chen, Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamic systems, accepted for publication by IEEE Trans. on Neural Networks, vol. 6, no. 4, pp. 911-917, 1995.
3. T. Chen and H. Chen, Approximation capability to functions of several variables, nonlinear functional and operators by radial basis function neural networks, accepted for publication by IEEE Trans. on Neural Networks, vol. 6, no. 4, pp. 904-910, 1995.
4. T. Chen, H. Chen, and R.-W. Liu, A constructive proof of cybenko's approximation theorem and its extensions, pp. 163-168 in Computing Science and Statistics, editors LePage and Page, Proc. of the 22nd Symposium on the Interface, East Lansing, MI, May 1990, Springer-Verlag, Berlin and New York, ISBN 0-387-97719-8.
5. n) by multilayer feedforward networks and related problems, IEEE Trans. on Neural Networks, vol. 6, no. 1, pp. 25-30, 1995.
6. G. Cybenko, Approximation by superpositions of a sigmoidal function, in Math. of Control, Signals and Systems, vol. 2, no, 4, pp. 303-314, 1989.
7. R. J. P. DeFigueiredo, Implication and applications of Kolmogorov's superposition theorem, IEEE Trans. Automatic Control, vol. AC-25, no. 6, pp. 1227-1230, 1980.
8. K. Hornik, Approximation capabilities of multilayer feedforward networks, Neural Networks, vol. 4, pp. 251-257, 1991.
9. K. Hornik, M. Stinchcombe, and H. White, Multi-layer feedforward networks are universal approximators, Neural Networks, vol. 2, pp. 359-366, 1989.
10. M. Leshno, V. Lin, A. Pinkus, and S. Schocken, Multilayer feedforward networks with a non-polynomial activation function can approximate any function, Neural Networks, vol. 6, no. 6, pp. 861-867, 1993.
11. H. N. Mhaskar and C. A. Micchelli, Approximation by superposition of sigmoidal and radial basis functions, Advances in Applied Mathematics, vol. 13, pp. 350-373, 1992.
12. J. Park and I. W. Sandberg, Nonlinear approximations using elliptic basis function networks, Circuits, Systems, and Signal Processing, vol. 13, no. 1, pp. 99-113, 1994.
13. I. W. Sandberg, Structure theorems for nonlinear systems, Multidimensional Systems and Signal Processing, vol. 2, no. 3, pp. 2647-286, 1991.
14. E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton University Press, Princeton, NJ, 1970.
15. E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton University Press, Princeton, NJ, 1971.