Estimates of the Number of Hidden Units and Variation with Respect to HalfSpaces

 KURKOVA Vera
 Institute of Computer Science, Czech Academy of Sciences, University of Texas at El Paso

 KAINEN Paul C.
 Industrial Math, University of Texas at El Paso

 KREINOVICH Vladik
 Department of Computer Science, University of Texas at El Paso
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Author(s)

 KURKOVA Vera
 Institute of Computer Science, Czech Academy of Sciences, University of Texas at El Paso

 KAINEN Paul C.
 Industrial Math, University of Texas at El Paso

 KREINOVICH Vladik
 Department of Computer Science, University of Texas at El Paso
Journal

 Neural Networks

Neural Networks 10(6), 10611068, 19970801
References: 22

1
 Cube slicing in R^d.

BALL K.
Proceedings of AMS 99, 110, 1986
Cited by (1)

2
 Neural net approximation.

BARRON A. R.
Proceedings of the 7th Yale Workshop on Adaptive and Learning Systems, 6972, 1992
Cited by (2)

3
 <no title>

COURANT R.
Methods of Mathematical Physics II, 1992
Cited by (1)

4
 Rate of approximation results motivated by robust neural network learning.

DARKEN C.
Proceedings of the 6th Annual ACM Conference on Computational Learning Theory, 303309, 1993
Cited by (3)

5
 Optimal nonlinear approximation

DEVORE R.
Manuscripta Mathematica 63, 469478, 1989
Cited by (3)

6
 <no title>

EDWARDS C. H.
Advanced calculus of several variables, 1994
Cited by (1)

7
 Approximation error bounds that use VCbounds

GIROSI F.
Proceedings of ICANN'95, 295302, 1995
Cited by (1)

8
 Rates of convergence for radial basis functions and neural networks

GIROSI F.
Artificial Neural Networks for Speech and Vision, 97113, 1993
Cited by (2)

9
 <no title>

HAMMING R. W.
Coding and Information Theory, 1986
Cited by (4)

10
 <no title>

HEWITT E.
Real and abstract analysis, 1965
Cited by (1)

11
 <no title>

KELLEY J. L.
General topology, 1955
Cited by (9)

12
 <no title>

MCSHANE E. J.
Integration, 1994
Cited by (1)

13
 <no title>

RUDIN W.
Principles of mathematical analysis, 1964
Cited by (1)

14
 <no title>

RUDIN W.
Functional Analysis, 1973
Cited by (8)

15
 Mapping between highdimensional representations of acoustic and speech signal

SEJNOWSKI T. J.
Computation and cognition, 5268, 1989
Cited by (1)

16
 <no title>

ZEMANIAN A. H.
Distribution theory and transform analysis, 1987
Cited by (1)

17
 Universal approximation bounds for superpositions of a sigmoidal function

BARRON A. R.
IEEE Trans. Inf. Theory 39(3), 930945, 1993
DOI Cited by (45)

18
 Representation of functions by superposition of a step or sigmoid function and their applications to neural network theory

ITO Y.
Neural Networks 4, 385394, 1991
Cited by (8)

19
 A simple lemma on greedy approximation in hilbert space and convergence rates for projection pursuit regression and neural network training

JONES L. K.
The Annals of Statistics 20(1), 608613, 1992
DOI Cited by (4)

20
 Kolmogorov's Theorem and multilayer neural networks

KURKOVA V.
Neural Networks 5, 501506, 1992
Cited by (7)

21
 Approximation by superposition of sigmoidal and radial basis functions

MHASKAR H. N.
Advances in Applied Mathematics 13, 350373, 1992
DOI Cited by (11)

22
 Approximation and radialbasisfunction networks

PARK J.
Neural Computation 5, 305316, 1993
DOI Cited by (20)
Cited by: 1

1
 Representations and rates of approximation of realvalued Boolean functions by neural networks

KUARKOVA V. , SAVICKY P. , HLAVACKOVA K.
Neural Networks 11(4), 651659, 19980601
References (22) Cited by (1)