On the approximation by neural networks with bounded number of neurons in hidden layers

被引：75

作者：

Ismailov, Vugar E. ^{[1
]}

机构：

[1] Azerbaijan Natl Acad Sci, Inst Math & Mech, AZ-1141 Baku, Azerbaijan

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2014年 / 417卷 / 02期

关键词：

Neural network; MLP model; Sigmoidal function; Approximation; Superposition; MULTILAYER FEEDFORWARD NETWORKS; SUPERPOSITION THEOREM; RIDGE FUNCTIONS; METRIC-SPACES; KOLMOGOROV; REPRESENTATION; VARIABLES; DIMENSION;

D O I：

10.1016/j.jmaa.2014.03.092

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the current note, we show that a two hidden layer neural network with d inputs, d neurons in the first hidden layer, 2d+2 neurons in the second hidden layer and with a specifically constructed sigmoidal and infinitely differentiable activation function can approximate any continuous multivariate function with arbitrary accuracy. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：963 / 969

页数：7

共 28 条

[1]

[Anonymous], P IEEE 1 ANN INT C N

[2]

[Anonymous], TRANSL MATH MONOGR

[3]

Arnold V.I., 1963, Amer. Math. Soc. Transl., V28, P51

[4] APPROXIMATION AND ESTIMATION BOUNDS FOR ARTIFICIAL NEURAL NETWORKS [J].

BARRON, AR .

MACHINE LEARNING, 1994, 14 (01) :115-133

[5] The estimate for approximation error of neural networks: A constructive approach [J].

Cao, Feilong ;

Xie, Tingfan ;

Xu, Zongben .

NEUROCOMPUTING, 2008, 71 (4-6) :626-630

[6] APPROXIMATIONS OF CONTINUOUS FUNCTIONALS BY NEURAL NETWORKS WITH APPLICATION TO DYNAMIC-SYSTEMS [J].

CHEN, TP ;

CHEN, H .

IEEE TRANSACTIONS ON NEURAL NETWORKS, 1993, 4 (06) :910-918

[7] APPROXIMATION BY RIDGE FUNCTIONS AND NEURAL NETWORKS WITH ONE HIDDEN LAYER [J].

CHUI, CK ;

LI, X .

JOURNAL OF APPROXIMATION THEORY, 1992, 70 (02) :131-141

[8]

Cybenko G., 1989, Mathematics of Control, Signals, and Systems, V2, P303, DOI 10.1007/BF02551274

[9]

FRIDMAN BL, 1967, DOKL AKAD NAUK SSSR+, V177, P1019

[10] Representation Properties of Networks: Kolmogorov's Theorem Is Irrelevant [J].

Girosi, Federico ;

Poggio, Tomaso .

NEURAL COMPUTATION, 1989, 1 (04) :465-469

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