A UNIVERSAL MAPPING FOR KOLMOGOROV SUPERPOSITION THEOREM

被引：43

作者：

SPRECHER, DA

机构：

来源：

NEURAL NETWORKS | 1993年 / 6卷 / 08期

关键词：

SUPERPOSITIONS; KOLMOGOROV; REPRESENTATIONS OF CONTINUOUS FUNCTIONS OF SEVERAL VARIABLES; FEEDFORWARD NEURAL NETWORKS; PROCESSING ELEMENTS; WEIGHTED SUMS; UNIFORM CONTINUITY;

D O I：

10.1016/S0893-6080(09)80020-8

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

Based on constructions of Kolmogorov and an earlier refinement of the author, we use a sequence of integrally independent positive numbers to construct a continuous function psi(x) having the following property: Every real-valued uniformly continuous function f(x1, . . . , x(n)) of n greater-than-or-equal-to 2 variables can be obtained as a superposition of continuous functions of one variable based on weighted sums of translates of the fixed function psi(x) that is independent of the number of variables n. From this is obtained a stronger version of the Hecht-Nielsen three-layer feed forward neural network for implementing f(x1, . . . , x(n)).

引用

页码：1089 / 1094

页数：6

共 6 条

[1]

HECHTNIELSEN R, 1987, 1ST IEEE INT C NEUR, V3, P11

[2]

HECHTNIELSEN R, 1987, P INT C NEURAL NETWO, V2, P19

[3]

Kolmogorov A. N., 1963, TRANSL AM MATH SOC, V2, P55

[4]

KOLMOGOROV AN, 1957, DOKL AKAD NAUK SSSR+, V114, P953

[5] KOLMOGOROV THEOREM AND MULTILAYER NEURAL NETWORKS [J].

KURKOVA, V .

NEURAL NETWORKS, 1992, 5 (03) :501-506

[6] ON STRUCTURE OF CONTINUOUS FUNCTIONS OF SEVERAL VARIABLES [J].

SPRECHER, DA .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1965, 115 (03) :340-&

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