Measure Theoretic Results for Approximation by Neural Networks with Limited Weights

被引：7

作者：

Ismailov, Vugar E. ^{[1
]}

Savas, Ekrem ^{[2
]}

机构：

[1] NAS Azerbaijan, Inst Math & Mech, 9 B Vahabzadeh Str, AZ-1141 Baku, Azerbaijan

[2] Istanbul Ticaret Univ, Dept Math, Istanbul, Turkey

来源：

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION | 2017年 / 38卷 / 07期

关键词：

Activation function; Borel measure; density; lightning bolt; neural network; orthogonal measure; orbit; weak convergence; 41A30; 41A63; 92B20; 28A33; 46E27; RIDGE FUNCTIONS; RECONSTRUCTION; REPRESENTATION; SUM;

D O I：

10.1080/01630563.2016.1254654

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we study approximation properties of single hidden layer neural networks with weights varying in finitely many directions and with thresholds from an open interval. We obtain a necessary and simultaneously sucient measure theoretic condition for density of such networks in the space of continuous functions. Further, we prove a density result for neural networks with a specifically constructed activation function and a fixed number of neurons.

引用

页码：819 / 830

页数：12

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