Approximation error of single hidden layer neural networks with fixed weights

IF 0.7 4区计算机科学 Q4 COMPUTER SCIENCE, INFORMATION SYSTEMS

Information Processing Letters Pub Date : 2023-12-01 DOI:10.1016/j.ipl.2023.106467

Vugar E. Ismailov

引用次数: 0

Abstract

Neural networks with finitely many fixed weights have the universal approximation property under certain conditions on compact subsets of the d-dimensional Euclidean space, where approximation process is considered. Such conditions were delineated in our paper [26]. But for many compact sets it is impossible to approximate multivariate functions with arbitrary precision and the question on estimation or efficient computation of approximation error arises. This paper provides an explicit formula for the approximation error of single hidden layer neural networks with two fixed weights.

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固定权值的单隐层神经网络的逼近误差

有限多个固定权值的神经网络在一定条件下在d维欧氏空间的紧子集上具有普遍的逼近性质，其中考虑了逼近过程。我们的论文[26]描述了这些条件。但是对于许多紧集，不可能以任意精度逼近多元函数，因而产生了逼近误差估计或有效计算的问题。本文给出了两个固定权值的单隐层神经网络近似误差的显式公式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Information Processing Letters 工程技术-计算机：信息系统

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

7.3 months

期刊介绍： Information Processing Letters invites submission of original research articles that focus on fundamental aspects of information processing and computing. This naturally includes work in the broadly understood field of theoretical computer science; although papers in all areas of scientific inquiry will be given consideration, provided that they describe research contributions credibly motivated by applications to computing and involve rigorous methodology. High quality experimental papers that address topics of sufficiently broad interest may also be considered. Since its inception in 1971, Information Processing Letters has served as a forum for timely dissemination of short, concise and focused research contributions. Continuing with this tradition, and to expedite the reviewing process, manuscripts are generally limited in length to nine pages when they appear in print.