论径向基函数神经网络的普遍逼近特性

IF 1.2 4区计算机科学 Q4 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

Annals of Mathematics and Artificial Intelligence Pub Date : 2023-10-16 DOI:10.1007/s10472-023-09901-x

Aysu Ismayilova, Muhammad Ismayilov

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引用次数: 0

摘要

在本文中，我们考虑了一类新的 RBF（径向基函数）神经网络，其中平滑因子被移位所取代。我们证明，在激活函数的某些条件下，这些网络能够逼近 d 维欧几里得空间任何紧凑子集上的任何连续多元函数。对于具有有限多个固定中心的 RBF 网络，我们描述了保证以任意精度逼近的条件。

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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On the universal approximation property of radial basis function neural networks

In this paper we consider a new class of RBF (Radial Basis Function) neural networks, in which smoothing factors are replaced with shifts. We prove under certain conditions on the activation function that these networks are capable of approximating any continuous multivariate function on any compact subset of the d-dimensional Euclidean space. For RBF networks with finitely many fixed centroids we describe conditions guaranteeing approximation with arbitrary precision.

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来源期刊

Annals of Mathematics and Artificial Intelligence 工程技术-计算机：人工智能

CiteScore

3.00

自引率

8.30%

发文量

审稿时长

>12 weeks

期刊介绍： Annals of Mathematics and Artificial Intelligence presents a range of topics of concern to scholars applying quantitative, combinatorial, logical, algebraic and algorithmic methods to diverse areas of Artificial Intelligence, from decision support, automated deduction, and reasoning, to knowledge-based systems, machine learning, computer vision, robotics and planning. The journal features collections of papers appearing either in volumes (400 pages) or in separate issues (100-300 pages), which focus on one topic and have one or more guest editors. Annals of Mathematics and Artificial Intelligence hopes to influence the spawning of new areas of applied mathematics and strengthen the scientific underpinnings of Artificial Intelligence.