<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>In this article, Feed-forward Neural Network is formalized in the Mizar system [1], [2]. First, the multilayer perceptron [6], [7], [8] is formalized using functional sequences. Next, we show that a set of functions generated by these neural networks satisfies equicontinuousness and equiboundedness property [10], [5]. At last, we formalized the compactness of the function set of these neural networks by using the Ascoli-Arzela’s theorem according to [4] and [3].</p>
</abstract>

In this article, Feed-forward Neural Network is formalized in the Mizar system [1], [2]. First, the multilayer perceptron [6], [7], [8] is formalized using functional sequences. Next, we show that a set of functions generated by these neural networks satisfies equicontinuousness and equiboundedness property [10], [5]. At last, we formalized the compactness of the function set of these neural networks by using the Ascoli-Arzela’s theorem according to [4] and [3].

Compactness of Neural Networks

Formalized Mathematics

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.

{"article-title":"Compactness of Neural Networks"}

In this article, Feed-forward Neural Network is formalized in the Mizar system [1], [2]. First, the multilayer perceptron [6], [7], [8] is formalized using...

神经网络的紧性

在线发布:2022年12月21日

页面范围： 13 - 21

认可的:2022年4月30日

内政部： https://doi.org/10.2478/forma-2022-0002

关键词
神经网络,密实度,Ascoli-Arzela定理,连续函数的等连续性,连续函数的等有界性

©2022 Keiichi Miyajima等人，Sciendo出版

本作品根据Creative Commons Attribution-ShareAlike 4.0 International License获得许可。