<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...

Compactness of Neural Networks

Published Online: Dec 21, 2022

Page range: 13 - 21

Accepted: Apr 30, 2022

DOI: https://doi.org/10.2478/forma-2022-0002

Keywords
neural network, compactness, Ascoli-Arzela’s theorem, equicontinuousness of continuous functions, equiboundedness of continuous functions

© 2022 Keiichi Miyajima et al., published by Sciendo

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

Compactness of Neural Networks

Published Online: Dec 21, 2022

Page range: 13 - 21

Accepted: Apr 30, 2022

DOI: https://doi.org/10.2478/forma-2022-0002

Keywordsneural network, compactness, Ascoli-Arzela’s theorem, equicontinuousness of continuous functions, equiboundedness of continuous functions

© 2022 Keiichi Miyajima et al., published by Sciendo

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

Keywords
neural network, compactness, Ascoli-Arzela’s theorem, equicontinuousness of continuous functions, equiboundedness of continuous functions