Compactness of Neural Networks

Pole DC	Wartość	Język
dc.contributor.author	Miyajima, Keiichi	-
dc.contributor.author	Yamazaki, Hiroshi	-
dc.date.accessioned	2022-12-29T09:36:16Z	-
dc.date.available	2022-12-29T09:36:16Z	-
dc.date.issued	2022	-
dc.identifier.citation	Formalized Mathematics, Volume 30, Issue 1, Pages 13-21	pl
dc.identifier.issn	1426-2630	-
dc.identifier.uri	http://hdl.handle.net/11320/14243	-
dc.description.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].	pl
dc.language.iso	en	pl
dc.publisher	DeGruyter Open	pl
dc.rights	Attribution-ShareAlike 3.0 Unported (CC BY-SA 3.0)	pl
dc.rights.uri	https://creativecommons.org/licenses/by-sa/3.0/	pl
dc.subject	neural network	pl
dc.subject	compactness	pl
dc.subject	Ascoli-Arzela’s theorem	pl
dc.subject	equicontinuousness of continuous functions	pl
dc.subject	equiboundedness of continuous functions	pl
dc.title	Compactness of Neural Networks	pl
dc.type	Article	pl
dc.rights.holder	© 2022 The Author(s)	pl
dc.rights.holder	CC BY-SA 3.0 license	pl
dc.identifier.doi	10.2478/forma-2022-0002	-
dc.description.Affiliation	Keiichi Miyajima - Ibaraki University, Faculty of Engineering, Hitachi, Ibaraki, Japan	pl
dc.description.Affiliation	Hiroshi Yamazaki - Nagano Prefectural Institute of Technology, Nagano, Japan	pl
dc.description.references	Grzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, Karol Pąk, and Josef Urban. Mizar: State-of-the-art and beyond. In Manfred Kerber, Jacques Carette, Cezary Kaliszyk, Florian Rabe, and Volker Sorge, editors, Intelligent Computer Mathematics, volume 9150 of Lecture Notes in Computer Science, pages 261–279. Springer International Publishing, 2015. ISBN 978-3-319-20614-1. doi:10.1007/978-3-319-20615-817.	pl
dc.description.references	Grzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, and Karol Pąk. The role of the Mizar Mathematical Library for interactive proof development in Mizar. Journal of Automated Reasoning, 61(1):9–32, 2018. doi:10.1007/s10817-017-9440-6.	pl
dc.description.references	Serge Lang. Real and Functional Analysis (Texts in Mathematics). Springer-Verlag, 1993.	pl
dc.description.references	Kazuo Matsuzaka. Sets and Topology (Introduction to Mathematics). IwanamiShoten, 2000.	pl
dc.description.references	Michael Read and Barry Simon. Functional Analysis (Methods of Modern Mathematical Physics). Academic Press, 1980.	pl
dc.description.references	Frank Rosenblatt. The Perceptron: A Probabilistic Model for Information Storage and Organization in the Brain. Psychological Review, 1958.	pl
dc.description.references	David Everett Rumelhart, Geoffrey Everes Hinton, and Ronald J. Williams. Learning representations by backpropagating errors. Nature, 1986.	pl
dc.description.references	Jürgen Schmidhuber. Deep Learning in Neural Networks: An Overview. Neural Networks, 2015.	pl
dc.description.references	Hiroshi Yamazaki, Keiichi Miyajima, and Yasunari Shidama. Ascoli-Arzelà theorem. Formalized Mathematics, 29(2):87–94, 2021. doi:10.2478/forma-2021-0009.	pl
dc.description.references	Kosaku Yosida. Functional Analysis. Springer, 1980.	pl
dc.identifier.eissn	1898-9934	-
dc.description.volume	30	pl
dc.description.issue	1	pl
dc.description.firstpage	13	pl
dc.description.lastpage	21	pl
dc.identifier.citation2	Formalized Mathematics	pl
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