Dynamical properties of a perceptron learning process : structural stability under numerics and shadowing

doi:10.1007/s00332-011-9094-1

Dynamical properties of a perceptron learning process : structural stability under numerics and shadowing

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Dynamical properties of a perceptron learning process : structural stability under numerics and shadowing

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dc.contributor.author	Bielecki, Andrzej [SAP11014736]	pl
dc.contributor.author	Ombach, Jerzy [SAP11008726]	pl
dc.date.accessioned	2019-05-16T08:31:48Z
dc.date.available	2019-05-16T08:31:48Z
dc.date.issued	2011	pl
dc.identifier.issn	0938-8974	pl
dc.identifier.uri	https://ruj.uj.edu.pl/xmlui/handle/item/74829
dc.language	eng	pl
dc.rights	Udzielam licencji. Uznanie autorstwa - Użycie niekomercyjne 4.0 Międzynarodowa	*
dc.rights.uri	http://creativecommons.org/licenses/by-nc/4.0/pl/legalcode	*
dc.title	Dynamical properties of a perceptron learning process : structural stability under numerics and shadowing	pl
dc.type	JournalArticle	pl
dc.abstract.en	In this paper two aspects of numerical dynamics are used for an artificial neural network (ANN) analysis. It is shown that topological conjugacy of gradient dynamical systems and both the shadowing and inverse shadowing properties have nontrivial implications in the analysis of a perceptron learning process. The main result is that, generically, any such process is stable under numerics and robust. Implementation aspects are discussed as well. The analysis is based on the theorem concerning global topological conjugacy of cascades generated by a gradient flow on a compact manifold without a boundary.	pl
dc.subject.en	dynamical system	pl
dc.subject.en	topological conjugacy	pl
dc.subject.en	shadowing	pl
dc.subject.en	inverse shadowing	pl
dc.subject.en	robustness	pl
dc.subject.en	perceptron learning process	pl
dc.subject.en	gradient differential equation	pl
dc.subject.en	Runge-Kutta methods	pl
dc.identifier.doi	10.1007/s00332-011-9094-1	pl
dc.identifier.eissn	1432-1467	pl
dc.title.journal	Journal of Nonlinear Science	pl
dc.language.container	eng	pl
dc.affiliation	Wydział Matematyki i Informatyki : Instytut Matematyki	pl
dc.subtype	Article	pl
dc.identifier.articleid	21:579
dc.rights.original	CC-BY-NC; inne; ostateczna wersja wydawcy; w momencie opublikowania; 0	pl
dc.identifier.project	ROD UJ / OP	pl
.pointsMNiSW	[2011 A]: 40