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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


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Udzielam licencji. Uznanie autorstwa - Użycie niekomercyjne 4.0 Międzynarodowa Except where otherwise noted, this item's license is described as Udzielam licencji. Uznanie autorstwa - Użycie niekomercyjne 4.0 Międzynarodowa