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Fractional stochastic search algorithms: modelling complex systems via AI

  • The aim of this article is to establish a stochastic search algorithm for neural networks based on the fractional stochastic processes {๐ต๐ป๐‘ก,๐‘กโ‰ฅ0} with the Hurst parameter ๐ปโˆˆ(0,1). We define and discuss the properties of fractional stochastic processes, {๐ต๐ป๐‘ก,๐‘กโ‰ฅ0}, which generalize a standard Brownian motion. Fractional stochastic processes capture useful yet different properties in order to simulate real-world phenomena. This approach provides new insights to stochastic gradient descent (SGD) algorithms in machine learning. We exhibit convergence properties for fractional stochastic processes.

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Metadaten
Author of HS ReutlingenHerzog, Bodo
URN:urn:nbn:de:bsz:rt2-opus4-46131
DOI:https://doi.org/10.3390/math11092061
Erschienen in:Mathematics
Publisher:MDPI
Place of publication:Basel
Document Type:Journal article
Language:English
Publication year:2023
Volume:11
Issue:9
Page Number:11
First Page:1
Last Page:11
Article Number:2061
DDC classes:510 Mathematik
Open access?:Ja
Licence (German):License Logoย ย Creative Commons - CC BY - Namensnennung 4.0 International