Memory and forecasting capacities of nonlinear recurrent networks

Gonon, Lukas; Grigoryeva, Lyudmila; Ortega, Juan-Pablo

Memory and forecasting capacities of nonlinear recurrent networks

Dateien

Gonon_2-1341f261k0x0z6.pdfGröße: 736.62 KBDownloads: 117

Datum

2020

Autor:innen

Gonon, Lukas

Grigoryeva, Lyudmila

Ortega, Juan-Pablo

Open Access-Veröffentlichung

Open Access Hybrid

Sammlungen

Mathematik und Statistik

Publikationstyp

Zeitschriftenartikel

Publikationsstatus

Published

Erschienen in

Physica D: Nonlinear Phenomena. Elsevier. 2020, 414, 132721. ISSN 0167-2789. eISSN 1872-8022. Available under: doi: 10.1016/j.physd.2020.132721

Zusammenfassung

The notion of memory capacity, originally introduced for echo state and linear networks with independent inputs, is generalized to nonlinear recurrent networks with stationary but dependent inputs. The presence of dependence in the inputs makes natural the introduction of the network forecasting capacity, that measures the possibility of forecasting time series values using network states. Generic bounds for memory and forecasting capacities are formulated in terms of the number of neurons of the nonlinear recurrent network and the autocovariance function or the spectral density of the input. These bounds generalize well-known estimates in the literature to a dependent inputs setup. Finally, for the particular case of linear recurrent networks with independent inputs it is proved that the memory capacity is given by the rank of the associated controllability matrix, a fact that has been for a long time assumed to be true without proof by the community.

Fachgebiet (DDC)

510 Mathematik

Schlagwörter

Memory capacity, Forecasting capacity, Recurrent neural network, Reservoir computing, Echo state network (ESN), Machine learning

Zitieren

ISO 690

GONON, Lukas, Lyudmila GRIGORYEVA, Juan-Pablo ORTEGA, 2020. Memory and forecasting capacities of nonlinear recurrent networks. In: Physica D: Nonlinear Phenomena. Elsevier. 2020, 414, 132721. ISSN 0167-2789. eISSN 1872-8022. Available under: doi: 10.1016/j.physd.2020.132721

BibTex

@article{Gonon2020Memor-55524,
  year={2020},
  doi={10.1016/j.physd.2020.132721},
  title={Memory and forecasting capacities of nonlinear recurrent networks},
  volume={414},
  issn={0167-2789},
  journal={Physica D: Nonlinear Phenomena},
  author={Gonon, Lukas and Grigoryeva, Lyudmila and Ortega, Juan-Pablo},
  note={Article Number: 132721}
}

RDF

<rdf:RDF
    xmlns:dcterms="http://purl.org/dc/terms/"
    xmlns:dc="http://purl.org/dc/elements/1.1/"
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:bibo="http://purl.org/ontology/bibo/"
    xmlns:dspace="http://digital-repositories.org/ontologies/dspace/0.1.0#"
    xmlns:foaf="http://xmlns.com/foaf/0.1/"
    xmlns:void="http://rdfs.org/ns/void#"
    xmlns:xsd="http://www.w3.org/2001/XMLSchema#" > 
  <rdf:Description rdf:about="https://kops.uni-konstanz.de/server/rdf/resource/123456789/55524">
    <bibo:uri rdf:resource="https://kops.uni-konstanz.de/handle/123456789/55524"/>
    <dcterms:issued>2020</dcterms:issued>
    <dc:language>eng</dc:language>
    <dc:contributor>Gonon, Lukas</dc:contributor>
    <dcterms:hasPart rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/55524/1/Gonon_2-1341f261k0x0z6.pdf"/>
    <dcterms:abstract xml:lang="eng">The notion of memory capacity, originally introduced for echo state and linear networks with independent inputs, is generalized to nonlinear recurrent networks with stationary but dependent inputs. The presence of dependence in the inputs makes natural the introduction of the network forecasting capacity, that measures the possibility of forecasting time series values using network states. Generic bounds for memory and forecasting capacities are formulated in terms of the number of neurons of the nonlinear recurrent network and the autocovariance function or the spectral density of the input. These bounds generalize well-known estimates in the literature to a dependent inputs setup. Finally, for the particular case of linear recurrent networks with independent inputs it is proved that the memory capacity is given by the rank of the associated controllability matrix, a fact that has been for a long time assumed to be true without proof by the community.</dcterms:abstract>
    <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2021-11-12T10:15:08Z</dcterms:available>
    <dcterms:title>Memory and forecasting capacities of nonlinear recurrent networks</dcterms:title>
    <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/>
    <dc:rights>Attribution 4.0 International</dc:rights>
    <dc:creator>Grigoryeva, Lyudmila</dc:creator>
    <dc:creator>Ortega, Juan-Pablo</dc:creator>
    <dc:creator>Gonon, Lukas</dc:creator>
    <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2021-11-12T10:15:08Z</dc:date>
    <foaf:homepage rdf:resource="http://localhost:8080/"/>
    <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <dc:contributor>Ortega, Juan-Pablo</dc:contributor>
    <dc:contributor>Grigoryeva, Lyudmila</dc:contributor>
    <dcterms:rights rdf:resource="http://creativecommons.org/licenses/by/4.0/"/>
    <dspace:hasBitstream rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/55524/1/Gonon_2-1341f261k0x0z6.pdf"/>
    <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
  </rdf:Description>
</rdf:RDF>

Universitätsbibliographie

Ja

Begutachtet

Unbekannt