Discrete-Time Signatures and Randomness in Reservoir Computing

Cuchiero, Christa; Gonon, Lukas; Grigoryeva, Lyudmila; Ortega, Juan-Pablo; Teichmann, Josef

Discrete-Time Signatures and Randomness in Reservoir Computing

Dateien

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Datum

2021

Autor:innen

Cuchiero, Christa

Gonon, Lukas

Grigoryeva, Lyudmila

Ortega, Juan-Pablo

Teichmann, Josef

Open Access-Veröffentlichung

Open Access Hybrid

Sammlungen

Mathematik und Statistik

Publikationstyp

Zeitschriftenartikel

Publikationsstatus

Published

Erschienen in

IEEE Transactions on Neural Networks and Learning Systems. IEEE. eISSN 2162-237X. Available under: doi: 10.1109/TNNLS.2021.3076777

Zusammenfassung

A new explanation of the geometric nature of the reservoir computing (RC) phenomenon is presented. RC is understood in the literature as the possibility of approximating input-output systems with randomly chosen recurrent neural systems and a trained linear readout layer. Light is shed on this phenomenon by constructing what is called strongly universal reservoir systems as random projections of a family of state-space systems that generate Volterra series expansions. This procedure yields a state-affine reservoir system with randomly generated coefficients in a dimension that is logarithmically reduced with respect to the original system. This reservoir system is able to approximate any element in the fading memory filters class just by training a different linear readout for each different filter. Explicit expressions for the probability distributions needed in the generation of the projected reservoir system are stated, and bounds for the committed approximation error are provided.

Fachgebiet (DDC)

510 Mathematik

Zitieren

ISO 690

CUCHIERO, Christa, Lukas GONON, Lyudmila GRIGORYEVA, Juan-Pablo ORTEGA, Josef TEICHMANN, 2021. Discrete-Time Signatures and Randomness in Reservoir Computing. In: IEEE Transactions on Neural Networks and Learning Systems. IEEE. eISSN 2162-237X. Available under: doi: 10.1109/TNNLS.2021.3076777

BibTex

@article{Cuchiero2021-05-26Discr-55523,
  year={2021},
  doi={10.1109/TNNLS.2021.3076777},
  title={Discrete-Time Signatures and Randomness in Reservoir Computing},
  journal={IEEE Transactions on Neural Networks and Learning Systems},
  author={Cuchiero, Christa and Gonon, Lukas and Grigoryeva, Lyudmila and Ortega, Juan-Pablo and Teichmann, Josef}
}

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