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Fading memory echo state networks are universal.

Lukas Gonon1, Juan-Pablo Ortega2

  • 1Ludwig-Maximilians-Universität München, Mathematics Institute, Theresienstrasse 39, D-80333 Munich, Germany.

Neural Networks : the Official Journal of the International Neural Network Society
|February 21, 2021
PubMed
Summary
This summary is machine-generated.

Echo state networks (ESNs) are universal approximants for input/output systems. This study constructs a universal family of ESNs with echo state and fading memory properties, even for uniformly bounded inputs.

Keywords:
Echo state networkEcho state propertyFading memory propertyMachine learningReservoir computingUniversality

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Area of Science:

  • Machine Learning
  • Dynamical Systems

Background:

  • Echo state networks (ESNs) are a type of recurrent neural network known for their efficiency in modeling complex dynamical systems.
  • Previous research established ESNs as universal approximants for input/output systems under certain L^p criteria.

Purpose of the Study:

  • To investigate the properties of universal families of Echo State Networks (ESNs) under the specific condition of uniformly bounded inputs (p=∞).
  • To demonstrate the existence of a universal family of ESNs that inherently possess both the echo state and fading memory properties in this scenario.

Main Methods:

  • The study focuses on the theoretical analysis of Echo State Networks (ESNs).
  • It examines the conditions for universal approximation, specifically addressing the L^p criteria for p=∞.
  • The core method involves constructing a specific family of ESNs and proving their properties.

Main Results:

  • A universal family of ESNs can be constructed for input/output systems with uniformly bounded inputs (p=∞).
  • All elements within this constructed universal family exhibit both the echo state property and the fading memory property.
  • This result extends previous findings by ensuring these crucial properties within the universal family.

Conclusions:

  • The findings confirm that universal Echo State Networks (ESNs) can be designed to possess essential dynamic properties like echo state and fading memory, even under uniform input boundedness.
  • This work provides a theoretical foundation for utilizing ESNs in applications requiring guaranteed stability and memory characteristics.
  • The presented construction offers a novel approach not previously achievable with existing literature methods.