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Echo state networks are universal.

Lyudmila Grigoryeva1, Juan-Pablo Ortega2

  • 1Department of Mathematics and Statistics, Universität Konstanz, Box 146, D-78457 Konstanz, Germany.

Neural Networks : the Official Journal of the International Neural Network Society
|October 15, 2018
PubMed
Summary
This summary is machine-generated.

Echo state networks are proven to be universal approximants for discrete-time fading memory systems. This demonstrates that complex fading memory systems can be modeled using simple neural network structures.

Keywords:
Echo state networks (ESN)Fading memory filtersMachine learningReservoir computing (RC)Uniform system approximationUniversality

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Area of Science:

  • Computational neuroscience
  • Machine learning theory

Background:

  • Fading memory filters are crucial for modeling systems with time-dependent behavior.
  • Echo state networks (ESNs) are a type of recurrent neural network known for their efficiency.

Purpose of the Study:

  • To establish echo state networks as universal uniform approximants for discrete-time fading memory filters.
  • To provide a theoretical guarantee for approximating fading memory systems with ESNs.

Main Methods:

  • Utilizing fundamental results on the topological nature of fading memory.
  • Analyzing reservoir computing systems generated by continuous reservoir maps.

Main Results:

  • Echo state networks are demonstrated to be universal uniform approximants.
  • Any discrete-time fading memory system can be realized by a finite-dimensional ESN with a linear readout map.
  • This approximation holds for infinite time intervals.

Conclusions:

  • ESNs offer a powerful and theoretically grounded framework for modeling discrete-time fading memory systems.
  • The findings bridge the gap between theoretical system properties and practical neural network implementations.