On the Interpretation and Characterization of Echo State Networks Dynamics: A Complex Systems Perspective

  • Filippo Maria Bianchi
  • Lorenzo Livi
  • Cesare AlippiEmail author
Part of the Studies in Computational Intelligence book series (SCI, volume 738)


In this chapter, we discuss recently developed methods for characterizing the dynamics of recurrent neural networks. Such methods rely on theory and concepts coming from the field of complex systems. We focus on a class of recurrent networks called echo state networks. First, we present a method to analyze and characterize the evolution of its internal state. This allows to provide a qualitative interpretation of the network dynamics. In addition, it allows to assess the stability of the system, a necessary requirement in many practical applications. Successively, we focus on the identification of the onset of criticality in such networks. We discuss an unsupervised method based on Fisher information, which can be used to tune the network hyperparameters. With respect to standard supervised techniques, we show that the proposed approach offers several advantages and is effective on a number of tasks.


Echo state networks Criticality Recurrence quantification analysis Fisher information matrix Unsupervised learning 


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© Springer International Publishing AG 2018

Authors and Affiliations

  • Filippo Maria Bianchi
    • 1
  • Lorenzo Livi
    • 2
    • 3
  • Cesare Alippi
    • 2
    • 3
    Email author
  1. 1.Machine Learning Group, Department of Physics and TechnologyUiT the Arctic University of NorwayTromsøNorway
  2. 2.Department of Electronics, Information, and BioengineeringPolitecnico di MilanoMilanItaly
  3. 3.Faculty of InformaticsUniversità della Svizzera ItalianaLuganoSwitzerland

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