Efficient Cross-Validation of Echo State Networks

  • Mantas LukoševičiusEmail author
  • Arnas Uselis
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11731)


Echo State Networks (ESNs) are known for their fast and precise one-shot learning of time series. But they often need good hyper-parameter tuning for best performance. For this good validation is key, but usually, a single validation split is used. In this rather practical contribution we suggest several schemes for cross-validating ESNs and introduce an efficient algorithm for implementing them. The component that dominates the time complexity of the already quite fast ESN training remains constant (does not scale up with k) in our proposed method of doing k-fold cross-validation. The component that does scale linearly with k starts dominating only in some not very common situations. Thus in many situations k-fold cross-validation of ESNs can be done for virtually the same time complexity as a simple single split validation. Space complexity can also remain the same. We also discuss when the proposed validation schemes for ESNs could be beneficial and empirically investigate them on several different real-world datasets.


Echo State Networks Reservoir computing Recurrent neural networks Cross-validation Time complexity 



This research was supported by the Research, Development and Innovation Fund of Kaunas University of Technology (grant No. PP-91K/19).


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Kaunas University of TechnologyKaunasLithuania

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