Modeling deterministic echo state network with loop reservoir

Xiao Chuan Sun*, Hong Yan Cui, Ren Ping Liu, Jian Ya Chen, Yun Jie Liu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)


Echo state network (ESN), which efficiently models nonlinear dynamic systems, has been proposed as a special form of recurrent neural network. However, most of the proposed ESNs consist of complex reservoir structures, leading to excessive computational cost. Recently, minimum complexity ESNs were proposed and proved to exhibit high performance and low computational cost. In this paper, we propose a simple deterministic ESN with a loop reservoir, i.e., an ESN with an adjacentfeedback loop reservoir. The novel reservoir is constructed by introducing regular adjacent feedback based on the simplest loop reservoir. Only a single free parameter is tuned, which considerably simplifies the ESN construction. The combination of a simplified reservoir and fewer free parameters provides superior prediction performance. In the benchmark datasets and real-world tasks, our scheme obtains higher prediction accuracy with relatively low complexity, compared to the classic ESN and the minimum complexity ESN. Furthermore, we prove that all the linear ESNs with the simplest loop reservoir possess the same memory capacity, arbitrarily converging to the optimal value.

Original languageEnglish
Pages (from-to)689-701
Number of pages13
JournalJournal of Zhejiang University: Science C
Issue number9
Publication statusPublished - Sep 2012
Externally publishedYes


  • Echo state networks
  • Loop reservoir structure
  • Memory capacity


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