Investigation on Dynamics of Echo State Networks

Dynamics is a key issue about understanding recurrent neural networks(RNNs).Because of the complexity,the problem still remains unanswered in spite of many important progresses.Echo state network(ESN)is a simple approach to design RNNs.It is possible to investigate ESNs’dynamics deeply.However,most of dynamic studies have mainly concentrated on the shallow ESNs and seldom of them explain the dynamics of the deep ones.Therefore,this paper investigates the dynamics of four typical ESNs under a unified theoretical framework.These ESNs contain both the shallow versions and the deep ones.This investigation is helpful to clarify the dynamics of ESNs in a general sense.Also,the short-term memory(STM)of different ESNs is analyzed,which is closely related to the dynamics.This analysis is helpful to determine the hyper-parameters of ESNs for given problems.In addition,the problem-solving abilities of ESNs are investigated through modeling two time series tasks.It further explains the influence of the dynamics on ESN’s performance.