Echo state networks are universal

06/03/2018

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by   Lyudmila Grigoryeva, et al.

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This paper shows that echo state networks are universal uniform approximants in the context of discrete-time fading memory filters with uniformly bounded inputs defined on negative infinite times. The proof uses newly introduced internal approximation results for filters associated to reservoir computing systems, as well as the external approximation properties of state affine systems proved in a previous work.