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Fading memory echo state networks are universal

22 October 2020
Lukas Gonon
Juan-Pablo Ortega
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Abstract

Echo state networks (ESNs) have been recently proved to be universal approximants for input/output systems with respect to various LpL ^pLp-type criteria. When 1≤p<∞1\leq p< \infty1≤p<∞, only ppp-integrability hypotheses need to be imposed, while in the case p=∞p=\inftyp=∞ a uniform boundedness hypotheses on the inputs is required. This note shows that, in the last case, a universal family of ESNs can be constructed that contains exclusively elements that have the echo state and the fading memory properties. This conclusion could not be drawn with the results and methods available so far in the literature.

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