Reservoir computing is a machine learning method that is closely linked to dynamical
systems theory. This connection is highlighted in a brief introduction to the general concept …

Abstract Echo State Networks (ESNs) are a class of single-layer recurrent neural networks
that have enjoyed recent attention. In this paper we prove that a suitable ESN, trained on a …

We survey current developments in the approximation theory of sequence modelling in
machine learning. Particular emphasis is placed on classifying existing results for various …

This work studies approximation based on single-hidden-layer feedforward and recurrent
neural networks with randomly generated internal weights. These methods, in which only …

Echo state networks (ESNs) have been recently proved to be universal approximants for
input/output systems with respect to various L p-type criteria. When 1≤ p<∞, only p …

The universal approximation property of various machine learning models is currently only
understood on a case-by-case basis, limiting the rapid development of new theoretically …

Several problems in stochastic analysis are defined through their geometry, and preserving
that geometric structure is essential to generating meaningful predictions. Nevertheless, how …

A new explanation of the geometric nature of the reservoir computing (RC) phenomenon is
presented. RC is understood in the literature as the possibility of approximating input–output …

Reservoir computing approximation and generalization bounds are proved for a new
concept class of input/output systems that extends the so-called generalized Barron …

Most existing results in the analysis of quantum reservoir computing (QRC) systems with
classical inputs have been obtained using the density matrix formalism. This paper shows …