Under contraction conditions, an ESN trained on one-dimensional observations of an invertible dynamical system induces a C1 embedding with positive probability, and a linear readout makes the autonomous ESN topologically conjugate to the original system.
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Embedding and Approximation Theorems for Echo State Networks
Under contraction conditions, an ESN trained on one-dimensional observations of an invertible dynamical system induces a C1 embedding with positive probability, and a linear readout makes the autonomous ESN topologically conjugate to the original system.