Universality of reservoir systems with recurrent neural networks

Approximation capability of reservoir systems whose reservoir is a recurrent neural network (RNN) is discussed. We show what we call uniform strong universality of RNN reservoir systems for a certain class of dynamical systems. This means that, given an approximation error to be achieved, one can construct an RNN reservoir system that approximates each target dynamical system in the class just via adjusting its linear readout. To show the universality, we construct an RNN reservoir system via parallel concatenation that has an upper bound of approximation error independent of each target in the class.