  Approximation capability of reservoir systems whose reservoir is a recurrent
neural network (RNN) is discussed. In our problem setting, a reservoir system
approximates a set of functions just by adjusting its linear readout while the
reservoir is fixed. We will show what we call uniform strong universality of a
family of RNN reservoir systems for a certain class of functions to be
approximated. This means that, for any positive number, we can construct a
sufficiently large RNN reservoir system whose approximation error for each
function in the class of functions to be approximated is bounded from above by
the positive number. Such RNN reservoir systems are constructed via parallel
concatenation of RNN reservoirs.
