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.

翻译：讨论了储备池为循环神经网络（RNN）的储备池系统的逼近能力。在我们的问题设定中，储备池系统仅通过调整其线性读出层来逼近一组函数，而储备池本身保持固定。我们将证明一类RNN储备池系统对于特定待逼近函数族具有所谓的统一强普适性。这意味着：对于任意正数，我们可以构造一个足够大的RNN储备池系统，使其对于待逼近函数族中每个函数的逼近误差均被该正数所界定。此类RNN储备池系统通过RNN储备池的并行级联方式构建。