Asymptotic evaluation of the information processing capacity in reservoir computing

Reservoir computing (RC) is becoming increasingly important because of its short training time. The squared error normalized by the target output is called the information processing capacity (IPC) and is used to evaluate the performance of an RC system. Since RC aims to learn the relationship between input and output time series, we should evaluate the IPC for infinitely long data rather than the IPC for finite-length data. However, a method for estimating it has not been established. We evaluated the IPC for infinitely long data using the asymptotic expansion of the IPC and weighted least-squares fitting. Then, we showed the validity of our method by numerical simulations. This work makes the performance evaluation of RC more evident.