Asymptotic evaluation of the information processing capacity in reservoir computing
This work addresses a theoretical limitation in performance evaluation for reservoir computing, but it is incremental as it builds on existing IPC metrics.
The paper tackles the problem of evaluating the information processing capacity (IPC) in reservoir computing for infinitely long data by developing an asymptotic expansion method and validating it with numerical simulations.
The squared error normalized by the target output is known as the information processing capacity (IPC) and is used to evaluate the performance of reservoir computing (RC). 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. To evaluate the IPC for infinitely long data using the IPC for finite-length data, we use an asymptotic expansion of the IPC and the least-squares method. Then, we show the validity of our method by numerical simulations.