🤖 AI Summary
Existing methods for estimating the information processing capacity (IPC) of reservoir computing (RC) systems lack theoretical rigor and suffer from systematic bias when applied to infinitely long time series, as they rely exclusively on finite-length data.
Method: This paper proposes a novel IPC estimation algorithm based on asymptotic expansion and least-squares estimation. It establishes, for the first time, a rigorous asymptotic expansion framework for IPC in the infinite-time limit, integrating stochastic dynamical systems modeling, asymptotic analysis, and least-squares regression to analytically characterize and efficiently estimate the leading-order term of IPC.
Results: Numerical experiments demonstrate consistently high accuracy and strong generalizability across diverse RC architectures—including echo state networks (ESNs) and liquid state machines (LSMs)—thereby significantly enhancing the reliability and theoretical soundness of long-term performance evaluation.
📝 Abstract
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.