On the attractor in a high-dimensional neural network dynamics of reservoir computing: Lyapunov analysis viewpoint

Abstract

Recent theoretical developments of reservoir computing have clarified a sufficient condition about which reservoir computing can capture the dynamics of a target system, enabling the reconstruction of dynamical invariants. Even when the condition is relaxed, the reservoir computing is found to succeed in reconstructing time series. In this study, we investigate numerically the dynamical structures underlying the embedding structure by comparing the Lyapunov spectrum of a high-dimensional neural network in a reservoir computing model with that of the actual system. We also compute Lyapunov exponents restricted to the tangent space of the inertial manifold in a high-dimensional neural network. Our results provide numerical evidence that reservoir computing can accurately identify the Lyapunov spectrum of the target system, including all negative exponents.