Analysis of reservoir computing focusing on the spectrum of bistable delayed dynamical systems

Reservoir computing (RC) is a machine-learning paradigm that is capable to process empirical time series data. This paradigm is based on a neural network with a fixed hidden layer having a high-dimensional state space, called a reservoir. Reservoirs including time delays are considered to be good candidates for practical applications because they make hardware realization of the high-dimensional reservoirs simple. Performance of the well-trained RCs depends both on dynamical properties of attractors of the reservoirs and tasks they solve. Therefore, in the conventional monostable RCs, there arise task-wise optimization problems of the reservoirs, which have been solved based on trial and error approaches. In this study, we analyzed the relationship between the dynamical properties of the time-delay reservoir and the performance in terms of the spectra of the delayed dynamical systems, which might facilitate the development of the unified systematic optimization techniques for the time-delay reservoirs. In addition, we propose a novel RC framework that performs well on distinct tasks without the task-wise optimization using bistable reservoir dynamics, which can reduce complicated hardware management of the reservoirs.