Reservoir Computing with Generalized Readout based on Generalized Synchronization

Abstract: Reservoir computing is a machine learning framework that exploits nonlinear dynamics, exhibiting significant computational capabilities. One of the defining characteristics of reservoir computing is its low cost and straightforward training algorithm, i.e. only the readout, given by a linear combination of reservoir variables, is trained. Inspired by recent mathematical studies based on dynamical system theory, in particular generalized synchronization, we propose a novel reservoir computing framework with generalized readout, including a nonlinear combination of reservoir variables. The first crucial advantage of using the generalized readout is its mathematical basis for improving information processing capabilities. Secondly, it is still within a linear learning framework, which preserves the original strength of reservoir computing. In summary, the generalized readout is naturally derived from mathematical theory and allows the extraction of useful basis functions from reservoir dynamics without sacrificing simplicity. In a numerical study, we find that introducing the generalized readout leads to a significant improvement in accuracy and an unexpected enhancement in robustness for the short- and long-term prediction of Lorenz chaos, with a particular focus on how to harness low-dimensional reservoir dynamics. A novel way and its advantages for physical implementations of reservoir computing with generalized readout are briefly discussed.