Optimizing time-shifts for reservoir computing using a rank-revealing QR algorithm

Reservoir computing, a recurrent neural network paradigm in which only the output layer is trained, has demonstrated remarkable performance on tasks such as prediction and control of nonlinear systems. Recently, it was demonstrated that adding time-shifts to the signals generated by a reservoir can provide large improvements in performance accuracy. In this work, we present a technique to choose the optimal time shifts. Our technique maximizes the rank of the reservoir matrix using a rank-revealing QR algorithm and is not task dependent. Further, our technique does not require a model of the system, and therefore is directly applicable to analog hardware reservoir computers. We demonstrate our time-shift optimization technique on two types of reservoir computer: one based on an opto-electronic oscillator and the traditional recurrent network with a $tanh$ activation function. We find that our technique provides improved accuracy over random time-shift selection in essentially all cases.