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

Reservoir computing is a recurrent neural network paradigm in which only the output layer is trained. 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.