Strange Properties of Linear Reservoirs in the Infinitely Large Limit for Prediction of Continuous-Time Signals

Large linear reservoirs, while not necessarily of practical utility, might provide insight to large nonlinear reservoirs. Our study of large linear reservoirs in the context of improving predictive capabilities suggests that: one desires to be near the edge of instability; and random matrix theory guarantees that the performance of large linear random matrices is only dependent on how weights in the weight matrix are chosen and not the individual weights. It also seems as though dynamic and static weights are quite different in performance. We comment on how these lessons may or may not apply to the large nonlinear reservoirs that are typically used for prediction applications.