Fig. 4: Memory and prediction in the formose reservoir computer.

a, Schematic of the prediction procedure to forecast inputs using the reservoir. A time-varying input is fed into the reservoir and the reservoir response recorded. Weights are trained on the reservoir state and the input at a time interval δt into the future. These trained weights are then used to forecast as-yet unseen future inputs. b, Time traces, error plots and comparison plots for forecasts of simultaneously varying DHA, NaOH and formaldehyde inputs that resemble the behaviour of a Lorenz attractor. True inputs are shown as purple, orange and red lines, and the forecasts (δt = 120 s) as blue lines. The ASEs (see Methods) over time are shown below the predictions. c, A schematic showing how a time-dependent input propagates through the formose network, with different compounds responding in distinct ways. Only the DHA input is shown (left). The response over time of four ion signals is shown, as well as comparison plots between the DHA input and each output. Below every plot, the direct mutual information between DHA input and ion signal is shown (I(u; x)). d, A plot of the mutual information between ion signals x(t + δt) and the formaldehyde, NaOH and DHA input patterns u(t) as a function of the lag parameter δt. Four traces corresponding to the ion signals in c are indicated.