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This paper extends the notion of information processing capacity for non-independent input signals in the context of reservoir computing (RC). The presence of input autocorrelation makes worthwhile the treatment of forecasting and filtering problems for which we explicitly compute this generalized capacity as a function of the reservoir parameter values using a streamlined model. The reservoir model leading to these developments is used to show that, whenever that approximation is valid, this computational paradigm satisfies the so called separation and fading memory properties that are usually associated with good information processing performances. We show that several standard memory, forecasting, and filtering problems that appear in the parametric stochastic time series context can be readily formulated and tackled via RC which, as we show, significantly outperforms standard techniques in some instances.

The aim of this presentation is to show how various ideas coming from the nonlinear stability theory of functional differential systems, stochastic modeling, and machine learning, can be put together in order to create an approximating model that explains the working mechanisms behind a certain type of reservoir computers. Reservoir computing is a recently introduced brain-inspired machine learning paradigm capable of excellent performances in the processing of empirical data. We focus on time-delay based reservoir computers that have been physically implemented using optical and electronic systems and have shown unprecedented data processing rates. Reservoir computing is well-known for the ease of the associated training scheme but also for the problematic sensitivity of its performance to architecture parameters. The reservoir design problem is addressed, which remains the biggest challenge in the applicability of this information processing scheme. Our results use the information available regarding the optimal reservoir working regimes in order to construct a functional link between the reservoir parameters and its performance. This function is used to explore various properties of the device and to choose the optimal reservoir architecture, thus replacing the tedious and time consuming parameter scannings used so far in the literature.