Quantifying Robustness and Capacity of Reservoir Computers with Consistency Profiles
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We study the consistency property in reservoir computers with noise. Consistency quantifies the functional dependence of a driven dynamical system on its input via replica tests. We characterise the high-dimensional profile of consistency in typical reservoirs subject to intrinsic and measurement noise. An integral of the consistency is introduced to measure capacity and act as an effective size of the reservoir. We observe a scaling law in the dependency of the consistency capacity on the noise amplitude and reservoir size, and demonstrate how this measure of capacity explains performance.