Quantifying Robustness and Capacity of Reservoir Computers with Consistency Profiles

Abstract

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 highdimensional 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.

Reservoir computing with swarms

“…Theoretically, any heterogeneity introduced to the equations of motion will remove the limit on consistency capacity. However, this is only a necessary but not sufficient criterion for performance 25 , meaning that the introduction of heterogeneity may affect other properties of the reservoir in an unfavourable way simultaneously to the increase of capacity.…”

“…The consistency profiles can be used to derive a special capacity measure which counts the linearly independent functions in presence of noise or chaos. This measure can be thought of as the effective size of such a reservoir and is predictive of performance 25 .…”