Complexities of feature-based learning systems, with application to reservoir computing

This paper studies complexity measures of reservoir systems. For this purpose, a more general model that we call a feature-based learning system, which is the composition of a feature map and of a final estimator, is studied. We study complexity measures such as growth function, VC-dimension, pseudo-dimension and Rademacher complexity. On the basis of the results, we discuss how the unadjustability of reservoirs and the linearity of readouts can affect complexity measures of the reservoir systems. Furthermore, some of the results generalize or improve the existing results.