Separation capacity of linear reservoirs with random connectivity matrix

Excerpt

arXiv:2404.17429v4 Announce Type: replace-cross Abstract: A natural hypothesis for the success of reservoir computing in generic tasks is the ability of the untrained reservoir to map distinct input time series to separable reservoir states, a property we term separation capacity. In this work, we develop a rigorous mathematical framework for analysing the separation capacity of random linear reservoirs. We show that the expected separation induced by a random reservoir is completely characteris