arXiv Machine Learning By Youness Boutaib

Separation capacity of linear reservoirs with random connectivity matrix

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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.

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arXiv Machine Learning
Sep 17

On Dominant Manifolds in Reservoir Computing Networks

The paper investigates how training shapes the geometry of recurrent network dynamics in Reservoir Computing (RC) networks used for temporal forecasting. It demonstrates that, in a linear continuous-time reservoir with infinite data, training data create an invariant subspace whose dimension matches the number of dominant modes. For a simplified diagonal linear reservoir, the study connects dominant eigenvalues and eigenvectors to the spectrum of a backward Dynamic Mode Decomposition matrix, providing a finite-dimensional approximation of the backward-time Koopman operator, and illustrates these phenomena through simulation while suggesting extensions to nonlinear RC.

By Noa Kaplan, Alberto Padoan, Anastasia Bizyaeva