title: Homeostatic plasticity for single node delay-coupled reservoir computing.
abstract: Supplementing a differential equation with delays results in an infinite-dimensional dynamical system. This property provides the basis for a reservoir computing architecture, where the recurrent neural network is replaced by a single nonlinear node, delay-coupled to itself. Instead of the spatial topology of a network, subunits in the delay-coupled reservoir are multiplexed in time along one delay span of the system. The computational power of the reservoir is contingent on this temporal multiplexing. Here, we learn optimal temporal multiplexing by means of a biologically inspired homeostatic plasticity mechanism. Plasticity acts locally and changes the distances between the subunits along the delay, depending on how responsive these subunits are to the input. After analytically deriving the learning mechanism, we illustrate its role in improving the reservoir's computational power. To this end, we investigate, first, the increase of the reservoir's memory capacity. Second, we predict a NARMA-10 time series, showing that plasticity reduces the normalized root-mean-square error by more than 20%. Third, we discuss plasticity's influence on the reservoir's input-information capacity, the coupling strength between subunits, and the distribution of the readout coefficients.
authors.affiliation: Neuroinformatics Department, Institute of Cognitive Science, University of Osnabrück, 49069 Osnabrück, Germany, and Department of Theoretical Neuroscience, Central Institute of Mental Health, Medical Faculty Mannheim of Heidelberg University, 68159 Mannheim, Germany hazem.toutounji@zi-mannheim.de.
authors.forename: Hazem
authors.initials: H
authors.lastname: Toutounji
authors.affiliation: Neuroinformatics Department, Institute of Cognitive Science, University of Osnabrück, 49069 Osnabrück, Germany joschuma@uni-osnabrueck.de.
authors.forename: Johannes
authors.initials: J
authors.lastname: Schumacher
authors.affiliation: Neuroinformatics Department, Institute of Cognitive Science, University of Osnabrück, 49069 Osnabrück, Germany gpipa@uni-osnabrueck.de.
authors.forename: Gordon
authors.initials: G
authors.lastname: Pipa