title: Nonlinear Memory Capacity of Parallel Time-Delay Reservoir Computers in the Processing of Multidimensional Signals.
abstract: This letter addresses the reservoir design problem in the context of delay-based reservoir computers for multidimensional input signals, parallel architectures, and real-time multitasking. First, an approximating reservoir model is presented in those frameworks that provides an explicit functional link between the reservoir architecture and its performance in the execution of a specific task. Second, the inference properties of the ridge regression estimator in the multivariate context are used to assess the impact of finite sample training on the decrease of the reservoir capacity. Finally, an empirical study is conducted that shows the adequacy of the theoretical results with the empirical performances exhibited by various reservoir architectures in the execution of several nonlinear tasks with multidimensional inputs. Our results confirm the robustness properties of the parallel reservoir architecture with respect to task misspecification and parameter choice already documented in the literature.
authors.affiliation: Department of Mathematics and Statistics, Universität Konstanz, D-78467 Konstanz, Germany Lyudmila.Grigoryeva@uni-konstanz.de.
authors.forename: Lyudmila
authors.initials: L
authors.lastname: Grigoryeva
authors.affiliation: Methodology and Quality of Life in Oncology Unit, CHRU Besançon, F-25000 Besançon, France jhenriques@chu-besancon.fr.
authors.forename: Julie
authors.initials: J
authors.lastname: Henriques
authors.affiliation: FEMTO-ST, UMR CNRS 6174, University Bourgogne Franche-Comté, F-25030 Besançon cedex, France laurent.larger@femto-st.fr.
authors.forename: Laurent
authors.initials: L
authors.lastname: Larger
authors.affiliation: Faculty of Mathematics and Statistics, Universität Sankt Gallen, CH-9000, Sankt Gallen, Switzerland, and Centre National de la Recherche Scientifique, France juan-pablo.ortega@unisg.ch.
authors.forename: Juan-Pablo
authors.initials: JP
authors.lastname: Ortega