title: Persistent Memory in Single Node Delay-Coupled Reservoir Computing.
abstract: Delays are ubiquitous in biological systems, ranging from genetic regulatory networks and synaptic conductances, to predator/pray population interactions. The evidence is mounting, not only to the presence of delays as physical constraints in signal propagation speed, but also to their functional role in providing dynamical diversity to the systems that comprise them. The latter observation in biological systems inspired the recent development of a computational architecture that harnesses this dynamical diversity, by delay-coupling a single nonlinear element to itself. This architecture is a particular realization of Reservoir Computing, where stimuli are injected into the system in time rather than in space as is the case with classical recurrent neural network realizations. This architecture also exhibits an internal memory which fades in time, an important prerequisite to the functioning of any reservoir computing device. However, fading memory is also a limitation to any computation that requires persistent storage. In order to overcome this limitation, the current work introduces an extended version to the single node Delay-Coupled Reservoir, that is based on trained linear feedback. We show by numerical simulations that adding task-specific linear feedback to the single node Delay-Coupled Reservoir extends the class of solvable tasks to those that require nonfading memory. We demonstrate, through several case studies, the ability of the extended system to carry out complex nonlinear computations that depend on past information, whereas the computational power of the system with fading memory alone quickly deteriorates. Our findings provide the theoretical basis for future physical realizations of a biologically-inspired ultrafast computing device with extended functionality.
authors: Neuroinformatics Department, Institute of Cognitive Science, University of Osnabrück, Osnabrück, Lower Saxony, Germany.
authors: André David
authors: http://orcid.org/0000-0002-6831-0916
authors: AD
authors: Kovac
authors: Neuroinformatics Department, Institute of Cognitive Science, University of Osnabrück, Osnabrück, Lower Saxony, Germany.
authors: Maximilian
authors: M
authors: Koall
authors: Neuroinformatics Department, Institute of Cognitive Science, University of Osnabrück, Osnabrück, Lower Saxony, Germany.
authors: Gordon
authors: G
authors: Pipa
authors: Department of Theoretical Neuroscience, Central Institute of Mental Health, Medical Faculty Mannheim of Heidelberg University, Mannheim, Baden-Württemberg, Germany.
authors: Hazem
authors: H
authors: Toutounji
mesh_terms: D003198:Computer Simulation; D008432:Mathematical Computing; D008962:Models, Theoretical; D017711:Nonlinear Dynamics; D016011:Normal Distribution