The Effect of System Timescale on Virtual Node Connectivity within Delay-Feedback Reservoirs

The delay-feedback reservoir is a branch of reservoir computing that has allowed for a more hardware friendly implementation by reducing the typically large number of inputs and outputs within neural networks to a single physical input and output. This is achieved by using a single non-linear node and time-multiplexing the input signal with a masking signal, to create many “virtual neurons” within a reservoir; emulating a larger spatial neural network. While the relationship of the number of virtual nodes, masking frequency, and overall delay length is well known, the effect that the timescale has on computational performance is not widely investigated or understood; usually because working with specific substrates implies the reservoir is confined to its inherent timescales. Hence, there is currently no general methodology for tuning delay-feedback reservoir systems to specific applications. Here, we create a parameterisable hardware-realistic computational model in order to simulate a delay-feedback reservoir operating at different timescales, and explore the effect this has on the connectivity between the virtual nodes and the computational performance of the system. Our results show that the timescale has indeed a significant effect on computational tasks with a long-term dependency on previous input stimuli. We then show that it is possible to emulate larger virtual node networks within smaller ones with little loss in performance and an increase in efficiency. This is an essential step towards understanding the function of the timescale within a delay-feedback reservoir, and a methodology to enable systematic tailoring of delay-feedback reservoirs to specific computational tasks across different timescales.