The time-delay-based reservoir computing setup has seen tremendous success in both experiment and simulation. It allows for the construction of large neuromorphic computing systems with only few components. However, until now the interplay of the different timescales has not been investigated thoroughly. In this manuscript, we investigate the effects of a mismatch between the time-delay and the clock cycle for a general model. Typically, these two time scales are considered to be equal. Here we show that the case of equal or rationally related time-delay and clock cycle could be actively detrimental and leads to an increase of the approximation error of the reservoir. In particular, we can show that non-resonant ratios of these time scales have maximal memory capacities. We achieve this by translating the periodically driven delay-dynamical system into an equivalent network. Networks that originate from a system with resonant delay-times and clock cycles fail to utilize all of their degrees of freedom, which causes the degradation of their performance.

The reservoir computing scheme is a machine learning mechanism which utilizes the naturally occurring computational capabilities of dynamical systems. One important subset of systems that has proven powerful both in experiments and theory are delay-systems. In this work, we investigate the reservoir computing performance of hybrid network-delay systems systematically by evaluating the NARMA10 and the Sante Fe task for varying system parameters. We construct 'multiplexed networks' that can be seen as intermediate steps on the scale from classical networks to the 'virtual networks' of delay systems. We find that the delay approach can be extended to the network case without loss of computational power, enabling the construction of faster reservoir computing systems.

Reservoir computing is a neuromorphic computing scheme inspired by the human brain. It has found great success as a versatile hardware-compatible application of machine learning concepts. In this paper, we highlight the fundamental working principles and important characteristics of reservoir computing with a particular focus on photonic systems and networks. These systems can further be enhanced by the inclusion of delayed variables to produce complex spatiotemporally mixed "time-multiplexed" networks. We use a simple nonlinear oscillator model, that is not only applicable to lasers, but can also describe a variety of other oscillating systems.