Distance-based delays in echo state networks

Physical reservoir computing, a paradigm bearing the promise of energy-efficient high-performance computing, has raised much attention in recent years. We argue though, that the effect of signal propagation delay on reservoir task performance, one of the most central aspects of physical reservoirs, is still insufficiently understood in a more general learning context. Such physically imposed delay has been found to play a crucial role in some specific physical realizations, such as integrated photonic reservoirs. While delays at the readout layer and input of Echo State Networks (ESNs) have been successfully exploited before to improve performance, to our knowledge this feature has not been studied in a more general setting. We introduce inter-node delays, based on physical distances, into ESNs as model systems for physical reservoir computing. We propose a novel ESN design that includes variable signal delays along the connections between neurons, comparable to varying axon lengths in biological neural networks or varying length delay lines in physical systems. We study the impact of the resulting variable inter-node delays in this setup in comparison with conventional ESNs and find that incorporating variable delays significantly improves reservoir performance on the NARMA-10 benchmark task