Reservoir computing using networks of memristors: effects of topology and heterogeneity.

Reservoir computing (RC) has attracted significant interest as a framework for the implementation of novel neuromorphic computing architectures. Previously attention has been focussed on software-based reservoirs, where it has been demonstrated that reservoir topology plays a role in task performance, and functional advantage has been attributed to small-world and scale-free connectivity. However in hardware systems, such as electronic memristor networks, the mechanisms responsible for the reservoir dynamics are very different and the role of reservoir topology is largely unknown. Here we compare the performance of a range of memristive reservoirs in several RC tasks that are chosen to highlight different system requirements. We focus on percolating networks of nanoparticles (PNNs) which are novel self-assembled nanoscale systems that exhibit scale-free and small-world properties. We find that the performance of regular arrays of uniform memristive elements is limited by their symmetry but that this symmetry can be broken either by a heterogeneous distribution of memristor properties or a scale-free topology. The best perfomance across all tasks is observed for a scale-free network with uniform memistor properties. These results provide insight into the role of topology in neuromorphic reservoirs as well as an overview of the computational performance of scale-free networks of memristors in a range of benchmark tasks.