Emerging memcapacitive nanoscale devices have the potential to perform computations in new ways. In this article, we systematically study, to the best of our knowledge for the first time, the computational capacity of complex memcapacitive networks, which function as reservoirs in
reservoir computing,
one of the brain-inspired computing architectures. Memcapacitive networks are composed of memcapacitive devices randomly connected through nanowires. Previous studies have shown that both regular and random reservoirs provide sufficient dynamics to perform simple tasks. How do complex memcapacitive networks illustrate their computational capability, and what are the topological structures of memcapacitive networks that solve complex tasks with efficiency? Studies show that small-world power-law (SWPL) networks offer an ideal trade-off between the communication properties and the wiring cost of networks. In this study, we illustrate the computing nature of SWPL memcapacitive reservoirs by exploring the two essential properties: fading memory and linear separation through measurements of kernel quality. Compared to ideal reservoirs, nanowire memcapacitive reservoirs had a better dynamic response and improved their performance by 4.67% on three tasks: MNIST, Isolated Spoken Digits, and CIFAR-10. On the same three tasks, compared to memristive reservoirs, nanowire memcapacitive reservoirs achieved comparable performance with much less power, on average, about 99× , 17×, and 277×, respectively. Simulation results of the topological transformation of memcapacitive networks reveal that that topological structures of the memcapacitive SWPL reservoirs did not affect their performance but significantly contributed to the wiring cost and the power consumption of the systems. The minimum trade-off between the wiring cost and the power consumption occurred at different network settings of
α
and
β
: 4.5 and 0.61 for
Biolek
reservoirs, 2.7 and 1.0 for
Mohamed
reservoirs, and 3.0 and 1.0 for
Najem
reservoirs. The results of our research illustrate the computational capacity of complex memcapacitive networks as reservoirs in reservoir computing. Such memcapacitive networks with an SWPL topology are energy-efficient systems that are suitable for low-power applications such as mobile devices and the Internet of Things.
Transfer theorems for topological structures
