Single-Electron Reservoir Computing Circuit with Online Learning

S. Watanabe, T. Oya
Yokohama National University,

Keywords: single-electron circuit, reservoir computing


We previously proposed a single-electron (SE) reservoir computing (RC) circuit and conducted evaluations of offline learning. In this study, we further implemented and evaluated online learning for the same SE RC circuit. An SE circuit, which primarily consists of tunnel junctions and controls individual electrons based on Coulomb blockade effect, exhibits unique characteristics such as nonlinear and stochastic behavior. However, information-processing ways appropriated for the SE circuit have yet to be discovered. An SE oscillator (SEO) is a type of the SE circuit and behaves like a biological neuron, which generates an action potential (or spike) when stimulated to reach a threshold. This is because when the SEO receives an impulse voltage and its node voltage exceeds the threshold voltage, the node voltage suddenly increases or decreases as a result of electron tunneling. The RC is a type of Recurrent Neural Network (RNN), which is made up of artificial neurons modeled after biological neurons that are connected to each other. RC has three layers: an input layer, a reservoir layer and an output layer. The weights of the reservoir layer are fixed and only the weights of the output layer are trained. This is a unique feature that allows the reservoir layer to be replaced with a nonlinear physical system. There have been several studies conducted on this topic. The SE circuit seems to be compatible with the RC, because the SEO, which is a sort of SE circuit, is like a biological neuron and RC is a kind of RNN, which consists of artificial neurons modeled after biological neurons. The SE RC circuit we designed consists of multiple SEOs. The SEOs are connected and arranged in a honeycomb pattern for the reservoir layer. Input layer has some voltage sources to serve as triggers for the SEOs (or to apply impulse voltage to SEOs). In the output layer is a node used to sum the product of each weight and the voltage values of randomly chosen SEOs in the reservoir layer. The RC circuit can be learned using two methods: offline learning (batch learning) and online learning. In previous research, we have reported the results of offline learning for the SE RC circuit. We, in the present study, implemented an online learning function for the SE RC circuit and conducted a demonstration of online learning for some waveforms, such as sine wave and sawtooth wave, through computer simulations. We investigated the variation in the forecasting output and the value of root-mean-square error (RMSE) value; RMSE is evaluation metric. We observed a decrease in the RMSE value as the learning progressed. This confirmed the effectiveness of the online learning for SE RC circuit and led us to expect that applying the RC to SE circuit (i.e., the SE RC circuit) is one of promising methods of information-process way for SE circuit.