Modeling and Evaluation of Echo-State Networks Using Spin Torque Nano-Oscillators

Abstract

An echo state network (ESN), capable of processing time-series data with high accuracy, is designed and benchmarked using spin torque nano-oscillators (STNOs) with easy-plane anisotropy. An ESN belongs to the category of reservoir computers, where the reservoir comprises a randomly initialized, recurrently connected, and untrained pool of neurons and acts as a high-dimensional expansion of the input signal. The readout function is used to glean a meaningful output representation. Here, we use STNOs as the basic building block of the ESN and apply the ESN to predict the Mackey-Glass (MG) time-series data. The design parameters of the STNO and the input data representation are selected to yield prediction errors as low as $4\times 10^{-3}$. We also quantify the short-term memory (STM) and the parity-check (PC) capacity of the ESN and obtain metrics that are comparable to or better than existing spintronics-based ESNs, as well as ESNs employing 'tanh' neurons. The peak STM is found to be approximately 8.8, while the peak PC capacity is found to be approximately 3.9. The impacts of thermal fluctuations and process variability on ESN performance are systematically quantified. Although the ESN's prediction and memory capability remain robust with temperature variations, a 10% variation in the dimensions of the STNO free layer can lead to around 40% increase in its prediction error for the MG time-series data.