Machine Learning with Stochastic Magnetic Domain Wall Synapses

Abstract

Despite their importance in a variety of technologies, the high energy cost of many forms of machine learning algorithms is a significant limitation[1]. One solution to this is to employ physical devices that can naturally mimic brain-like behaviour, known as neuromorphic computing [2]. Magnetic domain walls (DWs) are strong candidates for such devices, since they have potential for both data storage and logic operations [3] but stochastic effects limit the feasibility of creating viable devices. Here, we demonstrate how tunable stochastic pinning can be used to emulate synaptic properties for specialised neuromorphic devices.First we show measurements that demonstrate the feasibility of tuning stochastic processes by applying external stimuli. Focused magneto-optic Kerr effect measurements were used to probe the pinning of DWs at notch-shaped defects in 400 nm wide Permalloy nanowires. As shown in Fig 1, by modulating the propagation field (H) by an additional amount (dH) the pinning probability of the DW at the defect site was found to depend sigmoidally on dH and is observed on separate wires.Next, we model these wires as binary stochastic synapses in a neural network with properties based on the experimental measurements. By repeatedly sampling the network the stochastic total output can be converged to an analogue value to improve performance. It is found that for a single cycle of the network it can be trained to recognise handwritten digits with an error rate of 17%. Repeated sampling of the network decreased the error rate to 8% for 128 cycles, close to mean field performance, Fig. 2. We have also found that this performance is only slightly reduced when random individual wire properties are considered and additional neural layers mitigate stochasticity. Our work illustrates how the intrinsic stochasticity of DW devices can be harnessed to provide tunable bespoke hardware for machine learning tasks.  Tuning of domain wall pinning probability in notched magnetic nanowire synapse. Inset shows a schematic of the notched nanowire and applied field direction.  Test error rate of classifying handwritten digits using a single layer stochastic network for varying repeated sampling.