  By exploiting the intrinsic random nature of nanoscale devices, Memristor
Monte Carlo (MMC) is a promising enabler of edge learning systems. However, due
to multiple algorithmic and device-level limitations, existing demonstrations
have been restricted to very small neural network models and datasets. We
discuss these limitations, and describe how they can be overcome, by mapping
the stochastic gradient Langevin dynamics (SGLD) algorithm onto the physics of
magnetic domain-wall Memristors to scale-up MMC models by five orders of
magnitude. We propose the push-pull pulse programming method that realises SGLD
in-physics, and use it to train a domain-wall based ResNet18 on the CIFAR-10
dataset. On this task, we observe no performance degradation relative to a
floating point model down to an update precision of between 6 and 7-bits,
indicating we have made a step towards a large-scale edge learning system
leveraging noisy analogue devices.
