Dense crossbar arrays of non-volatile memory (NVM) devices represent one possible path for implementing massively-parallel and highly energy-efficient neuromorphic computing systems. We first review recent advances in the application of NVM devices to three computing paradigms: spiking neural networks (SNNs), deep neural networks (DNNs), and 'Memcomputing'. In SNNs, NVM synaptic connections are updated by a local learning rule such as spike-timing-dependent-plasticity, a computational approach directly inspired by biology. For DNNs, NVM arrays can represent matrices of synaptic weights, implementing the matrix-vector multiplication needed for algorithms such as backpropagation in an analog yet massively-parallel fashion. This approach could provide significant improvements in power and speed compared to GPU-based DNN training, for applications of commercial significance. We then survey recent research in which different types of NVM devices-including phase change memory, conductive-bridging RAM, filamentary and nonfilamentary RRAM, and other NVMs-have been proposed, either as a synapse or as a neuron, for use within a neuromorphic computing application. The relevant virtues and limitations of these devices are assessed, in terms of properties such as conductance dynamic range, (non)linearity and (a)symmetry of conductance response, retention, endurance, required switching power, and device variability.

Neural-network training can be slow and energy intensive, owing to the need to transfer the weight data for the network between conventional digital memory chips and processor chips. Analogue non-volatile memory can accelerate the neural-network training algorithm known as backpropagation by performing parallelized multiply-accumulate operations in the analogue domain at the location of the weight data. However, the classification accuracies of such in situ training using non-volatile-memory hardware have generally been less than those of software-based training, owing to insufficient dynamic range and excessive weight-update asymmetry. Here we demonstrate mixed hardware-software neural-network implementations that involve up to 204,900 synapses and that combine long-term storage in phase-change memory, near-linear updates of volatile capacitors and weight-data transfer with 'polarity inversion' to cancel out inherent device-to-device variations. We achieve generalization accuracies (on previously unseen data) equivalent to those of software-based training on various commonly used machine-learning test datasets (MNIST, MNIST-backrand, CIFAR-10 and CIFAR-100). The computational energy efficiency of 28,065 billion operations per second per watt and throughput per area of 3.6 trillion operations per second per square millimetre that we calculate for our implementation exceed those of today's graphical processing units by two orders of magnitude. This work provides a path towards hardware accelerators that are both fast and energy efficient, particularly on fully connected neural-network layers.

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Neuromorphic computing has emerged as a promising avenue towards building the next generation of intelligent computing systems. It has been proposed that memristive devices, which exhibit history-dependent conductivity modulation, could efficiently represent the synaptic weights in artificial neural networks. However, precise modulation of the device conductance over a wide dynamic range, necessary to maintain high network accuracy, is proving to be challenging. To address this, we present a multi-memristive synaptic architecture with an efficient global counter-based arbitration scheme. We focus on phase change memory devices, develop a comprehensive model and demonstrate via simulations the effectiveness of the concept for both spiking and non-spiking neural networks. Moreover, we present experimental results involving over a million phase change memory devices for unsupervised learning of temporal correlations using a spiking neural network. The work presents a significant step towards the realization of large-scale and energy-efficient neuromorphic computing systems.