Machine learning (ML) encompasses a broad range of algorithms and modeling tools used for a vast array of data processing tasks, which has entered most scientific disciplines in recent years. This article reviews in a selective way the recent research on the interface between machine learning and the physical sciences. This includes conceptual developments in ML motivated by physical insights, applications of machine learning techniques to several domains in physics, and cross fertilization between the two fields. After giving a basic notion of machine learning methods and principles, examples are described of how statistical physics is used to understand methods in ML. This review then describes applications of ML methods in particle physics and cosmology, quantum many-body physics, quantum computing, and chemical and material physics. Research and development into novel computing architectures aimed at accelerating ML are also highlighted. Each of the sections describe recent successes as well as domain-specific methodology and challenges.

Machine learning and the physical sciences

Memristor-enabled neuromorphic computing systems provide a fast and energy-efficient approach to training neural networks1–4. However, convolutional neural networks (CNNs)—one of the most important models for image recognition5—have not yet been fully hardware-implemented using memristor crossbars, which are cross-point arrays with a memristor device at each intersection. Moreover, achieving software-comparable results is highly challenging owing to the poor yield, large variation and other non-ideal characteristics of devices6–9. Here we report the fabrication of high-yield, high-performance and uniform memristor crossbar arrays for the implementation of CNNs, which integrate eight 2,048-cell memristor arrays to improve parallel-computing efficiency. In addition, we propose an effective hybrid-training method to adapt to device imperfections and improve the overall system performance. We built a five-layer memristor-based CNN to perform MNIST10 image recognition, and achieved a high accuracy of more than 96 per cent. In addition to parallel convolutions using different kernels with shared inputs, replication of multiple identical kernels in memristor arrays was demonstrated for processing different inputs in parallel. The memristor-based CNN neuromorphic system has an energy efficiency more than two orders of magnitude greater than that of state-of-the-art graphics-processing units, and is shown to be scalable to larger networks, such as residual neural networks. Our results are expected to enable a viable memristor-based non-von Neumann hardware solution for deep neural networks and edge computing. A fully hardware-based memristor convolutional neural network using a hybrid training method achieves an energy efficiency more than two orders of magnitude greater than that of graphics-processing units.

Fully hardware-implemented memristor convolutional neural network

With their working mechanisms based on ion migration, the switching dynamics and electrical behaviour of memristive devices resemble those of synapses and neurons, making these devices promising candidates for brain-inspired computing. Built into large-scale crossbar arrays to form neural networks, they perform efficient in-memory computing with massive parallelism by directly using physical laws. The dynamical interactions between artificial synapses and neurons equip the networks with both supervised and unsupervised learning capabilities. Moreover, their ability to interface with analogue signals from sensors without analogue/digital conversions reduces the processing time and energy overhead. Although numerous simulations have indicated the potential of these networks for brain-inspired computing, experimental implementation of large-scale memristive arrays is still in its infancy. This Review looks at the progress, challenges and possible solutions for efficient brain-inspired computation with memristive implementations, both as accelerators for deep learning and as building blocks for spiking neural networks.

Memristive crossbar arrays for brain-inspired computing

Traditional von Neumann computing systems involve separate processing and memory units. However, data movement is costly in terms of time and energy and this problem is aggravated by the recent explosive growth in highly data-centric applications related to artificial intelligence. This calls for a radical departure from the traditional systems and one such non-von Neumann computational approach is in-memory computing. Hereby certain computational tasks are performed in place in the memory itself by exploiting the physical attributes of the memory devices. Both charge-based and resistance-based memory devices are being explored for in-memory computing. In this Review, we provide a broad overview of the key computational primitives enabled by these memory devices as well as their applications spanning scientific computing, signal processing, optimization, machine learning, deep learning and stochastic computing. This Review provides an overview of memory devices and the key computational primitives for in-memory computing, and examines the possibilities of applying this computing approach to a wide range of applications.

Memory devices and applications for in-memory computing

The rapid increase in information in the big-data era calls for changes to information-processing paradigms, which, in turn, demand new circuit-building blocks to overcome the decreasing cost-effectiveness of transistor scaling and the intrinsic inefficiency of using transistors in non-von Neumann computing architectures. Accordingly, resistive switching materials (RSMs) based on different physical principles have emerged for memories that could enable energy-efficient and area-efficient in-memory computing. In this Review, we survey the four physical mechanisms that lead to such resistive switching: redox reactions, phase transitions, spin-polarized tunnelling and ferroelectric polarization. We discuss how these mechanisms equip RSMs with desirable properties for representation capability, switching speed and energy, reliability and device density. These properties are the key enablers of processing-in-memory platforms, with applications ranging from neuromorphic computing and general-purpose memcomputing to cybersecurity. Finally, we examine the device requirements for such systems based on RSMs and provide suggestions to address challenges in materials engineering, device optimization, system integration and algorithm design. Resistive switching materials enable novel, in-memory information processing, which may resolve the von Neumann bottleneck. This Review focuses on how the switching mechanisms and the resultant electrical properties lead to various computing applications.

Resistive switching materials for information processing

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.

Yassine Jaoudi

Papers

Equivalent-accuracy accelerated neural-network training using analogue memory