Computational complexity continuum within Ising formulation of NP problems

A promising approach to achieve computational supremacy over the classical von Neumann architecture explores classical and quantum hardware as Ising machines. The minimisation of the Ising Hamiltonian is known to be NP-hard problem yet not all problem instances are equivalently hard to optimise. Given that the operational principles of Ising machines are suited to the structure of some problems but not others, we propose to identify computationally simple instances with an ‘optimisation simplicity criterion’. Neuromorphic architectures based on optical, photonic, and electronic systems can naturally operate to optimise instances satisfying this criterion, which are therefore often chosen to illustrate the computational advantages of new Ising machines. As an example, we show that the Ising model on the Möbius ladder graph is ‘easy’ for Ising machines. By rewiring the Möbius ladder graph to random 3-regular graphs, we probe an intermediate computational complexity between P and NP-hard classes with several numerical methods. Significant fractions of polynomially simple instances are further found for a wide range of small size models from spin glasses to maximum cut problems. A compelling approach for distinguishing easy and hard instances within the same NP-hard class of problems can be a starting point in developing a standardised procedure for the performance evaluation of emerging physical simulators and physics-inspired algorithms.

2022 roadmap on neuromorphic computing and engineering

Modern computation based on the von Neumann architecture is today a mature cutting-edge science. In the Von Neumann architecture, processing and memory units are implemented as separate blocks interchanging data intensively and continuously. This data transfer is responsible for a large part of the power consumption. The next generation computer technology is expected to solve problems at the exascale with 1018 calculations each second. Even though these future computers will be incredibly powerful, if they are based on von Neumann type architectures, they will consume between 20 and 30 megawatts of power and will not have intrinsic physically built-in capabilities to learn or deal with complex data as our brain does. These needs can be addressed by neuromorphic computing systems which are inspired by the biological concepts of the human brain. This new generation of computers has the potential to be used for the storage and processing of large amounts of digital information with much lower power consumption than conventional processors. Among their potential future applications, an important niche is moving the control from data centers to edge devices. The aim of this Roadmap is to present a snapshot of the present state of neuromorphic technology and provide an opinion on the challenges and opportunities that the future holds in the major areas of neuromorphic technology, namely materials, devices, neuromorphic circuits, neuromorphic algorithms, applications, and ethics. The Roadmap is a collection of perspectives where leading researchers in the neuromorphic community provide their own view about the current state and the future challenges for each research area. We hope that this Roadmap will be a useful resource by providing a concise yet comprehensive introduction to readers outside this field, for those who are just entering the field, as well as providing future perspectives for those who are well established in the neuromorphic computing community.

Spiking Neural Networks in Spintronic Computational RAM

Spiking Neural Networks (SNNs) represent a biologically inspired computation model capable of emulating neural computation in human brain and brain-like structures. The main promise is very low energy consumption. Classic Von Neumann architecture based SNN accelerators in hardware, however, often fall short of addressing demanding computation and data transfer requirements efficiently at scale. In this article, we propose a promising alternative to overcome scalability limitations, based on a network of in-memory SNN accelerators, which can reduce the energy consumption by up to 150.25= when compared to a representative ASIC solution. The significant reduction in energy comes from two key aspects of the hardware design to minimize data communication overheads: (1) each node represents an in-memory SNN accelerator based on a spintronic Computational RAM array, and (2) a novel, De Bruijn graph based architecture establishes the SNN array connectivity.

Memristive System Based Image Processing Technology: A Review and Perspective

As the acquisition, transmission, storage and conversion of images become more efficient, image data are increasing explosively. At the same time, the limitations of conventional computational processing systems based on the Von Neumann architecture continue to emerge, and thus, improving the efficiency of image processing has become a key issue that has bothered scholars working on images for a long time. Memristors with non-volatile, synapse-like, as well as integrated storage-and-computation properties can be used to build intelligent processing systems that are closer to the structure and function of biological brains. They are also of great significance when constructing new intelligent image processing systems with non-Von Neumann architecture and for achieving the integrated storage and computation of image data. Based on this, this paper analyses the mathematical models of memristors and discusses their applications in conventional image processing based on memristive systems as well as image processing based on memristive neural networks, to investigate the potential of memristive systems in image processing. In addition, recent advances and implications of memristive system-based image processing are presented comprehensively, and its development opportunities and challenges in different major areas are explored as well. By establishing a complete spectrum of image processing technologies based on memristive systems, this review attempts to provide a reference for future studies in the field, and it is hoped that scholars can promote its development through interdisciplinary academic exchanges and cooperation.

The challenges of modern computing and new opportunities for optics

In recent years, the explosive development of artificial intelligence implementing by artificial neural networks (ANNs) creates inconceivable demands for computing hardware. However, conventional computing hardware based on electronic transistor and von Neumann architecture cannot satisfy such an inconceivable demand due to the unsustainability of Moore’s Law and the failure of Dennard’s scaling rules. Fortunately, analog optical computing offers an alternative way to release unprecedented computational capability to accelerate varies computing drained tasks. In this article, the challenges of the modern computing technologies and potential solutions are briefly explained in Chapter 1. In Chapter 2, the latest research progresses of analog optical computing are separated into three directions: vector/matrix manipulation, reservoir computing and photonic Ising machine. Each direction has been explicitly summarized and discussed. The last chapter explains the prospects and the new challenges of analog optical computing.

Memristive Artificial Synapses for Neuromorphic Computing

Neuromorphic computing simulates the operation of biological brain function for information processing and can potentially solve the bottleneck of the von Neumann architecture. This computing is realized based on memristive hardware neural networks in which synaptic devices that mimic biological synapses of the brain are the primary units. Mimicking synaptic functions with these devices is critical in neuromorphic systems. In the last decade, electrical and optical signals have been incorporated into the synaptic devices and promoted the simulation of various synaptic functions. In this review, these devices are discussed by categorizing them into electrically stimulated, optically stimulated, and photoelectric synergetic synaptic devices based on stimulation of electrical and optical signals. The working mechanisms of the devices are analyzed in detail. This is followed by a discussion of the progress in mimicking synaptic functions. In addition, existing application scenarios of various synaptic devices are outlined. Furthermore, the performances and future development of the synaptic devices that could be significant for building efficient neuromorphic systems are prospected.

One Step in-Memory Solution of Inverse Algebraic Problems

Machine learning requires to process large amount of irregular data and extract meaningful information. Von-Neumann architecture is being challenged by such computation, in fact a physical separation between memory and processing unit limits the maximum speed in analyzing lots of data and the majority of time and energy are spent to make information travel from memory to the processor and back. In-memory computing executes operations directly within the memory without any information travelling. In particular, thanks to emerging memory technologies such as memristors, it is possible to program arbitrary real numbers directly in a single memory device in an analog fashion and at the array level, execute algebraic operation in-memory and in one step. In this chapter the latest results in accelerating inverse operation, such as the solution of linear systems, in-memory and in a single computational cycle will be presented.

Designing artificial sodium ion reservoirs to emulate biological synapses

Emulating neurons/synapses in the brain is an important step to realizing highly efficient computers. This fact makes neuromorphic devices important emerging solutions to the limitations imposed by the current computing architecture. To mimic synaptic functions in the brain, it is critical to replicate ionic movements in the nervous system. It is therefore important to note that ions move easily in liquids. In this study, we demonstrate a liquid-based neuromorphic device that is capable of mimicking the movement of ions in the nervous system by controlling Na+ movement in an aqueous solution. The concentration of Na+ in the solution can control the ionic conductivity of the device. The device shows short-term and long-term plasticity such as excitatory postsynaptic current, paired-pulse facilitation, potentiation, and depression, which are key properties for memorization and computation in the brain. This device has the potential to overcome the limitations of current von Neumann architecture-based computing systems and substantially advance the technology of neuromorphic computing.

Complexity continuum within Ising formulation of NP problems

A promising approach to achieve computational supremacy over the classical von Neumann architecture explores classical and quantum hardware as Ising machines. The minimisation of the Ising Hamiltonian is known to be NP-hard problem for certain interaction matrix classes, yet not all problem instances are equivalently hard to optimise. We propose to identify computationally simple instances with an `optimisation simplicity criterion'. Such optimisation simplicity can be found for a wide range of models from spin glasses to k-regular maximum cut problems. Many optical, photonic, and electronic systems are neuromorphic architectures that can naturally operate to optimise problems satisfying this criterion and, therefore, such problems are often chosen to illustrate the computational advantages of new Ising machines. We further probe an intermediate complexity for sparse and dense models by analysing circulant coupling matrices, that can be `rewired' to introduce greater complexity. A compelling approach for distinguishing easy and hard instances within the same NP-hard class of problems can be a starting point in developing a standardised procedure for the performance evaluation of emerging physical simulators and physics-inspired algorithms.