Associative memory realized by a reconfigurable memristive Hopfield neural network

Heterogeneous coexisting attractors, large-scale amplitude control and finite-time synchronization of central cyclic memristive neural networks

Memristors are of great theoretical and practical significance for chaotic dynamics research of brain-like neural networks due to their excellent physical properties such as brain synapse-like memorability and nonlinearity, especially crucial for the promotion of AI big models, cloud computing, and intelligent systems in the artificial intelligence field. In this paper, we introduce memristors as self-connecting synapses into a four-dimensional Hopfield neural network, constructing a central cyclic memristive neural network (CCMNN), and achieving its effective control. The model adopts a central loop topology and exhibits a variety of complex dynamic behaviors such as chaos, bifurcation, and homogeneous and heterogeneous coexisting attractors. The complex dynamic behaviors of the CCMNN are investigated in depth numerically by equilibrium point stability analysis as well as phase trajectory maps, bifurcation maps, time-domain maps, and LEs. It is found that with the variation of the internal parameters of the memristor, asymmetric heterogeneous attractor coexistence phenomena appear under different initial conditions, including the multi-stable coexistence behaviors of periodic-periodic, periodic-stable point, periodic-chaotic, and stable point-chaotic. In addition, by adjusting the structural parameters, a wide range of amplitude control can be realized without changing the chaotic state of the system. Finally, based on the CCMNN model, an adaptive synchronization controller is designed to achieve finite-time synchronization control, and its application prospect in simple secure communication is discussed. A microcontroller-based hardware circuit and NIST test are conducted to verify the correctness of the numerical results and theoretical analysis.

SSTE: Syllable-Specific Temporal Encoding to FORCE-learn audio sequences with an associative memory approach

The circuitry and pathways in the brains of humans and other species have long inspired researchers and system designers to develop accurate and efficient systems capable of solving real-world problems and responding in real-time. We propose the Syllable-Specific Temporal Encoding (SSTE) to learn vocal sequences in a reservoir of Izhikevich neurons, by forming associations between exclusive input activities and their corresponding syllables in the sequence. Our model converts the audio signals to cochleograms using the CAR-FAC model to simulate a brain-like auditory learning and memorization process. The reservoir is trained using a hardware-friendly approach to FORCE learning. Reservoir computing could yield associative memory dynamics with far less computational complexity compared to RNNs. The SSTE-based learning enables competent accuracy and stable recall of spatiotemporal sequences with fewer reservoir inputs compared with existing encodings in the literature for similar purpose, offering resource savings. The encoding points to syllable onsets and allows recalling from a desired point in the sequence, making it particularly suitable for recalling subsets of long vocal sequences. The SSTE demonstrates the capability of learning new signals without forgetting previously memorized sequences and displays robustness against occasional noise, a characteristic of real-world scenarios. The components of this model are configured to improve resource consumption and computational intensity, addressing some of the cost-efficiency issues that might arise in future implementations aiming for compactness and real-time, low-power operation. Overall, this model proposes a brain-inspired pattern generation network for vocal sequences that can be extended with other bio-inspired computations to explore their potentials for brain-like auditory perception. Future designs could inspire from this model to implement embedded devices that learn vocal sequences and recall them as needed in real-time. Such systems could acquire language and speech, operate as artificial assistants, and transcribe text to speech, in the presence of natural noise and corruption on audio data.

Approaching the Ideal Linearity in Epitaxial Crystalline-Type Memristor by Controlling Filament Growth

Brain-inspired neuromorphic computing has attracted widespread attention owing to its ability to perform parallel and energy-efficient computation. However, the synaptic weight of amorphous/polycrystalline oxide based memristor usually exhibits large nonlinear behavior with high asymmetry, which aggravates the complexity of peripheral circuit system. Controllable growth of conductive filaments is highly demanded for achieving the highly linear conductance modulation. However, the stochastic behavior of the filament growth in commonly used amorphous/polycrystalline oxide memristor makes it very challenging. Here, the epitaxially grown Hf0.5Zr0.5O2-based memristor with the linearity and symmetry approaching ideal case is reported. A layer of Cu nanoparticles is inserted into epitaxially grown Hf0.5Zr0.5O2 film to form the grain boundaries due to the breaking of the epitaxial growth. By combining with the local electric field enhancement, the growth of filament is confined in the grain boundaries due to the fact that the diffusion of oxygen vacancy in crystalline lattice is more difficult than that in the grain boundaries. Furthermore, the decimal operation and high-accuracy neural network are demonstrated by utilizing the highly linear and multi-level conductance modulation capacity. This method opens an avenue to control the filament growth for the application of resistance random access memory (RRAM) and neuromorphic computing.

Elementary cellular automata realized by stateful three-memristor logic operations

Cellular automata (CA) are computational systems that exhibit complex global behavior arising from simple local rules, making them a fascinating candidate for various research areas. However, challenges such as limited flexibility and efficiency on conventional hardware platforms still exist. In this study, we propose a memristor-based circuit for implementing elementary cellular automata (ECA) by extending the stateful three-memristor logic operations derived from material implication (IMP) logic gates. By leveraging the inherent physical properties of memristors, this approach offers simplicity, minimal operational steps, and high flexibility in implementing ECA rules by adjusting the circuit parameters. The mathematical principles governing circuit parameters are analyzed, and the evolution of multiple ECA rules is successfully demonstrated, showcasing the robustness in handling the stochastic nature of memristors. This approach provides a hardware solution for ECA implementation and opens up new research opportunities in the hardware implementation of CA.

Integrated In-Memory Sensor and Computing of Artificial Vision Based on Full-vdW Optoelectronic Ferroelectric Field-Effect Transistor

The development and application of artificial intelligence have led to the exploitation of low-power and compact intelligent information-processing systems integrated with sensing, memory, and neuromorphic computing functions. The 2D van der Waals (vdW) materials with abundant reservoirs for arbitrary stacking based on functions and enabling continued device downscaling offer an attractive alternative for continuously promoting artificial intelligence. In this study, full 2D SnS2 /h-BN/CuInP2 S6 (CIPS)-based ferroelectric field-effect transistors (Fe-FETs) and utilized light-induced ferroelectric polarization reversal to achieve excellent memory properties and multi-functional sensing-memory-computing vision simulations are designed. The device exhibits a high on/off current ratio of over 105 , long retention time (>104  s), stable cyclic endurance (>350 cycles), and 128 multilevel current states (7-bit). In addition, fundamental synaptic plasticity characteristics are emulated including paired-pulse facilitation (PPF), short-term plasticity (STP), long-term plasticity (LTP), long-term potentiation, and long-term depression. A ferroelectric optoelectronic reservoir computing system for the Modified National Institute of Standards and Technology (MNIST) handwritten digital recognition achieved a high accuracy of 93.62%. Furthermore, retina-like light adaptation and Pavlovian conditioning are successfully mimicked. These results provide a strategy for developing a multilevel memory and novel neuromorphic vision systems with integrated sensing-memory-processing.

Reconfigurable Neuromorphic Computing: Materials, Devices, and Integration

Neuromorphic computing has been attracting ever-increasing attention due to superior energy efficiency, with great promise to promote the next wave of artificial general intelligence in the post-Moore era. Current approaches are, however, broadly designed for stationary and unitary assignments, thus encountering reluctant interconnections, power consumption, and data-intensive computing in that domain. Reconfigurable neuromorphic computing, an on-demand paradigm inspired by the inherent programmability of brain, can maximally reallocate finite resources to perform the proliferation of reproducibly brain-inspired functions, highlighting a disruptive framework for bridging the gap between different primitives. Although relevant research has flourished in diverse materials and devices with novel mechanisms and architectures, a precise overview remains blank and urgently desirable. Herein, the recent strides along this pursuit are systematically reviewed from material, device, and integration perspectives. At the material and device level, one comprehensively conclude the dominant mechanisms for reconfigurability, categorized into ion migration, carrier migration, phase transition, spintronics, and photonics. Integration-level developments for reconfigurable neuromorphic computing are also exhibited. Finally, a perspective on the future challenges for reconfigurable neuromorphic computing is discussed, definitely expanding its horizon for scientific communities.

Moiré synaptic transistor with room-temperature neuromorphic functionality

Moiré quantum materials host exotic electronic phenomena through enhanced internal Coulomb interactions in twisted two-dimensional heterostructures1-4. When combined with the exceptionally high electrostatic control in atomically thin materials5-8, moiré heterostructures have the potential to enable next-generation electronic devices with unprecedented functionality. However, despite extensive exploration, moiré electronic phenomena have thus far been limited to impractically low cryogenic temperatures9-14, thus precluding real-world applications of moiré quantum materials. Here we report the experimental realization and room-temperature operation of a low-power (20 pW) moiré synaptic transistor based on an asymmetric bilayer graphene/hexagonal boron nitride moiré heterostructure. The asymmetric moiré potential gives rise to robust electronic ratchet states, which enable hysteretic, non-volatile injection of charge carriers that control the conductance of the device. The asymmetric gating in dual-gated moiré heterostructures realizes diverse biorealistic neuromorphic functionalities, such as reconfigurable synaptic responses, spatiotemporal-based tempotrons and Bienenstock-Cooper-Munro input-specific adaptation. In this manner, the moiré synaptic transistor enables efficient compute-in-memory designs and edge hardware accelerators for artificial intelligence and machine learning.

Effect of the electromagnetic induction on a modified memristive neural map model

The significance of discrete neural models lies in their mathematical simplicity and computational ease. This research focuses on enhancing a neural map model by incorporating a hyperbolic tangent-based memristor. The study extensively explores the impact of magnetic induction strength on the model's dynamics, analyzing bifurcation diagrams and the presence of multistability. Moreover, the investigation extends to the collective behavior of coupled memristive neural maps with electrical, chemical, and magnetic connections. The synchronization of these coupled memristive maps is examined, revealing that chemical coupling exhibits a broader synchronization area. Additionally, diverse chimera states and cluster synchronized states are identified and discussed.

Memristive competitive hopfield neural network for image segmentation application

Image segmentation implementation provides simplified and effective feature information of image. Neural network algorithms have made significant progress in the application of image segmentation task. However, few studies focus on the implementation of hardware circuits with high-efficiency analog calculations and parallel operations for image segmentation problem. In this paper, a memristor-based competitive Hopfield neural network circuit is proposed to deal with the image segmentation problem. In this circuit, the memristive cross array is applied to store synaptic weights and perform matrix operations. The competition module based on the Winner-take-all mechanism is composed of the competition neurons and the competition control circuit, which simplifies the energy function of the Hopfield neural network and realizes the output function. Operational amplifiers and ABM modules are used to integrate operations and process external input information, respectively. Based on these designs, the circuit can automatically implement iteration and update of data. A series of PSPICE simulations are designed to verify the image segmentation capability of this circuit. Comparative experimental results and analysis show that this circuit has effective improvements both in processing speed and segmentation accuracy compared with other methods. Moreover, the proposed circuit shows good robustness to noise and memristive variation.

Memristive Neural Networks for Predicting Seizure Activity

The aim of the study is to assess the possibilities of predicting epileptiform activity using the neuronal activity data recorded from the hippocampus and medial entorhinal cortex of mice with chronic epileptiform activity. To reach this goal, a deep artificial neural network (ANN) has been developed and its implementation based on memristive devices has been demonstrated.

Materials and Methods

The biological part of the investigation. Young healthy outbred CD1 mice were used in our study. They were divided into two groups: control (n=6) and the group with induced chronic epileptiform activity (n=6). Local field potentials (LFP) were recorded from the hippocampus and medial entorhinal cortex of the mice of both groups to register neuronal activity. The LFP recordings were used for deep ANN training. Epileptiform activity in mice was modeled by intraperitoneal injection of pilocarpine (280 mg/kg). LFP were recorded in the awake mice a month after the induction of epileptiform activity.Mathematical part of the investigation. A deep long short-term memory (LSTM) ANN capable of predicting biological signals of neuronal activity in mice has been developed. The ANN implementation is based on memristive devices, which are described by the equations of the redox processes running in the memristive thin metal-oxide-metal films, e.g., Au/ZrO2(Y)/TiN/Ti and Au/SiO2(Y)/TiN/Ti. In order to train the developed ANN to predict epileptiform activity, a supervised learning algorithm was used, which allowed us to adjust the network parameters and train LSTM on the described recordings of neuronal activity.

Results

After training on the LFP recordings from the hippocampus and medial entorhinal cortex of the mice with chronic epileptiform activity, the proposed deep ANN has demonstrated high values of evaluation metric (root-mean-square error, RMSE) and successfully predicted epileptiform activity shortly before its occurrence (40 ms). The results of the numerical experiments have shown that the RMSE value of 0.019 was reached, which indicates the efficacy of proposed approach. The accuracy of epileptiform activity prediction 40 ms before its occurrence is a significant result and shows the potential of the developed neural network architecture.

Conclusion

The proposed deep ANN can be used to predict pathological neuronal activity including epileptic seizure (focal) activity in mice before its actual occurrence. Besides, it can be applied for building a long-term prognosis of the disease course based on the LFP data. Thus, the proposed ANN based on memristive devices represents a novel approach to the prediction and analysis of pathological neuronal activity possessing a potential for improving the diagnosis and prognostication of epileptic seizures and other diseases associated with neuronal activity.

Thermally stable threshold selector based on CuAg alloy for energy-efficient memory and neuromorphic computing applications

As a promising candidate for high-density data storage and neuromorphic computing, cross-point memory arrays provide a platform to overcome the von Neumann bottleneck and accelerate neural network computation. In order to suppress the sneak-path current problem that limits their scalability and read accuracy, a two-terminal selector can be integrated at each cross-point to form the one-selector-one-memristor (1S1R) stack. In this work, we demonstrate a CuAg alloy-based, thermally stable and electroforming-free selector device with tunable threshold voltage and over 7 orders of magnitude ON/OFF ratio. A vertically stacked 64 × 64 1S1R cross-point array is further implemented by integrating the selector with SiO₂-based memristors. The 1S1R devices exhibit extremely low leakage currents and proper switching characteristics, which are suitable for both storage class memory and synaptic weight storage. Finally, a selector-based leaky integrate-and-fire neuron is designed and experimentally implemented, which expands the application prospect of CuAg alloy selectors from synapses to neurons.

Braille recognition by E-skin system based on binary memristive neural network

Braille system is widely used worldwide for communication by visually impaired people. However, there are still some visually impaired people who are unable to learn Braille system due to various factors, such as the age (too young or too old), brain damage, etc. A wearable and low-cost Braille recognition system may substantially help these people recognize Braille or assist them in Braille learning. In this work, we fabricated polydimethylsiloxane (PDMS)-based flexible pressure sensors to construct an electronic skin (E-skin) for the application of Braille recognition. The E-skin mimics human touch sensing function for collecting Braille information. Braille recognition is realized with a neural network based on memristors. We utilize a binary neural network algorithm with only two bias layers and three fully connected layers. Such neural network design remarkably reduces the calculation burden and, thus, the system cost. Experiments show that the system can achieve a recognition accuracy of up to 91.25%. This work demonstrates the possibility of realizing a wearable and low-cost Braille recognition system and a Braille learning-assistance system.

Ultra-High-Speed Accelerator Architecture for Convolutional Neural Network Based on Processing-in-Memory Using Resistive Random Access Memory

Processing-in-Memory (PIM) based on Resistive Random Access Memory (RRAM) is an emerging acceleration architecture for artificial neural networks. This paper proposes an RRAM PIM accelerator architecture that does not use Analog-to-Digital Converters (ADCs) and Digital-to-Analog Converters (DACs). Additionally, no additional memory usage is required to avoid the need for a large amount of data transportation in convolution computation. Partial quantization is introduced to reduce the accuracy loss. The proposed architecture can substantially reduce the overall power consumption and accelerate computation. The simulation results show that the image recognition rate for the Convolutional Neural Network (CNN) algorithm can reach 284 frames per second at 50 MHz using this architecture. The accuracy of the partial quantization remains almost unchanged compared to the algorithm without quantization.

Palimpsest memories stored in memristive synapses

Biological synapses store multiple memories on top of each other in a palimpsest fashion and at different time scales. Palimpsest consolidation is facilitated by the interaction of hidden biochemical processes governing synaptic efficacy during varying lifetimes. This arrangement allows idle memories to be temporarily overwritten without being forgotten, while previously unseen memories are used in the short term. While embedded artificial intelligence can greatly benefit from this functionality, a practical demonstration in hardware is missing. Here, we show how the intrinsic properties of metal-oxide volatile memristors emulate the processes supporting biological palimpsest consolidation. Our memristive synapses exhibit an expanded doubled capacity and protect a consolidated memory while up to hundreds of uncorrelated short-term memories temporarily overwrite it, without requiring specialized instructions. We further demonstrate this technology in the context of visual working memory. This showcases how emerging memory technologies can efficiently expand the capabilities of artificial intelligence hardware toward more generalized learning memories.

Research Progress of Biomimetic Memristor Flexible Synapse

With the development of the Internet of things, artificial intelligence, and wearable devices, massive amounts of data are generated and need to be processed. High standards are required to store and analyze this information. In the face of the explosive growth of information, the memory used in data storage and processing faces great challenges. Among many types of memories, memristors have received extensive attentions due to their low energy consumption, strong tolerance, simple structure, and strong miniaturization. However, they still face many problems, especially in the application of artificial bionic synapses, which call for higher requirements in the mechanical properties of the device. The progress of integrated circuit and micro-processing manufacturing technology has greatly promoted development of the flexible memristor. The use of a flexible memristor to simulate nerve synapses will provide new methods for neural network computing and bionic sensing systems. In this paper, the materials and structure of the flexible memristor are summarized and discussed, and the latest configuration and new materials are described. In addition, this paper will focus on its application in artificial bionic synapses and discuss the challenges and development direction of flexible memristors from this perspective.

Combinatorial optimization by weight annealing in memristive hopfield networks

The increasing utility of specialized circuits and growing applications of optimization call for the development of efficient hardware accelerator for solving optimization problems. Hopfield neural network is a promising approach for solving combinatorial optimization problems due to the recent demonstrations of efficient mixed-signal implementation based on emerging non-volatile memory devices. Such mixed-signal accelerators also enable very efficient implementation of various annealing techniques, which are essential for finding optimal solutions. Here we propose a "weight annealing" approach, whose main idea is to ease convergence to the global minima by keeping the network close to its ground state. This is achieved by initially setting all synaptic weights to zero, thus ensuring a quick transition of the Hopfield network to its trivial global minima state and then gradually introducing weights during the annealing process. The extensive numerical simulations show that our approach leads to a better, on average, solutions for several representative combinatorial problems compared to prior Hopfield neural network solvers with chaotic or stochastic annealing. As a proof of concept, a 13-node graph partitioning problem and a 7-node maximum-weight independent set problem are solved experimentally using mixed-signal circuits based on, correspondingly, a 20 × 20 analog-grade TiO2 memristive crossbar and a 12 × 10 eFlash memory array.

Global Exponential Stability of Memristive Neural Networks With Mixed Time-Varying Delays

This article investigates the Lagrange exponential stability and the Lyapunov exponential stability of memristive neural networks with discrete and distributed time-varying delays (DMNNs). By means of inequality techniques, theories of the M-matrix, and the comparison strategy, the Lagrange exponential stability of the underlying DMNNs is considered in the sense of Filippov, and the globally exponentially attractive set is estimated through employing the M-matrix and external input. Especially, when the external input is not concerned, the Lyapunov exponential stability of the corresponding DMNNs is developed immediately in the form of an M-matrix, which contains some published outcomes as special cases. Furthermore, by constructing an M-matrix-based differential system, the Lyapunov exponential stability of the DMNNs is studied, which is less conservative than some existing ones. Finally, three simulation examples are carried out to examine the validness of the theories.

Hardware Implementation of Differential Oscillatory Neural Networks Using VO 2-Based Oscillators and Memristor-Bridge Circuits

Oscillatory Neural Networks (ONNs) are currently arousing interest in the research community for their potential to implement very fast, ultra-low-power computing tasks by exploiting specific emerging technologies. From the architectural point of view, ONNs are based on the synchronization of oscillatory neurons in cognitive processing, as occurs in the human brain. As emerging technologies, VO₂ and memristive devices show promising potential for the efficient implementation of ONNs. Abundant literature is now becoming available pertaining to the study and building of ONNs based on VO₂ devices and resistive coupling, such as memristors. One drawback of direct resistive coupling is that physical resistances cannot be negative, but from the architectural and computational perspective this would be a powerful advantage when interconnecting weights in ONNs. Here we solve the problem by proposing a hardware implementation technique based on differential oscillatory neurons for ONNs (DONNs) with VO₂-based oscillators and memristor-bridge circuits. Each differential oscillatory neuron is made of a pair of VO₂ oscillators operating in anti-phase. This way, the neurons provide a pair of differential output signals in opposite phase. The memristor-bridge circuit is used as an adjustable coupling function that is compatible with differential structures and capable of providing both positive and negative weights. By combining differential oscillatory neurons and memristor-bridge circuits, we propose the hardware implementation of a fully connected differential ONN (DONN) and use it as an associative memory. The standard Hebbian rule is used for training, and the weights are then mapped to the memristor-bridge circuit through a proposed mapping rule. The paper also introduces some functional and hardware specifications to evaluate the design. Evaluation is performed by circuit-level electrical simulations and shows that the retrieval accuracy of the proposed design is comparable to that of classic Hopfield Neural Networks.

Hybrid oxide brain-inspired neuromorphic devices for hardware implementation of artificial intelligence

The state-of-the-art artificial intelligence technologies mainly rely on deep learning algorithms based on conventional computers with classical von Neumann computing architectures, where the memory and processing units are separated resulting in an enormous amount of energy and time consumed in the data transfer process. Inspired by the human brain acting like an ultra-highly efficient biological computer, neuromorphic computing is proposed as a technology for hardware implementation of artificial intelligence. Artificial synapses are the main component of a neuromorphic computing architecture. Memristors are considered to be a relatively ideal candidate for artificial synapse applications due to their high scalability and low power consumption. Oxides are most widely used in memristors due to the ease of fabrication and high compatibility with complementary metal-oxide-semiconductor processes. However, oxide memristors suffer from unsatisfactory stability and reliability. Oxide-based hybrid structures can effectively improve the device stability and reliability, therefore providing a promising prospect for the application of oxide memristors to neuromorphic computing. This work reviews the recent advances in the development of hybrid oxide memristive synapses. The discussion is organized according to the blending schemes as well as the working mechanisms of hybrid oxide memristors.

Examining Experimental Raman Mode Behavior in Mono- and Bilayer 2H-TaSe2 via Density Functional Theory: Implications for Quantum Information Science

Tantalum diselenide (TaSe2) is a metallic transition metal dichalcogenide whose structure and vibrational behavior strongly depend on temperature and thickness, and this behavior includes the emergence of charge density wave (CDW) states at very low temperatures. In this work, observed Raman modes for mono- and bilayer are described across several spectral regions and compared to those seen in the bulk case. These modes, which include an experimentally observed forbidden Raman mode and low-frequency CDWs, are then matched to corresponding vibrations predicted by density functional theory (DFT). The reported match between experimental and computational results supports the presented vibrational visualizations of these modes. Support is also provided by experimental phonons observed in additional Raman spectra as a function of temperature and thickness. These results highlight the importance of understanding CDWs since they are likely to play a fundamental role in the future realization of solid-state quantum information platforms based on nonequilibrium phenomena.

From Memristive Materials to Neural Networks

The information technologies have been increasing exponentially following Moore's law over the past decades. This has fundamentally changed the ways of work and life. However, further improving data process efficiency is facing great challenges because of physical and architectural limitations. More powerful computational methodologies are crucial to fulfill the technology gap in the post-Moore's law period. The memristor exhibits promising prospects in information storage, high-performance computing, and artificial intelligence. Since the memristor was theoretically predicted by L. O. Chua in 1971 and experimentally confirmed by HP Laboratories in 2008, it has attracted great attention from worldwide researchers. The intrinsic properties of memristors, such as simple structure, low power consumption, compatibility with the complementary metal oxide-semiconductor (CMOS) process, and dual functionalities of the data storage and computation, demonstrate great prospects in many applications. In this review, we cover the memristor-relevant computing technologies, from basic materials to in-memory computing and future prospects. First, the materials and mechanisms in the memristor are discussed. Then, we present the development of the memristor in the domains of the synapse simulating, in-memory logic computing, deep neural networks (DNNs) and spiking neural networks (SNNs). Finally, the existent technology challenges and outlook of the state-of-art applications are proposed.

Amoeba-inspired analog electronic computing system integrating resistance crossbar for solving the travelling salesman problem

Combinatorial optimization to search for the best solution across a vast number of legal candidates requires the development of a domain-specific computing architecture that can exploit the computational power of physical processes, as conventional general-purpose computers are not powerful enough. Recently, Ising machines that execute quantum annealing or related mechanisms for rapid search have attracted attention. These machines, however, are hard to map application problems into their architecture, and often converge even at an illegal candidate. Here, we demonstrate an analogue electronic computing system for solving the travelling salesman problem, which mimics efficient foraging behaviour of an amoeboid organism by the spontaneous dynamics of an electric current in its core and enables a high problem-mapping flexibility and resilience using a resistance crossbar circuit. The system has high application potential, as it can determine a high-quality legal solution in a time that grows proportionally to the problem size without suffering from the weaknesses of Ising machines.

Transiently chaotic simulated annealing based on intrinsic nonlinearity of memristors for efficient solution of optimization problems

Optimization problems are ubiquitous in scientific research, engineering, and daily lives. However, solving a complex optimization problem often requires excessive computing resource and time and faces challenges in easily getting trapped into local optima. Here, we propose a memristive optimizer hardware based on a Hopfield network, which introduces transient chaos to simulated annealing in aid of jumping out of the local optima while ensuring convergence. A single memristor crossbar is used to store the weight parameters of a fully connected Hopfield network and adjust the network dynamics in situ. Furthermore, we harness the intrinsic nonlinearity of memristors within the crossbar to implement an efficient and simplified annealing process for the optimization. Solutions of continuous function optimizations on sphere function and Matyas function as well as combinatorial optimization on Max-cut problem are experimentally demonstrated, indicating great potential of the transiently chaotic memristive network in solving optimization problems in general.

Polaritonic Neuromorphic Computing Outperforms Linear Classifiers

Machine learning software applications are ubiquitous in many fields of science and society for their outstanding capability to solve computationally vast problems like the recognition of patterns and regularities in big data sets. In spite of these impressive achievements, such processors are still based on the so-called von Neumann architecture, which is a bottleneck for faster and power-efficient neuromorphic computation. Therefore, one of the main goals of research is to conceive physical realizations of artificial neural networks capable of performing fully parallel and ultrafast operations. Here we show that lattices of exciton-polariton condensates accomplish neuromorphic computing with outstanding accuracy thanks to their high optical nonlinearity. We demonstrate that our neural network significantly increases the recognition efficiency compared with the linear classification algorithms on one of the most widely used benchmarks, the MNIST problem, showing a concrete advantage from the integration of optical systems in neural network architectures.

Long-range temporal correlations in scale-free neuromorphic networks

Biological neuronal networks are the computing engines of the mammalian brain. These networks exhibit structural characteristics such as hierarchical architectures, small-world attributes, and scale-free topologies, providing the basis for the emergence of rich temporal characteristics such as scale-free dynamics and long-range temporal correlations. Devices that have both the topological and the temporal features of a neuronal network would be a significant step toward constructing a neuromorphic system that can emulate the computational ability and energy efficiency of the human brain. Here we use numerical simulations to show that percolating networks of nanoparticles exhibit structural properties that are reminiscent of biological neuronal networks, and then show experimentally that stimulation of percolating networks by an external voltage stimulus produces temporal dynamics that are self-similar, follow power-law scaling, and exhibit long-range temporal correlations. These results are expected to have important implications for the development of neuromorphic devices, especially for those based on the concept of reservoir computing.

Biological neuronal networks exhibit well-defined properties such as hierarchical structures and scale-free topologies, as well as a high degree of local clustering and short path lengths between nodes. These structural properties are intimately connected to the observed long-range temporal correlations in the network dynamics. Fabrication of artificial networks with similar structural properties would facilitate brain-like (“neuromorphic”) computing. Here we show experimentally that percolating networks of nanoparticles exhibit similar long-range temporal correlations to those of biological neuronal networks and use simulations to demonstrate that the dynamics arise from an underlying scale-free network architecture. We discuss similarities between the biological and percolating systems and highlight the potential for the percolating networks to be used in neuromorphic computing applications.

Nonsynaptic Error Backpropagation in Long-Term Cognitive Networks

We introduce a neural cognitive mapping technique named long-term cognitive network (LTCN) that is able to memorize long-term dependencies between a sequence of input and output vectors, especially in those scenarios that require predicting the values of multiple dependent variables at the same time. The proposed technique is an extension of a recently proposed method named short-term cognitive network that aims at preserving the expert knowledge encoded in the weight matrix while optimizing the nonlinear mappings provided by the transfer function of each neuron. A nonsynaptic, backpropagation-based learning algorithm powered by stochastic gradient descent is put forward to iteratively optimize four parameters of the generalized sigmoid transfer function associated with each neuron. Numerical simulations over 35 multivariate regression and pattern completion data sets confirm that the proposed LTCN algorithm attains statistically significant performance differences with respect to other well-known state-of-the-art methods.

Logic Gate Functions Built with Nonvolatile Resistive Switching and Thermoresponsive Memory Based on Biologic Proteins

Logic gate functions built with nonvolatile resistive switching and thermoresponsive memory based on biologic proteins were investigated. The "NAND" and "NOR" functions of logic gates in soya protein devices have been built at room temperature by their nonvolatile ternary WORM resistive switching behaviors. Furthermore, heating the devices from room temperature to 358 K results in a switch from tristable state to bistable state WORM resistive switching behavior, indicating that the thermoresponsiveness can be efficiently memorized. The biologic transient nonvolatile memory device consisting of soya protein is illustrated. This device exhibits a long data retention time (104 s) and significant HRS/LRS ratio (∼105); the transient response of the current to voltage of an as-fabricated device is also explored. The soya protein based memory device on a gelatin film substrate is also assessed to validate the feasibility of degradation and biological compatibility for the implantable biological electronic device, that is, innoxious and avirulent to the human body. This can offer alternative avenues for exploring prospective bioelectronic devices.

Asymptotic Behavior of Memristive Circuits

The interest in memristors has risen due to their possible application both as memory units and as computational devices in combination with CMOS. This is in part due to their nonlinear dynamics, and a strong dependence on the circuit topology. We provide evidence that also purely memristive circuits can be employed for computational purposes. In the present paper we show that a polynomial Lyapunov function in the memory parameters exists for the case of DC controlled memristors. Such a Lyapunov function can be asymptotically approximated with binary variables, and mapped to quadratic combinatorial optimization problems. This also shows a direct parallel between memristive circuits and the Hopfield-Little model. In the case of Erdos-Renyi random circuits, we show numerically that the distribution of the matrix elements of the projectors can be roughly approximated with a Gaussian distribution, and that it scales with the inverse square root of the number of elements. This provides an approximated but direct connection with the physics of disordered system and, in particular, of mean field spin glasses. Using this and the fact that the interaction is controlled by a projector operator on the loop space of the circuit. We estimate the number of stationary points of the approximate Lyapunov function and provide a scaling formula as an upper bound in terms of the circuit topology only.

Weighted p -Bits for FPGA Implementation of Probabilistic Circuits

Probabilistic spin logic is a recently proposed computing paradigm based on unstable stochastic units called probabilistic bits ( p -bits) that can be correlated to form probabilistic circuits (p-circuits). These p-circuits can be used to solve the problems of optimization, inference, and implement precise Boolean functions in an "inverted" mode, where a given Boolean circuit can operate in reverse to find the input combinations that are consistent with a given output. In this brief, we present a scalable field-programmable gate array implementation of such invertible p-circuits. We implement a "weighted" p -bit that combines stochastic units with localized memory structures. We also present a generalized tile of weighted p -bits to which a large class of problems beyond invertible Boolean logic can be mapped and how invertibility can be applied to interesting problems such as the NP-complete subset sum problem by solving a small instance of this problem in hardware.

Exponential Stabilization of Fuzzy Memristive Neural Networks With Hybrid Unbounded Time-Varying Delays

This paper is concerned with exponential stabilization for a class of Takagi-Sugeno fuzzy memristive neural networks (FMNNs) with unbounded discrete and distributed time-varying delays. Under the framework of Filippov solutions, algebraic criteria are established to guarantee exponential stabilization of the addressed FMNNs with hybrid unbounded time delays via designing a fuzzy state feedback controller by exploiting inequality techniques, calculus theorems, and theories of fuzzy sets. The obtained results in this paper enhance and generalize some existing ones. Meanwhile, a general theoretical framework is proposed to investigate the dynamical behaviors of various neural networks with mixed infinite time delays. Finally, two simulation examples are performed to illustrate the validity of the derived outcomes.

Deep associative neural network for associative memory based on unsupervised representation learning

This paper presents a deep associative neural network (DANN) based on unsupervised representation learning for associative memory. In brain, the knowledge is learnt by associating different types of sensory data, such as image and voice. The associative memory models which imitate such a learning process have been studied for decades but with simpler architectures they fail to deal with large scale complex data as compared with deep neural networks. Therefore, we define a deep architecture consisting of a perception layer and hierarchical propagation layers. To learn the network parameters, we define a probabilistic model for the whole network inspired from unsupervised representation learning models. The model is optimized by a modified contrastive divergence algorithm with a novel iterated sampling process. After training, given a new data or corrupted data, the correct label or corrupted part is associated by the network. The DANN is able to achieve many machine learning problems, including not only classification, but also depicting the data given a label and recovering corrupted images. Experiments on MNIST digits and CIFAR-10 datasets demonstrate the learning capability of the proposed DANN.

Quasi-Hodgkin-Huxley Neurons with Leaky Integrate-and-Fire Functions Physically Realized with Memristive Devices

Artificial neurons with functions such as leaky integrate-and-fire (LIF) and spike output are essential for brain-inspired computation with high efficiency. However, previously implemented artificial neurons, e.g., Hodgkin-Huxley (HH) neurons, integrate-and-fire (IF) neurons, and LIF neurons, only achieve partial functionality of a biological neuron. In this work, quasi-HH neurons with leaky integrate-and-fire functions are physically demonstrated with a volatile memristive device, W/WO₃ /poly(3,4-ethylenedioxythiophene): polystyrene sulfonate/Pt. The resistive switching behavior of the device can be attributed to the migration of protons, unlike the migration of oxygen ions normally involved in oxide-based memristors. With multifunctions similar to their biological counterparts, quasi-HH neurons are advantageous over the reported HH and LIF neurons, demonstrating their potential for neuromorphic computing applications.

A Photoelectric-Stimulated MoS2 Transistor for Neuromorphic Engineering

The von Neumann bottleneck has spawned the rapid expansion of neuromorphic engineering and brain-like networks. Synapses serve as bridges for information transmission and connection in the biological nervous system. The direct implementation of neural networks may depend on novel materials and devices that mimic natural neuronal and synaptic behavior. By exploiting the interfacial effects between MoS₂ and AlOx, we demonstrate that an h-BN-encapsulated MoS₂ artificial synapse transistor can mimic the basic synaptic behaviors, including EPSC, PPF, LTP, and LTD. Efficient optoelectronic spikes enable simulation of synaptic gain, frequency, and weight plasticity. The Pavlov classical conditioning experiment was successfully simulated by electrical tuning, showing associated learning behavior. In addition, h-BN encapsulation effectively improves the environmental time stability of our devices. Our h-BN-encapsulated MoS₂ artificial synapse provides a new paradigm for hardware implementation of neuromorphic engineering.

Memristors for the Curious Outsiders

We present both an overview and a perspective of recent experimental advances and proposed new approaches to performing computation using memristors. A memristor is a 2-terminal passive component with a dynamic resistance depending on an internal parameter. We provide an brief historical introduction, as well as an overview over the physical mechanism that lead to memristive behavior. This review is meant to guide nonpractitioners in the field of memristive circuits and their connection to machine learning and neural computation.

Handwritten-Digit Recognition by Hybrid Convolutional Neural Network based on HfO2 Memristive Spiking-Neuron

Although there is a huge progress in complementary-metal-oxide-semiconductor (CMOS) technology, construction of an artificial neural network using CMOS technology to realize the functionality comparable with that of human cerebral cortex containing 1010-1011 neurons is still of great challenge. Recently, phase change memristor neuron has been proposed to realize a human-brain level neural network operating at a high speed while consuming a small amount of power and having a high integration density. Although memristor neuron can be scaled down to nanometer, integration of 1010-1011 neurons still faces many problems in circuit complexity, chip area, power consumption, etc. In this work, we propose a CMOS compatible HfO2 memristor neuron that can be well integrated with silicon circuits. A hybrid Convolutional Neural Network (CNN) based on the HfO2 memristor neuron is proposed and constructed. In the hybrid CNN, one memristive neuron can behave as multiple physical neurons based on the Time Division Multiplexing Access (TDMA) technique. Handwritten digit recognition is demonstrated in the hybrid CNN with a memristive neuron acting as 784 physical neurons. This work paves the way towards substantially shrinking the amount of neurons required in hardware and realization of more complex or even human cerebral cortex level memristive neural networks.

Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits

The progress in the field of neural computation hinges on the use of hardware more efficient than the conventional microprocessors. Recent works have shown that mixed-signal integrated memristive circuits, especially their passive (0T1R) variety, may increase the neuromorphic network performance dramatically, leaving far behind their digital counterparts. The major obstacle, however, is immature memristor technology so that only limited functionality has been reported. Here we demonstrate operation of one-hidden layer perceptron classifier entirely in the mixed-signal integrated hardware, comprised of two passive 20 × 20 metal-oxide memristive crossbar arrays, board-integrated with discrete conventional components. The demonstrated network, whose hardware complexity is almost 10× higher as compared to previously reported functional classifier circuits based on passive memristive crossbars, achieves classification fidelity within 3% of that obtained in simulations, when using ex-situ training. The successful demonstration was facilitated by improvements in fabrication technology of memristors, specifically by lowering variations in their I-V characteristics.

Unsupervised Hebbian learning experimentally realized with analogue memristive crossbar arrays

Conventional transistor electronics are reaching their limits in terms of scalability, power dissipation, and the underlying Boolean system architecture. To overcome this obstacle neuromorphic analogue systems are recently highly investigated. Particularly, the use of memristive devices in VLSI analogue concepts provides a promising pathway to realize novel bio-inspired computing architectures, which are able to unravel the foreseen difficulties of traditional electronics. Currently, a variety of materials and device structures are being studied along with novel computing schemes to make use of the attractive features of memristive devices for neuromorphic computing. However, a number of obstacles still have to be overcome to cast memristive devices into hardware systems. Most important is a physical implementation of memristive devices, which can cope with the high complexity of neural networks. This includes the integration of analogue and electroforming-free memristive devices into crossbar structures with no additional electronic components, such as selector devices. Here, an unsupervised, bio-motivated Hebbian based learning platform for visual pattern recognition is presented. The heart of the system is a crossbar array (16 × 16) which consists of selector-free and forming-free (non-filamentary) memristive devices, which exhibit analogue I-V characteristics.

Photonic Potentiation and Electric Habituation in Ultrathin Memristive Synapses Based on Monolayer MoS2

Monolayer of 2D transition metal dichalcogenides, with a thickness of less than 1 nm, paves a feasible path to the development of ultrathin memristive synapses, to fulfill the requirements for constructing large-scale high density 3D stacking neuromorphic chips. Herein, memristive devices based on monolayer n-MoS₂ on p-Si substrate with a large self-rectification ratio, exhibiting photonic potentiation and electric habituation, are successfully fabricated. Versatile synaptic neuromorphic functions, such as potentiation/habituation, short-term/long-term plasticity, and paired-pulse facilitation, are successfully mimicked based on the inherent persistent photoconductivity performance and the volatile resistive switching behavior. These findings demonstrate the potential applications of ultrathin transition metal dichalcogenides for memristive synapses. These memristive synapses with the combination of photonic and electric neuromorphic functions have prospective in the applications of synthetic retinas and optoelectronic interfaces for integrated photonic circuits based on mixed-mode electro-optical operation.