Avalanches and edge-of-chaos learning in neuromorphic nanowire networks

Magnetization Vector Rotation Reservoir Computing Operated by Redox Mechanism

Physical reservoir computing is a promising way to develop efficient artificial intelligence using physical devices exhibiting nonlinear dynamics. Although magnetic materials have advantages in miniaturization, the need for a magnetic field and large electric current results in high electric power consumption and a complex device structure. To resolve these issues, we propose a redox-based physical reservoir utilizing the planar Hall effect and anisotropic magnetoresistance, which are phenomena described by different nonlinear functions of the magnetization vector that do not need a magnetic field to be applied. The expressive power of this reservoir based on a compact all-solid-state redox transistor is higher than the previous physical reservoir. The normalized mean square error of the reservoir on a second-order nonlinear equation task was 1.69 × 10-3, which is lower than that of a memristor array (3.13 × 10-3) even though the number of reservoir nodes was fewer than half that of the memristor array.

Experimental Demonstration of Reservoir Computing with Self-Assembled Percolating Networks of Nanoparticles

The complex self-assembled network of neurons and synapses that comprises the biological brain enables natural information processing with remarkable efficiency. Percolating networks of nanoparticles (PNNs) are complex self-assembled nanoscale systems that have been shown to possess many promising brain-like attributes and which are therefore appealing systems for neuromorphic computation. Here experiments are performed that show that PNNs can be utilized as physical reservoirs within a nanoelectronic reservoir computing framework and demonstrate successful computation for several benchmark tasks (chaotic time series prediction, nonlinear transformation, and memory capacity). For each task, relevant literature results are compiled and it is shown that the performance of the PNNs compares favorably to that previously reported from nanoelectronic reservoirs. It is then demonstrated experimentally that PNNs can be used for spoken digit recognition with state-of-the-art accuracy. Finally, a parallel reservoir architecture is emulated, which increases the dimensionality and richness of the reservoir outputs and results in further improvements in performance across all tasks.

Few- and single-molecule reservoir computing experimentally demonstrated with surface-enhanced Raman scattering and ion gating

Molecule-based reservoir computing (RC) is promising for achieving low power consumption neuromorphic computing, although the information-processing capability of small numbers of molecules is not clear. Here, we report a few- and single-molecule RC that uses the molecular vibration dynamics in the para-mercaptobenzoic acid (pMBA) detected by surface-enhanced Raman scattering (SERS) with tungsten oxide nanorod/silver nanoparticles. The Raman signals of the pMBA molecules, adsorbed at the SERS active site of the nanorod, were reversibly perturbated by the application of voltage-induced local pH changes near the molecules, and then used to perform time-series analysis tasks. Despite the small number of molecules used, our system achieved good performance, including >95% accuracy in various nonlinear waveform transformations, 94.3% accuracy in solving a second-order nonlinear dynamic system, and a prediction error of 25.0 milligrams per deciliter in a 15-minute-ahead blood glucose level prediction. Our work provides a concept of few-molecular computing with practical computation capabilities.

Silver Nanowire Networks with Moisture-Enhanced Learning Ability

The human brain possesses a remarkable ability to memorize information with the assistance of a specific external environment. Therefore, mimicking the human brain's environment-enhanced learning abilities in artificial electronic devices is essential but remains a considerable challenge. Here, a network of Ag nanowires with a moisture-enhanced learning ability, which can mimic long-term potentiation (LTP) synaptic plasticity at an ultralow operating voltage as low as 0.01 V, is presented. To realize a moisture-enhanced learning ability and to adjust the aggregations of Ag ions, we introduced a thin polyvinylpyrrolidone (PVP) coating layer with moisture-sensitive properties to the surfaces of the Ag nanowires of Ag ions. That Ag nanowire network was shown to exhibit, in response to the humidity of its operating environment, different learning speeds during the LTP process. In high-humidity environments, the synaptic plasticity was significantly strengthened with a higher learning speed compared with that in relatively low-humidity environments. Based on experimental and simulation results, we attribute this enhancement to the higher electric mobility of the Ag ions in the water-absorbed PVP layer. Finally, we demonstrated by simulation that the moisture-enhanced synaptic plasticity enabled the device to adjust connection weights and delivery modes based on various input patterns. The recognition rate of a handwritten data set reached 94.5% with fewer epochs in a high-humidity environment. This work shows the feasibility of building our electronic device to achieve artificial adaptive learning abilities.

Tailoring Classical Conditioning Behavior in TiO2 Nanowires: ZnO QDs-Based Optoelectronic Memristors for Neuromorphic Hardware

Neuromorphic hardware equipped with associative learning capabilities presents fascinating applications in the next generation of artificial intelligence. However, research into synaptic devices exhibiting complex associative learning behaviors is still nascent. Here, an optoelectronic memristor based on Ag/TiO2 Nanowires: ZnO Quantum dots/FTO was proposed and constructed to emulate the biological associative learning behaviors. Effective implementation of synaptic behaviors, including long and short-term plasticity, and learning-forgetting-relearning behaviors, were achieved in the device through the application of light and electrical stimuli. Leveraging the optoelectronic co-modulated characteristics, a simulation of neuromorphic computing was conducted, resulting in a handwriting digit recognition accuracy of 88.9%. Furthermore, a 3 × 7 memristor array was constructed, confirming its application in artificial visual memory. Most importantly, complex biological associative learning behaviors were emulated by mapping the light and electrical stimuli into conditioned and unconditioned stimuli, respectively. After training through associative pairs, reflexes could be triggered solely using light stimuli. Comprehensively, under specific optoelectronic signal applications, the four features of classical conditioning, namely acquisition, extinction, recovery, and generalization, were elegantly emulated. This work provides an optoelectronic memristor with associative behavior capabilities, offering a pathway for advancing brain-machine interfaces, autonomous robots, and machine self-learning in the future.

Electrochemical rewiring through quantum conductance effects in single metallic memristive nanowires

Memristive devices have been demonstrated to exhibit quantum conductance effects at room temperature. In these devices, a detailed understanding of the relationship between electrochemical processes and ionic dynamic underlying the formation of atomic-sized conductive filaments and corresponding electronic transport properties in the quantum regime still represents a challenge. In this work, we report on quantum conductance effects in single memristive Ag nanowires (NWs) through a combined experimental and simulation approach that combines advanced classical molecular dynamics (MD) algorithms and quantum transport simulations (DFT). This approach provides new insights on quantum conductance effects in memristive devices by unravelling the intrinsic relationship between electronic transport and atomic dynamic reconfiguration of the nanofilment, by shedding light on deviations from integer multiples of the fundamental quantum of conductance depending on peculiar dynamic trajectories of nanofilament reconfiguration and on conductance fluctuations relying on atomic rearrangement due to thermal fluctuations.

Toward a Brain-Neuromorphics Interface

Brain-computer interfaces (BCIs) that enable human-machine interaction have immense potential in restoring or augmenting human capabilities. Traditional BCIs are realized based on complementary metal-oxide-semiconductor (CMOS) technologies with complex, bulky, and low biocompatible circuits, and suffer with the low energy efficiency of the von Neumann architecture. The brain-neuromorphics interface (BNI) would offer a promising solution to advance the BCI technologies and shape the interactions with machineries. Neuromorphic devices and systems are able to provide substantial computation power with extremely high energy-efficiency by implementing in-materia computing such as in situ vector-matrix multiplication (VMM) and physical reservoir computing. Recent progresses on integrating neuromorphic components with sensing and/or actuating modules, give birth to the neuromorphic afferent nerve, efferent nerve, sensorimotor loop, and so on, which has advanced the technologies for future neurorobotics by achieving sophisticated sensorimotor capabilities as the biological system. With the development on the compact artificial spiking neuron and bioelectronic interfaces, the seamless communication between a BNI and a bioentity is reasonably expectable. In this review, the upcoming BNIs are profiled by introducing the brief history of neuromorphics, reviewing the recent progresses on related areas, and discussing the future advances and challenges that lie ahead.

Redox-based ion-gating reservoir consisting of (104) oriented LiCoO2 film, assisted by physical masking

Reservoir computing (RC) is a machine learning framework suitable for processing time series data, and is a computationally inexpensive and fast learning model. A physical reservoir is a hardware implementation of RC using a physical system, which is expected to become the social infrastructure of a data society that needs to process vast amounts of information. Ion-gating reservoirs (IGR) are compact and suitable for integration with various physical reservoirs, but the prediction accuracy and operating speed of redox-IGRs using WO3 as the channel are not sufficient due to irreversible Li+ trapping in the WO3 matrix during operation. Here, in order to enhance the computation performance of redox-IGRs, we developed a redox-based IGR using a (104) oriented LiCoO2 thin film with high electronic and ionic conductivity as a trap-free channel material. The subject IGR utilizes resistance change that is due to a redox reaction (LiCoO2 ⟺ Li1-xCoO2 + xLi+ + xe-) with the insertion and desertion of Li+. The prediction error in the subject IGR was reduced by 72% and the operation speed was increased by 4 times compared to the previously reported WO3, which changes are due to the nonlinear and reversible electrical response of LiCoO2 and the high dimensionality enhanced by a newly developed physical masking technique. This study has demonstrated the possibility of developing high-performance IGRs by utilizing materials with stronger nonlinearity and by increasing output dimensionality.

Shaping dynamical neural computations using spatiotemporal constraints

Dynamics play a critical role in computation. The principled evolution of states over time enables both biological and artificial networks to represent and integrate information to make decisions. In the past few decades, significant multidisciplinary progress has been made in bridging the gap between how we understand biological versus artificial computation, including how insights gained from one can translate to the other. Research has revealed that neurobiology is a key determinant of brain network architecture, which gives rise to spatiotemporally constrained patterns of activity that underlie computation. Here, we discuss how neural systems use dynamics for computation, and claim that the biological constraints that shape brain networks may be leveraged to improve the implementation of artificial neural networks. To formalize this discussion, we consider a natural artificial analog of the brain that has been used extensively to model neural computation: the recurrent neural network (RNN). In both the brain and the RNN, we emphasize the common computational substrate atop which dynamics occur-the connectivity between neurons-and we explore the unique computational advantages offered by biophysical constraints such as resource efficiency, spatial embedding, and neurodevelopment.

Online dynamical learning and sequence memory with neuromorphic nanowire networks

Nanowire Networks (NWNs) belong to an emerging class of neuromorphic systems that exploit the unique physical properties of nanostructured materials. In addition to their neural network-like physical structure, NWNs also exhibit resistive memory switching in response to electrical inputs due to synapse-like changes in conductance at nanowire-nanowire cross-point junctions. Previous studies have demonstrated how the neuromorphic dynamics generated by NWNs can be harnessed for temporal learning tasks. This study extends these findings further by demonstrating online learning from spatiotemporal dynamical features using image classification and sequence memory recall tasks implemented on an NWN device. Applied to the MNIST handwritten digit classification task, online dynamical learning with the NWN device achieves an overall accuracy of 93.4%. Additionally, we find a correlation between the classification accuracy of individual digit classes and mutual information. The sequence memory task reveals how memory patterns embedded in the dynamical features enable online learning and recall of a spatiotemporal sequence pattern. Overall, these results provide proof-of-concept of online learning from spatiotemporal dynamics using NWNs and further elucidate how memory can enhance learning.

Realizing avalanche criticality in neuromorphic networks on a 2D hBN platform

Networks and systems which exhibit brain-like behavior can analyze information from intrinsically noisy and unstructured data with very low power consumption. Such characteristics arise due to the critical nature and complex interconnectivity of the brain and its neuronal network. We demonstrate a system comprising of multilayer hexagonal boron nitride (hBN) films contacted with silver (Ag), which can uniquely host two different self-assembled networks, which are self-organized at criticality (SOC). This system shows bipolar resistive switching between the high resistance state (HRS) and the low resistance state (LRS). In the HRS, Ag clusters (nodes) intercalate in the van der Waals gaps of hBN forming a network of tunnel junctions, whereas the LRS contains a network of Ag filaments. The temporal avalanche dynamics in both these states exhibit power-law scaling, long-range temporal correlation, and SOC. These networks can be tuned from one to another with voltage as a control parameter. For the first time, two different neural networks are realized in a single CMOS compatible, 2D material platform.

A scalable solution recipe for a Ag-based neuromorphic device

Integration and scalability have posed significant problems in the advancement of brain-inspired intelligent systems. Here, we report a self-formed Ag device fabricated through a chemical dewetting process using an Ag organic precursor, which offers easy processing, scalability, and flexibility to address the above issues to a certain extent. The conditions of spin coating, precursor dilution, and use of solvents were varied to obtain different dewetted structures (broadly classified as bimodal and nearly unimodal). A microscopic study is performed to obtain insight into the dewetting mechanism. The electrical behavior of selected bimodal and nearly unimodal devices is related to the statistical analysis of their microscopic structures. A capacitance model is proposed to relate the threshold voltage (Vth) obtained electrically to the various microscopic parameters. Synaptic functionalities such as short-term potentiation (STP) and long-term potentiation (LTP) were emulated in a representative nearly unimodal and bimodal device, with the bimodal device showing a better performance. One of the cognitive behaviors, associative learning, was emulated in a bimodal device. Scalability is demonstrated by fabricating more than 1000 devices, with 96% exhibiting switching behavior. A flexible device is also fabricated, demonstrating synaptic functionalities (STP and LTP).

Tomography of memory engrams in self-organizing nanowire connectomes

Self-organizing memristive nanowire connectomes have been exploited for physical (in materia) implementation of brain-inspired computing paradigms. Despite having been shown that the emergent behavior relies on weight plasticity at single junction/synapse level and on wiring plasticity involving topological changes, a shift to multiterminal paradigms is needed to unveil dynamics at the network level. Here, we report on tomographical evidence of memory engrams (or memory traces) in nanowire connectomes, i.e., physicochemical changes in biological neural substrates supposed to endow the representation of experience stored in the brain. An experimental/modeling approach shows that spatially correlated short-term plasticity effects can turn into long-lasting engram memory patterns inherently related to network topology inhomogeneities. The ability to exploit both encoding and consolidation of information on the same physical substrate would open radically new perspectives for in materia computing, while offering to neuroscientists an alternative platform to understand the role of memory in learning and knowledge.

Solving classification tasks by a receptron based on nonlinear optical speckle fields

Among several approaches to tackle the problem of energy consumption in modern computing systems, two solutions are currently investigated: one consists of artificial neural networks (ANNs) based on photonic technologies, the other is a different paradigm compared to ANNs and it is based on random networks of non-linear nanoscale junctions resulting from the assembling of nanoparticles or nanowires as substrates for neuromorphic computing. These networks show the presence of emergent complexity and collective phenomena in analogy with biological neural networks characterized by self-organization, redundancy, and non-linearity. Starting from this background, we propose and formalize a generalization of the perceptron model to describe a classification device based on a network of interacting units where the input weights are non-linearly dependent. We show that this model, called "receptron", provides substantial advantages compared to the perceptron as, for example, the solution of non-linearly separable Boolean functions with a single device. The receptron model is used as a starting point for the implementation of an all-optical device that exploits the non-linearity of optical speckle fields produced by a solid scatterer. By encoding these speckle fields we generated a large variety of target Boolean functions. We demonstrate that by properly setting the model parameters, different classes of functions with different multiplicity can be solved efficiently. The optical implementation of the receptron scheme opens the way for the fabrication of a completely new class of optical devices for neuromorphic data processing based on a very simple hardware.

Recent Advances in Cerium Oxide-Based Memristors for Neuromorphic Computing

This review article attempts to provide a comprehensive review of the recent progress in cerium oxide (CeO2)-based resistive random-access memories (RRAMs). CeO2 is considered the most promising candidate because of its multiple oxidation states (Ce3+ and Ce4+), remarkable resistive-switching (RS) uniformity in DC mode, gradual resistance transition, cycling endurance, long data-retention period, and utilization of the RS mechanism as a dielectric layer, thereby exhibiting potential for neuromorphic computing. In this context, a detailed study of the filamentary mechanisms and their types is required. Accordingly, extensive studies on unipolar, bipolar, and threshold memristive behaviors are reviewed in this work. Furthermore, electrode-based (both symmetric and asymmetric) engineering is focused for the memristor's structures such as single-layer, bilayer (as an oxygen barrier layer), and doped switching-layer-based memristors have been proved to be unique CeO2-based synaptic devices. Hence, neuromorphic applications comprising spike-based learning processes, potentiation and depression characteristics, potentiation motion and synaptic weight decay process, short-term plasticity, and long-term plasticity are intensively studied. More recently, because learning based on Pavlov's dog experiment has been adopted as an advanced synoptic study, it is one of the primary topics of this review. Finally, CeO2-based memristors are considered promising compared to previously reported memristors for advanced synaptic study in the future, particularly by utilizing high-dielectric-constant oxide memristors.

Self-Organized Memristive Ensembles of Nanoparticles Below the Percolation Threshold: Switching Dynamics and Phase Field Description

Percolative memristive networks based on self-organized ensembles of silver and gold nanoparticles are synthesized and investigated. Using cyclic voltammetry, pulse and step voltage excitations, we study switching between memristive and capacitive states below the percolation threshold. The resulting systems demonstrate scale-free (self-similar) temporal dynamics, long-term correlations, and synaptic plasticity. The observed plasticity can be manipulated in a controlled manner. The simplified stochastic model of resistance dynamics in memristive networks is testified. A phase field model based on the Cahn-Hilliard and Ginzburg-Landau equations is proposed to describe the dynamics of a self-organized network during the dissolution of filaments.

Criticality and Neuromorphic Sensing in a Single Memristor

Resistive random access memory (RRAM) is an important technology for both data storage and neuromorphic computation, where the dynamics of nanoscale conductive filaments lies at the core of the technology. Here, we analyze the current noise of various silicon-based memristors that involves the creation of a percolation path at the intermediate phase of filament growth. Remarkably, we find that these atomic switching events follow scale-free avalanche dynamics with exponents satisfying the criteria for criticality. We further prove that the switching dynamics are universal and show little dependence on device sizes or material features. Utilizing criticality in memristors, we simulate the functionality of hair cells in auditory sensory systems by observing the frequency selectivity of input stimuli with tunable characteristic frequency. We further demonstrate a single-memristor-based sensing primitive for representation of input stimuli that exceeds the theoretical limits dictated by the Nyquist-Shannon theorem.

All-ferroelectric implementation of reservoir computing

Reservoir computing (RC) offers efficient temporal information processing with low training cost. All-ferroelectric implementation of RC is appealing because it can fully exploit the merits of ferroelectric memristors (e.g., good controllability); however, this has been undemonstrated due to the challenge of developing ferroelectric memristors with distinctly different switching characteristics specific to the reservoir and readout network. Here, we experimentally demonstrate an all-ferroelectric RC system whose reservoir and readout network are implemented with volatile and nonvolatile ferroelectric diodes (FDs), respectively. The volatile and nonvolatile FDs are derived from the same Pt/BiFeO₃/SrRuO₃ structure via the manipulation of an imprint field (E_imp). It is shown that the volatile FD with E_imp exhibits short-term memory and nonlinearity while the nonvolatile FD with negligible E_imp displays long-term potentiation/depression, fulfilling the functional requirements of the reservoir and readout network, respectively. Hence, the all-ferroelectric RC system is competent for handling various temporal tasks. In particular, it achieves an ultralow normalized root mean square error of 0.017 in the Hénon map time-series prediction. Besides, both the volatile and nonvolatile FDs demonstrate long-term stability in ambient air, high endurance, and low power consumption, promising the all-ferroelectric RC system as a reliable and low-power neuromorphic hardware for temporal information processing.

Neuromorphic learning, working memory, and metaplasticity in nanowire networks

Nanowire networks (NWNs) mimic the brain's neurosynaptic connectivity and emergent dynamics. Consequently, NWNs may also emulate the synaptic processes that enable higher-order cognitive functions such as learning and memory. A quintessential cognitive task used to measure human working memory is the n-back task. In this study, task variations inspired by the n-back task are implemented in a NWN device, and external feedback is applied to emulate brain-like supervised and reinforcement learning. NWNs are found to retain information in working memory to at least n = 7 steps back, remarkably similar to the originally proposed "seven plus or minus two" rule for human subjects. Simulations elucidate how synapse-like NWN junction plasticity depends on previous synaptic modifications, analogous to "synaptic metaplasticity" in the brain, and how memory is consolidated via strengthening and pruning of synaptic conductance pathways.

The fractal brain: scale-invariance in structure and dynamics

The past 40 years have witnessed extensive research on fractal structure and scale-free dynamics in the brain. Although considerable progress has been made, a comprehensive picture has yet to emerge, and needs further linking to a mechanistic account of brain function. Here, we review these concepts, connecting observations across different levels of organization, from both a structural and functional perspective. We argue that, paradoxically, the level of cortical circuits is the least understood from a structural point of view and perhaps the best studied from a dynamical one. We further link observations about scale-freeness and fractality with evidence that the environment provides constraints that may explain the usefulness of fractal structure and scale-free dynamics in the brain. Moreover, we discuss evidence that behavior exhibits scale-free properties, likely emerging from similarly organized brain dynamics, enabling an organism to thrive in an environment that shares the same organizational principles. Finally, we review the sparse evidence for and try to speculate on the functional consequences of fractality and scale-freeness for brain computation. These properties may endow the brain with computational capabilities that transcend current models of neural computation and could hold the key to unraveling how the brain constructs percepts and generates behavior.

To be and not to be: wide-field Ca2+ imaging reveals neocortical functional segmentation combines stability and flexibility

The stability and flexibility of the functional parcellation of the cerebral cortex is fundamental to how familiar and novel information is both represented and stored. We leveraged new advances in Ca2+ sensors and microscopy to understand the dynamics of functional segmentation in the dorsal cerebral cortex. We performed wide-field Ca2+ imaging in head-fixed mice and used spatial independent component analysis (ICA) to identify independent spatial sources of Ca2+ fluorescence. The imaging data were evaluated over multiple timescales and discrete behaviors including resting, walking, and grooming. When evaluated over the entire dataset, a set of template independent components (ICs) were identified that were common across behaviors. Template ICs were present across a range of timescales, from days to 30 seconds, although with lower occurrence probability at shorter timescales, highlighting the stability of the functional segmentation. Importantly, unique ICs emerged at the shorter duration timescales that could act to transiently refine the cortical network. When data were evaluated by behavior, both common and behavior-specific ICs emerged. Each behavior is composed of unique combinations of common and behavior-specific ICs. These observations suggest that cerebral cortical functional segmentation exhibits considerable spatial stability over time and behaviors while retaining the flexibility for task-dependent reorganization.

Emerging memristive neurons for neuromorphic computing and sensing

Inspired by the principles of the biological nervous system, neuromorphic engineering has brought a promising alternative approach to intelligence computing with high energy efficiency and low consumption. As pivotal components of neuromorphic system, artificial spiking neurons are powerful information processing units and can achieve highly complex nonlinear computations. By leveraging the switching dynamic characteristics of memristive device, memristive neurons show rich spiking behaviors with simple circuit. This report reviews the memristive neurons and their applications in neuromorphic sensing and computing systems. The switching mechanisms that endow memristive devices with rich dynamics and nonlinearity are highlighted, and subsequently various nonlinear spiking neuron behaviors emulated in these memristive devices are reviewed. Then, recent development is introduced on neuromorphic system with memristive neurons for sensing and computing. Finally, we discuss challenges and outlooks of the memristive neurons toward high-performance neuromorphic hardware systems and provide an insightful perspective for the development of interactive neuromorphic electronic systems.

Edge-of-chaos learning achieved by ion-electron-coupled dynamics in an ion-gating reservoir

Physical reservoir computing has recently been attracting attention for its ability to substantially reduce the computational resources required to process time series data. However, the physical reservoirs that have been reported to date have had insufficient computational capacity, and most of them have a large volume, which makes their practical application difficult. Here, we describe the development of a Li⁺ electrolyte-based ion-gating reservoir (IGR), with ion-electron-coupled dynamics, for use in high-performance physical reservoir computing. A variety of synaptic responses were obtained in response to past experience, which were stored as transient charge density patterns in an electric double layer, at the Li⁺ electrolyte/diamond interface. Performance for a second-order nonlinear dynamical equation task is one order of magnitude higher than memristor-based reservoirs. The edge-of-chaos state of the IGR enabled the best computational capacity. The IGR described here opens the way for high-performance and integrated neural network devices.

Conduction Mechanism Analysis of Abrupt- and Gradual-Switching InGaZnO Memristors

In this work, two types of InGaZnO (IGZO) memristors were fabricated to confirm the conduction mechanism and degradation characteristics of memristors with different electrode materials. The IGZO memristor exhibits abrupt switching characteristics with the Pd electrode owing to the formation and destruction of conductive filaments but shows gradual switching characteristics with the p-type Si electrode according to the amount of generated oxygen vacancy. The electrical characteristics and conduction mechanisms of the device are analyzed using an energy band diagram and experimentally verified with random telegraph noise characteristics confirming the trap effects on the device conduction.

Dynamical properties of neuromorphic Josephson junctions

Neuromorphic computing exploits the dynamical analogy between many physical systems and neuron biophysics. Superconductor systems, in particular, are excellent candidates for neuromorphic devices due to their capacity to operate at great speeds and with low energy dissipation compared to their silicon counterparts. In this paper, we revisit a prior work on Josephson Junction-based neurons to identify the exact dynamical mechanisms underlying the system's neuronlike properties and reveal complex behaviors which are relevant for neurocomputation and the design of superconducting neuromorphic devices. Our paper lies at the intersection of superconducting physics and theoretical neuroscience, both viewed under a common framework-that of nonlinear dynamics theory.

Generation of Multi-Lobe Chua Corsage Memristor and Its Neural Oscillation

The Chua corsage memristor (CCM) is considered as one of the candidates for the realization of biological neuron models due to its rich neuromorphic behaviors. In this paper, a universal model for m-lobe CCM memristor is proposed. Moreover, a novel small-signal equivalent circuit with one capacitor is derived based on the proposed model to determine the edge of chaos and obtain the zero-pole diagrams and analyze the frequency response and oscillation mechanism of the m-lobe CCM system, which are discussed in detail. In view of existence of the edge of chaos, the frequency response and the oscillation mechanism of the simplest oscillator is analysed using the proposed model. Finally, the proposed model has exhibited some essential neural oscillation, including the stable limit cycle, supercritical Hopf bifurcation, spiking and bursting oscillation. This study also reveals a previously undiscovered behavior of bursting oscillation in a CCM system.

Quantum Conductance in Memristive Devices: Fundamentals, Developments, and Applications

Quantum effects in novel functional materials and new device concepts represent a potential breakthrough for the development of new information processing technologies based on quantum phenomena. Among the emerging technologies, memristive elements that exhibit resistive switching, which relies on the electrochemical formation/rupture of conductive nanofilaments, exhibit quantum conductance effects at room temperature. Despite the underlying resistive switching mechanism having been exploited for the realization of next-generation memories and neuromorphic computing architectures, the potentialities of quantum effects in memristive devices are still rather unexplored. Here, a comprehensive review on memristive quantum devices, where quantum conductance effects can be observed by coupling ionics with electronics, is presented. Fundamental electrochemical and physicochemical phenomena underlying device functionalities are introduced, together with fundamentals of electronic ballistic conduction transport in nanofilaments. Quantum conductance effects including quantum mode splitting, stability, and random telegraph noise are analyzed, reporting experimental techniques and challenges of nanoscale metrology for the characterization of memristive phenomena. Finally, potential applications and future perspectives are envisioned, discussing how memristive devices with controllable atomic-sized conductive filaments can represent not only suitable platforms for the investigation of quantum phenomena but also promising building blocks for the realization of integrated quantum systems working in air at room temperature.

Brain-like critical dynamics and long-range temporal correlations in percolating networks of silver nanoparticles and functionality preservation after integration of insulating matrix

Random networks of nanoparticle-based memristive switches enable pathways for emulating highly complex and self-organized synaptic connectivity together with their emergent functional behavior known from biological neuronal networks. They therefore embody a distinct class of neuromorphic hardware architectures and provide an alternative to highly regular arrays of memristors. Especially, networks of memristive nanoparticles (NPs) poised at the percolation threshold are promising due to their capabilities of showing brain-like activity such as critical dynamics or long-range temporal correlation (LRTC), which are closely connected to the computational capabilities in biological neuronal networks. Here, we adapt this concept to networks of Ag-NPs poised at the electrical percolation threshold, where the memristive properties are governed by electro-chemical metallization. We show that critical dynamics and LRTC are preserved although the nature of individual memristive gaps throughout the network is fundamentally changed by filling the gaps with an insulating matrix. The results in this work generate important contributions towards the practical applicability of critical dynamics and LRTC in percolating NP networks by elucidating the consequences of NP network encapsulation, which is considered as an important step towards device integration.

Dynamical stochastic simulation of complex electrical behavior in neuromorphic networks of metallic nanojunctions

Nanostructured Au films fabricated by the assembling of nanoparticles produced in the gas phase have shown properties suitable for neuromorphic computing applications: they are characterized by a non-linear and non-local electrical behavior, featuring switches of the electric resistance whose activation is typically triggered by an applied voltage over a certain threshold. These systems can be considered as complex networks of metallic nanojunctions where thermal effects at the nanoscale cause the continuous rearrangement of regions with low and high electrical resistance. In order to gain a deeper understanding of the electrical properties of this nano granular system, we developed a model based on a large three dimensional regular resistor network with non-linear conduction mechanisms and stochastic updates of conductances. Remarkably, by increasing enough the number of nodes in the network, the features experimentally observed in the electrical conduction properties of nanostructured gold films are qualitatively reproduced in the dynamical behavior of the system. In the activated non-linear conduction regime, our model reproduces also the growing trend, as a function of the subsystem size, of quantities like Mutual and Integrated Information, which have been extracted from the experimental resistance series data via an information theoretic analysis. This indicates that nanostructured Au films (and our model) possess a certain degree of activated interconnection among different areas which, in principle, could be exploited for neuromorphic computing applications.

Reservoir computing with 3D nanowire networks

Networks of nanowires are currently being explored for a range of applications in brain-like (or neuromorphic) computing, and especially in reservoir computing (RC). Fabrication of real-world computing devices requires that the nanowires are deposited sequentially, leading to stacking of the wires on top of each other. However, most simulations of computational tasks using these systems treat the nanowires as 1D objects lying in a perfectly 2D plane - the effect of stacking on RC performance has not yet been established. Here we use detailed simulations to compare the performance of perfectly 2D and quasi-3D (stacked) networks of nanowires in two tasks: memory capacity and nonlinear transformation. We also show that our model of the junctions between nanowires is general enough to describe a wide range of memristive networks, and consider the impact of physically realistic electrode configurations on performance. We show that the various networks and configurations have a strikingly similar performance in RC tasks, which is surprising given their radically different topologies. Our results show that networks with an experimentally achievable number of electrodes perform close to the upper bounds achievable when using the information from every wire. However, we also show important differences, in particular that the quasi-3D networks are more resilient to changes in the input parameters, generalizing better to noisy training data. Since previous literature suggests that topology plays an important role in computing performance, these results may have important implications for future applications of nanowire networks in neuromorphic computing.

Thermodynamic State Machine Network

We describe a model system—a thermodynamic state machine network—comprising a network of probabilistic, stateful automata that equilibrate according to Boltzmann statistics, exchange codes over unweighted bi-directional edges, update a state transition memory to learn transitions between network ground states, and minimize an action associated with fluctuation trajectories. The model is grounded in four postulates concerning self-organizing, open thermodynamic systems—transport-driven self-organization, scale-integration, input-functionalization, and active equilibration. After sufficient exposure to periodically changing inputs, a diffusive-to-mechanistic phase transition emerges in the network dynamics. The evolved networks show spatial and temporal structures that look much like spiking neural networks, although no such structures were incorporated into the model. Our main contribution is the articulation of the postulates, the development of a thermodynamically motivated methodology addressing them, and the resulting phase transition. As with other machine learning methods, the model is limited by its scalability, generality, and temporality. We use limitations to motivate the development of thermodynamic computers—engineered, thermodynamically self-organizing systems—and comment on efforts to realize them in the context of this work. We offer a different philosophical perspective, thermodynamicalism, addressing the limitations of the model and machine learning in general.

Superconducting disordered neural networks for neuromorphic processing with fluxons

In superconductors, magnetic fields are quantized into discrete fluxons (flux quanta Φ₀), made of microscopic circulating supercurrents. We introduce a multiterminal synapse network comprising a disordered array of superconducting loops with Josephson junctions. The loops can trap fluxons defining memory, while the junctions allow their movement between loops. Dynamics of fluxons through such a disordered system through a complex reconfigurable energy landscape represents brain-like spiking information flow. In this work, we experimentally demonstrate a three-loop network using YBa₂Cu₃O_{7 - δ}-based superconducting loops and Josephson junctions, which exhibit stable memory configurations of trapped flux in loops that determine the rate of flow of fluxons through synaptic connections. The memory states are, in turn, affected by the applied input signals but can also be externally configured electrically through control current/feedback terminals. These results establish a previously unexplored, biologically similar architectural approach to neuromorphic computing that is scalable while dissipating energy of atto Joules/spike.

Edge of Chaos in Memristor Cellular Nonlinear Networks

Information processing in the brain takes place in a dense network of neurons connected through synapses. The collaborative work between these two components (Synapses and Neurons) allows for basic brain functions such as learning and memorization. The so-called von Neumann bottleneck, which limits the information processing capability of conventional systems, can be overcome by the efficient emulation of these computational concepts. To this end, mimicking the neuronal architectures with silicon-based circuits, on which neuromorphic engineering is based, is accompanied by the development of new devices with neuromorphic functionalities. We shall study different memristor cellular nonlinear networks models. The rigorous mathematical analysis will be presented based on local activity theory, and the edge of chaos domain will be determined in the models under consideration. Simulations of these models working on the edge of chaos will show the generation of static and dynamic patterns.

Optimal reinforcement learning near the edge of a synchronization transition

Recent experimental and theoretical studies have indicated that the putative criticality of cortical dynamics may correspond to a synchronization phase transition. The critical dynamics near such a critical point needs further investigation specifically when compared to the critical behavior near the standard absorbing state phase transition. Since the phenomena of learning and self-organized criticality (SOC) at the edge of synchronization transition can emerge jointly in spiking neural networks due to the presence of spike-timing dependent plasticity (STDP), it is tempting to ask the following: what is the relationship between synchronization and learning in neural networks? Further, does learning benefit from SOC at the edge of synchronization transition? In this paper, we intend to address these important issues. Accordingly, we construct a biologically inspired model of a cognitive system which learns to perform stimulus-response tasks. We train this system using a reinforcement learning rule implemented through dopamine-modulated STDP. We find that the system exhibits a continuous transition from synchronous to asynchronous neural oscillations upon increasing the average axonal time delay. We characterize the learning performance of the system and observe that it is optimized near the synchronization transition. We also study neuronal avalanches in the system and provide evidence that optimized learning is achieved in a slightly supercritical state.

Neuromorphic behaviour in discontinuous metal films

Physical systems that exhibit brain-like behaviour are currently under intense investigation as platforms for neuromorphic computing. We show that discontinuous metal films, comprising irregular flat islands on a substrate and formed using simple evaporation processes, exhibit correlated avalanches of electrical signals that mimic those observed in the cortex. We further demonstrate that these signals meet established criteria for criticality. We perform a detailed experimental investigation of the atomic-scale switching processes that are responsible for these signals, and show that they mimic the integrate-and-fire mechanism of biological neurons. Using numerical simulations and a simple circuit model, we show that the characteristic features of the switching events are dependent on the network state and the local position of the switch within the complex network. We conclude that discontinuous films provide an interesting potential platform for brain-inspired computing.

Consciousness is supported by near-critical slow cortical electrodynamics

Mounting evidence suggests that during conscious states, the electrodynamics of the cortex are poised near a critical point or phase transition and that this near-critical behavior supports the vast flow of information through cortical networks during conscious states. Here, we empirically identify a mathematically specific critical point near which waking cortical oscillatory dynamics operate, which is known as the edge-of-chaos critical point, or the boundary between stability and chaos. We do so by applying the recently developed modified 0-1 chaos test to electrocorticography (ECoG) and magnetoencephalography (MEG) recordings from the cortices of humans and macaques across normal waking, generalized seizure, anesthesia, and psychedelic states. Our evidence suggests that cortical information processing is disrupted during unconscious states because of a transition of low-frequency cortical electric oscillations away from this critical point; conversely, we show that psychedelics may increase the information richness of cortical activity by tuning low-frequency cortical oscillations closer to this critical point. Finally, we analyze clinical electroencephalography (EEG) recordings from patients with disorders of consciousness (DOC) and show that assessing the proximity of slow cortical oscillatory electrodynamics to the edge-of-chaos critical point may be useful as an index of consciousness in the clinical setting.

In materia reservoir computing with a fully memristive architecture based on self-organizing nanowire networks

Neuromorphic computing aims at the realization of intelligent systems able to process information similarly to our brain. Brain-inspired computing paradigms have been implemented in crossbar arrays of memristive devices; however, this approach does not emulate the topology and the emergent behaviour of biological neuronal circuits, where the principle of self-organization regulates both structure and function. Here, we report on in materia reservoir computing in a fully memristive architecture based on self-organized nanowire networks. Thanks to the functional synaptic connectivity with nonlinear dynamics and fading memory properties, the designless nanowire complex network acts as a network-wide physical reservoir able to map spatio-temporal inputs into a feature space that can be analysed by a memristive resistive switching memory read-out layer. Computing capabilities, including recognition of spatio-temporal patterns and time-series prediction, show that the emergent memristive behaviour of nanowire networks allows in materia implementation of brain-inspired computing paradigms characterized by a reduced training cost.

Evolution and modulation of Ag filament dynamics within memristive devices based on necklace-like Ag@TiO2nanowire networks

Random nanowire networks (NWNs) are regarded as promising memristive materials for applications in information storage, selectors, and neuromorphic computing. The further insight to understand their resistive switching properties and conduction mechanisms is crucial to realize the full potential of random NWNs. Here, a novel planar memristive device based on necklace-like structure Ag@TiO₂NWN is reported, in which a strategy only using water to tailor the TiO₂shell on Ag core for necklace-like core-shell structure is developed to achieve uniform topology connectivity. With analyzing the influence of compliance current on resistive switching characteristics and further tracing evolution trends of resistance state during the repetitive switching cycles, two distinctive evolution trends of low resistance state failure and high resistance state failure are revealed, which bear resemblance to memory loss and consolidation in biological systems. The underlying conduction mechanisms are related to the modulation of the Ag accumulation dynamics inside the filaments at cross-point junctions within conductive paths of NWNs. An optimizing principle is then proposed to design reproducible and reliable threshold switching devices by tuning the NWN density and electrical stimulation. The optimized threshold switching devices have a high ON/OFF ratio of ∼10⁷with threshold voltage as low as 0.35 V. This work will provide insights into engineering random NWNs for diverse functions by modulating external excitation and optimizing NWN parameters to satisfy specific applications, transforming from neuromorphic systems to threshold switching devices as selectors.

Global minimization via classical tunneling assisted by collective force field formation

Simple elements interacting in networks can give rise to intricate emergent behaviors. Examples such as synchronization and phase transitions often apply in many contexts, as many different systems may reduce to the same effective model. Here, we demonstrate such a behavior in a model inspired by memristors. When weakly driven, the system is described by movement in an effective potential, but when strongly driven, instabilities cause escapes from local minima, which can be interpreted as an unstable tunneling mechanism. We dub this collective and nonperturbative effect a “Lyapunov force,” which steers the system toward the global minimum of the potential function, even if the full system has a constellation of equilibrium points growing exponentially with the system size. This mechanism is appealing for its physical relevance in nanoscale physics and for its possible applications in optimization, Monte Carlo schemes, and machine learning.

Chaos in the Real World: Recent Applications to Communications, Computing, Distributed Sensing, Robotic Motion, Bio-Impedance Modelling and Encryption Systems

Most of the papers published so far in literature have focused on the theoretical phenomena underlying the formation of chaos, rather than on the investigation of potential applications of chaos to the real world. This paper aims to bridge the gap between chaos theory and chaos applications by presenting a survey of very recent applications of chaos. In particular, the manuscript covers the last three years by describing different applications of chaos as reported in the literature published during the years 2018 to 2020, including the matter related to the symmetry properties of chaotic systems. The topics covered herein include applications of chaos to communications, to distributed sensing, to robotic motion, to bio-impedance modelling, to hardware implementation of encryption systems, to computing and to random number generation.