Near-sensor and In-sensor Computing 3031115058, 9783031115059

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Yang Chai Fuyou Liao   Editors

Near-sensor and In-sensor Computing

Near-sensor and In-sensor Computing

Yang Chai  •  Fuyou Liao Editors

Near-sensor and In-sensor Computing

Editors Yang Chai Department of Applied Physics The Hong Kong Polytechnic University Hong Kong, China

Fuyou Liao The Hong Kong Polytechnic University Shenzhen Research Institute Shenzen, China

ISBN 978-3-031-11505-9    ISBN 978-3-031-11506-6 (eBook) https://doi.org/10.1007/978-3-031-11506-6 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Contents

1

 Neuromorphic Computing Based on Memristor Dynamics����������������    1 Qingxi Duan, Zhuojian Xiao, Ke Yang, and Yuchao Yang

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Short-Term Plasticity in 2D Materials for Neuromorphic Computing������������������������������������������������������������������������������������������������   33 Heejun Yang

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 Bioinspired In-Sensor Computing Devices for Visual Adaptation������   55 Fuyou Liao and Yang Chai

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 Neuromorphic Vision Based on van der Waals Heterostructure Materials ��������������������������������������������������������������������������������������������������   67 Shuang Wang, Shi-Jun Liang, and Feng Miao

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Neuromorphic Vision Chip���������������������������������������������������������������������   81 Liyuan Liu, Mingxin Zhao, Ke Ning, Xu Yang, Xuemin Zheng, and Nanjian Wu

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Collision Avoidance Systems and Emerging Bio-inspired Sensors for Autonomous Vehicles ����������������������������������������������������������  121 Darsith Jayachandran and Saptarshi Das

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Emerging Devices for Sensing-Memory-­Computing Applications����������������������������������������������������������������������������������������������  143 Lin Chen, Tianyu Wang, Jialin Meng, Qingxuan Li, Yuqing Fang, and Jiajie Yu

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 Neural Computing with Photonic Media����������������������������������������������  199 Erfan Khoram, Zhicheng Wu, and Zongfu Yu

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Multimodal Sensory Computing������������������������������������������������������������  225 Sijie Ma, Fuyou Liao, and Yang Chai

Index������������������������������������������������������������������������������������������������������������������  239

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Chapter 1

Neuromorphic Computing Based on Memristor Dynamics Qingxi Duan, Zhuojian Xiao, Ke Yang, and Yuchao Yang

1.1 Introduction In recent years, deep learning technology has made great progress, especially in image and video recognition and natural language processing [1–3]. Unlike previous scientific computing tasks involving a small amount of data, the artificial neural network (ANN) algorithm involves heavy vector matrix multiplication, requiring a large amount of data movement in the traditional von Neumann hardware with separation of storage and computing, thus limiting computational throughput and energy efficiency. In order to solve this problem, a direct technical route is to break the boundary between computing and storage and perform VMM operations in the storage array. In order to solve this problem, a direct technical route is to break the boundary between computing and storage and perform VMM operations in the memory array. Memristor is a new principle nano-device with resistive switching behavior, which was realized in experiment by HP in 2008 [4]. Memristor has the characteristics of fast operation speed, low power consumption, scalability, good reliability, simple manufacturing process, and so on, which has been widely favored

Q. Duan · Z. Xiao · K. Yang Key Laboratory of Microelectronic Devices and Circuits (MOE), Department of Micro/ Nanoelectronics, Peking University, Beijing, China Y. Yang (*) Key Laboratory of Microelectronic Devices and Circuits (MOE), Department of Micro/ Nanoelectronics, Peking University, Beijing, China Center for Brain Inspired Chips, Institute for Artificial Intelligence, Peking University, Beijing, China Center for Brain Inspired Intelligence, Chinese Institute for Brain Research (CIBR), Beijing, Beijing, China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 Y. Chai, F. Liao (eds.), Near-sensor and In-sensor Computing, https://doi.org/10.1007/978-3-031-11506-6_1

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[5, 6]. Its emergence provides a new course to develop non-von Neumann computing architecture with strong computing capability and high energy efficiency. In general, each crosspoint of the crossbar array is a memristive device. The Vj is the voltage applied in the jth column. According to Ohm’s law and Kirchhoff’s law, m

the total of the ith row is described as I i  Gij  V j , where Gij is the conductancevj 1

alue of the memristive device located in the jth column and the ith row. Based on this theory, the memristive crossbar array plays an important role in accelerating VMM operation, where the memristive device at each crosspoint can store the weight matrix value. The input and output of the network are connected to the rows and columns of the crossbar array, respectively. During the inference process, the read voltage pulse is inputted to the row corresponding to the input signal, and the output current of the crossbar is collected in the column. The VMM operation of the memristor crossbar array has high parallelism, which brings excellent computing throughput and high energy efficiency [7]. In addition, the conductance of the memristive device can be adjusted by positive or negative pulses with special update rules, allowing the system to use training algorithms to achieve online learning. Based on this principle, the acceleration of perceptrons [7–9], convolutional neural networks (CNN) [10, 11], long short-term memory (LSTM) [12], Hopfield networks [13], and so on have been implemented. Similarly, VMM based on memristors can also be used in the hardware implementation of other machine learning algorithms, including K-means clustering [14], sparse coding [15], and partial differential equation solving in scientific computing tasks [16] and matrix equation solving [17]. These works demonstrate the potential of memristor arrays to accelerate linear operations utilizing physical laws. However, compared with biological neural networks, artificial neural networks have high power consumption, simple tasks, and limited cognitive ability. This may be because ANN is a highly simplified and abstract model of the nervous system and many key dynamic characteristics of the brain as a high-dimensional nonlinear system are ignored in the modeling process. The construction of neuromorphic systems in the real sense will be based on the understanding of the brain as a high-­ dimensional nonlinear system. As shown in Fig. 1.1, in the human nervous system, the human brain performs various computational functions, such as recognition, memorization, and even creation, through the activities of numerous biological neural networks. Our brain, a huge system with hundreds of billions of neurons, and each neuron are connected with tens of thousands of synapses, which is an advanced intelligent system with low power consumption, high density, and high tolerance for parallel computing [18–20]. Therefore, learning from the brain’s architecture and information processing methods, neuromorphic computing merging computing and memory has become the research mainstream [21]. The basic and most important part of the brain-inspired computing system is the neuromorphic devices. Fortunately, the rich ion dynamic gives memristor a much more complicated nonlinear space and time evolution behavior. For example, the transportation and diffusion process of ions in memristor is similar to that in biological synapses and neuron. The physical

1  Neuromorphic Computing Based on Memristor Dynamics

Biological synapse

Biological neuron

Artificial synapse

Artificial neuron Synaptic weight

∑

Biological Biollogiicall neuronall network

Artificial neuronal network

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Human brain

Neuromorphic system

Output neuron

Activation

Fig. 1.1  Comparison of the human nervous system and artificial neural system in neuromorphic devices

similarity gives memristor the ability to mimic many information processing functions of synapses and neuron such as long-term plasticity (LTP), short-term plasticity (STP), and leaky integrate-and-fire (LIF). By integrating these memristor-based highly efficient signal processing units, many neuromorphic computing systems like spiking neural network (SNN), chaotic neural network, and attractor neural network have been built. Neuromorphic computing systems with memristor have lower scale and power consumption as well as better tolerance to the defects of the computing system when compared to COMS-based method. This chapter reviews the memristor using its rich dynamics to emulate the performance of synapses and neurons and their applications in the construction of neuromorphic dynamic systems. We first showed how to use memristor dynamics to emulate artificial synapses and artificial neurons. It further summarizes typical examples of neuromorphic systems based on memristor dynamics, including memristive reservoir, memristive oscillatory neural network, memristive continuous attractor neural network, memristive spiking neural network, and memristive chaotic computing. Finally, we give an outlook for the development of neuromorphic dynamic systems.

1.2 Artificial Synapses Synapses are important parts where cells contact and transmit information with each other. The realization of emulating the synapses in hardware is also a key step in neuromorphic computing. Here, memristors are considered as the first choice to

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emulate the synapses, due to  their simple structure, high  speed, low power consumption, high density, continuous conductance states, and compatibility with CMOS processes [22–25]. One of the important characteristics of synapses is synaptic plasticity, which is also the biological basis of human learning and memory activities. At the same time, for the artificial neural network, it mainly uses the learning and memory functions of neural cells, so it is necessary to apply the relevant theories about synaptic plasticity. Synaptic plasticity mainly includes short-term plasticity and long-term plasticity. Short-term plasticity refers to a behavior that increasing or inhibiting synaptic strength lasts for only a few hours or days after the stimulus. It plays an important role in attracting attention, sleep rhythms, memory and learning [26, 27], etc. Meanwhile, it is also important for processing time information on related time scales. Long-term plasticity refers to a behavior that increasing or inhibiting synaptic strength lasts for several hours or several days after the stimulus. It is not only the main mechanisms that learning and memory in the brain [28, 29] but also meets the requirement to continuously adjust the weights when training neural networks [15]. Therefore, using hardware to emulate synaptic plasticity is also the key to emulating biological synapses.

1.2.1 Long-Term Plasticity Long-term plasticity was first reported by Bliss and his colleagues in 1973 [30]. They found that continuous stimulus of excitatory synapses in the hippocampus leads to increase the synaptic weights, which can last for hours or even days, so a phenomenon was defined as long-term potentiation (LTP). As further research found, in addition to LTP, it also accompanied the existence of long-term depression (LTD). Therefore, the methods for realizing LTP and LTD using synaptic devices have been proposed in recent years. In 2010, the research group of Wei Lu [31] used an Ag:Si/Si device to achieve LTP and LTD. The device can still maintain a stable LTP and LTD characteristics after 108 repeated cycles. Similar behavior can also be seen in VCM memristors like TaOx-based memristors [32]. But it needs to be pointed out that for most filamentary-type memristors, the process suffers from the nonlinearity issues, which will influence the performance of memristive device-­ based synapse in the network. Fortunately, the nonlinearity issues can be alleviated through the  innovation of structure mechanism and operation method. The diffusion limiting layer (DLL) can be introduced into the device to solve the nonlinearity issues. For example, the DLL SiO2 was introduced to form a SiO2/TaOx bilayer structure [32]. The inserted DLL effectively limits the ion migration rate to reduce the number of ions involved at the beginning of weight update, thereby suppressing the abrupt process of filament formation and optimizing the weight update linearity. Figure 1.2a shows great linear long-term plasticity in ion-gated synaptic devices based on 2D materials [33] which is achieved by gate bias-controlled Li+ ion motion. Also, Fig. 1.2b further

1  Neuromorphic Computing Based on Memristor Dynamics

a

Long-term plasticity b

g

5 Short-term plasticity h

Synapse c

d

i

e

f

j

k

Fig. 1.2 (a) Continuous LTP and LTD process in the ion-gated synaptic device based on 2D materials. (b) Continuous LTP and LTD process by programming of an ionic floating-gate cell at different write voltages. (c) STDP behavior using the TiN/SiO2–1 nm/TaOx/Pt device. The inset shows the applied pulse scheme. (d) Triplet-STDP results in Pt/WO3 − x/W memristors, where potentiation or depression with different synaptic weights is obtained using different spike sequences and different timing intervals. The insets show the schematic of “post-pre-post” and “pre-post-pre” sequences. (e) Schematic of a three-terminal device structure for emulating heterosynaptic plasticity. (f) Multi-terminal memtransistors mimicking heterosynaptic plasticity. (g) Short-term potentiation observed in diffusive memristor. (h) Short-term potentiation observed in WO3-based VCM memristors. (i) Short-term potentiation converts to long-term potentiation in Li+-based WSe2 transistors. (j) SRDP behavior in artificial synapse based on Li+-based WSe2 transistors by changing the width of the pulse. (k) SRDP behavior in artificial synapse based on the diffusive memristor and drift memristor by modifying the duration between the applied pulses

shows good linearity of an ionic floating-gate cell [34] at different write voltages, indicating great potential in this kind of device. As one of the manifestations of long-term plasticity, the spiking time-dependent plasticity (STDP) rule is the basic mechanism of learning and memory. When pre-­ synaptic stimuli are applied prior to post-synaptic stimuli, synaptic weights are strengthened, that is, LTP is increased. When the post-synaptic stimuli is applied later than pre-synaptic stimuli, the synapse weights are weakened, that is, the LTD is decreased [35]. As shown in Fig. 1.2c, by applying carefully designed voltage spikes on both pre-synaptic and post-synaptic terminals in TiN/SiO2(1 nm)/TaOx/Pt device [32], the time difference between pre-synaptic and post-synaptic spikes can be converted to the height of the overlapping spikes. In the results, this above pulse application scheme can lead to different conductance states related to spike time. This behavior is similar to the STDP behavior observed in the organism. In parallel with the pair-based STDP rules introduced above, the triplet-STDP rule is considered as another important property of the synapse [36–38] in which the change of synaptic strength is involved with three action potentials. Triplet-STDP can reflect the unavoidable interaction of spike pairs in a spike train through the short-term suppression effect. The triplet-STDP can be implemented using second-order

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memristors [39] with one state variable governing short-term dynamics similar to the biological neural system as shown in Fig. 1.2d. Besides, another long-term plasticity is heterosynaptic plasticity, in which the synaptic behavior can be regulated by the third modulatory terminal. The schematic structure is shown in Fig. 1.2e, which plays an important role in biological learning functions, including associative learning, long-term plasticity, etc. [40]. By modulating the voltage on the third electrode to change the distribution of the internal electric field of the device, it can affect the ion transport in the switching layer and effectively regulate the growth dynamics of the filament. Meanwhile, similar behavior was observed in MoS2-based multi-terminal memtransistors [41], which allow facile tuning through the modulation of the local Schottky barrier at each terminal and heterosynaptic plasticity through the gate electrode as illustrated in Fig. 1.2f.

1.2.2 Short-Term Plasticity The short-term potentiation (STP) and short-term depression (STD), or equivalently called short-term plasticity, are a temporary potentiation/depression of neural connections. While the long-term plasticity is believed to be related to learning and memory functions, the short-term plasticity is thought to perform critical computational function relevant to spatiotemporal information processing in biological neural system. By taking advantage of the volatility of memristive devices, the short-term plasticity can be successfully implemented, for example, Ag-based diffusive memristor (shown in Fig. 1.2g) [42], WO3-based VCM memristors (shown in Fig. 1.2h) [43], and Li+-based WSe2 transistors (shown in Fig. 1.2i) [33], which both use the instability of the ion movement to form a conductive path in the device to achieve short-­ term plasticity. Besides, STP can be converted to LTP through repeated rehearsals, which involves a physical change in the structure of synapse [33], as shown in Fig. 1.2i. In biology, synaptic plasticity behavior based on pulse frequency is also very common, which is called spiking-rate-dependent plasticity (SRDP). In the test, by changing the width of the pulse [33] or modifying the duration between the applied pulses [42], the change of the channel conductance is observed, as shown in Fig. 1.2j and k.

Fig. 1.3 (continued) reset to the initial state after its conductance reaching a threshold. (i) Schematic of a metal-oxide-based artificial dendrite and its nonlinear current responses to the applied voltage which show integration and filtering property. ((b–d) Reproduced with permission [47]. Copyright 2012, Springer Nature. (e–g) Reproduced with permission [49]. (h) Reproduced with permission [50]. Copyright 2020, Springer Nature. (i) Reproduced with permission [51]. Copyright 2020, Springer Nature)

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Fig. 1.3 (a) A schematic diagram of biological neuron which is composed of dendrites, a soma, and an axon. (b) The thresholding switching character of NbOx under voltage sweeping, with a typical scanning electron micrograph in the inset. (c) Circuit diagram of the memristive H-H neuron. The channels are emulated by Mott memristors; each is paralleled with a and is biased with opposite polarity voltage sources. (d) Experimental and simulated spike outputs of the memristive H-H neuron with different circuit parameters. (e) Illustration of an ion channel embedded in cell membrane of a biological neuron. The leaky integrate-and-fire (LIF) circuit with the NbOx device is proposed to mimic the biological membrane. (f) Characterization of the LIF neuron under a continuous pulse train and the influence of varying capacitance (Cm) and resistance (RL). (g) The firing response of the spiking neuron under different input and circuit conditions. (h) Response of phase-change device conductance when applied a series of crystallizing pulses, which allows the integrate-and-fire dynamics in a phase-change neuron. The phase-change device is automatically-

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1.3 Artificial Neuron As mentioned above, the memristive devices to emulate artificial synapse have been made in significant progress, and abundant synaptic functions have been emulated in a single compact memristive device. In biology, neuron is a nonlinear processing unit serving as the building block of the nervous systems. Aiming at the biological neuron, it can be basically divided into three parts (Fig. 1.3a) [44]. The first one is the input area receiving external information inputted through receptors on the cell or dendritic membrane. The second one is the integrated information area, which can add up numerous post-synaptic potentials in the cell and generate action potentials when threshold potentials are reached; the third one is the information transmission area, conducting action potentials through axons. The basic characteristics of neuron include all-or-nothing action potentials, refractory period, threshold-­ driven spiking, strength-modulated spike frequency, and so on. Affected by the composition, distribution, and characteristics of the ion channels and even space shape of the cell, more than 20 different spiking modes have been found in the experiment, which is also an important basis for emulating the neuron function [45]. Therefore, the realization of artificial neurons is also fundamentally important for implementing artificial neuromorphic systems.

1.3.1 H-H Neuron The Hodgkin-Huxley (H-H) model [46] is the most accurate and complex neuron model based on the electrochemical process of biological neurons, which can well approximate the various spiking behaviors of biological neurons. It is a four-­ dimensional continuous model composed of differential equations describing the conductance of each ion channel on the cell membrane, two of which are gated variables serving as abstraction for Na+ and K+ ion channels, respectively. As shown in Fig. 1.3b and c, two of the NbOx memristors have a parallel capacitor and are powered by a DC power source of opposite polarity to emulate the opening and closing of Na+ and K+ ion channels in the model [47]. It can capture complex neural dynamics, including the all-or-nothing spiking, bifurcation threshold to a continuous spiking regime, signal gain, and refractory period (Fig. 1.3d). Further, up to 23 types of known biological neuron spiking behaviors have been reported in the Mott H-H neuron [48].

1.3.2 LIF Neurons The abovementioned H-H neuron based on Mott memristor can reproduce the firing behavior of biological neurons with its rich dynamic characteristics and has a higher area and energy efficiency than H-H neurons based on CMOS circuits [47, 48].

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However, based on the characteristics that neuron must exceed a certain threshold potential to generate action potentials, some people have considered the dynamic process of neurons as an integrated process and combine with a mechanism that triggers action potentials above the threshold voltage, creating a LIF model to emulate biological neuron function. The LIF model is relatively simple and only describes the process of generating action potentials, which not include the process of ion dynamics. Therefore, hardware realization of LIF model using emerging two terminal devices is attractive due to its high scaling potential and high efficiency [52]. To date, a LIF neuron was reported by a Pt/Ti/NbOx/Pt/Ti threshold switching (TS) device connected in series with a resistor and a capacitor in parallel, as shown in Fig. 1.3e [49]. The TS behavior of NbOx devices can mimic the dynamic of an ion channel located near the soma of a neuron, while the membrane capacitance and axial resistance are composed of Cm and RL. When an input pulse is applied to this LIF neuron, the capacitor (Cm) begins to charge, and most of the voltage drops on the NbOx device (ROFF > RL). When the voltage across the NbOx device reaches its Vth, the device switches from HRS to LRS.  At this time, the capacitor begins to discharge, but when the voltage across the device drops to its Vhold, the NbOx device returns to HRS, resulting in a current spike (Fig. 1.3f). Further, the leaky integrate-­ and-­fire response of this neuron can be adjusted by changing the parameters of the circuit around the device. As shown in Fig 1.3f, g, a smaller Cm makes the integration process faster, and a larger RL makes the charge process slower, hence delaying or preventing the firing. In addition, a series of pulses with different amplitudes (1, 1.1, 1.2, and 1.3 V) and pulse width (0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.5 μs) are applied to the artificial neuron, as shown in Fig. 1.3g. The spiking frequency increases significantly with the input pulse amplitude/width increases. At the same time, when the amplitude/width of the input pulse is fixed, but the pulse interval is different, it finds that the smaller the pulse interval, the higher the firing frequency. Moreover, the spiking frequency decreases as the pulse interval increases due to leakage of the charge through the Pt/Ti/NbOx/Pt/Ti device in parallel with Cm, thus implementing the leaky dynamics in a LIF neuron. As can be seen from the above structure, the three important elements to emulation of LIF neurons are to realize leaky, integration, and fire in the hardware. Therefore, we have summarized how to use device dynamics to achieve these three elements. First, leaky characteristic can be emulated by the relaxation process in the device, including heat dissipation in Mott devices [49, 53], ion diffusion in diffused memristors [42], and spontaneous depolarization in the ferroelectric layer [54–56] and backward ion diffusion in ion-gated transistors [57]. The leakage dynamics in artificial neurons is an important basis for the spatiotemporal integration of signals and nonlinear calculation functions. Second, various methods have been proposed to realize integration characteristics using the nonlinear internal physical processes in memristors. For example, when a voltage pulse is applied to Mott memristors, the current generated heats the Mott material and induces thermal accumulation [49, 58]. The migration of ions under an electric field in metal ion-based redox memristors and the formation of conductive filaments can be regarded as an integration process [42]. In addition, the gradual reversal process of ferroelectric domains in

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ferroelectric materials under voltage pulses [54–56] and the growth of the crystalline phase during incremental amorphous to crystalline phase transition induced by electrical pulses in PCM [50] can also naturally realize the accumulation dynamics. The integration function of artificial neurons can also be realized in some emerging devices. For example, the process of electrochemical doping of ions under an electric field in ion-gate transistors can also emulate the integration dynamics [57], and the distance in skyrmion can also be used as a cumulative state variable [59]. Third, on the one hand, the rising edge of the action potential is triggered by the strong nonlinear transition process in the memristor, such as the formation of conductive filaments in the Mott memristor [49, 53], diffusion memristor [42], and PCM [50], which can cause the abrupt increase of conductance in the devices. It can also be induced by the sudden switch-on of the field effect transistor as a result of sufficient ferroelectric polarization in FeFET [54–56]. On the other hand, the dropping edge of the action potential often comes originates from a volatile inverse process, such as the metal-insulator transition in Mott memristors [49, 53] or the minimization of interfacial energy between the Ag and dielectric that caused the rupture of Ag filaments [42]. It should be noted that not all devices can spontaneously realize the firing characteristics and need to add other circuit modules for assistance. For example, in Fig. 1.4h, because the phase-change neuron does not have the characteristic of spontaneously returning to the high-resistance state due to its nonvolatile nature, an external reset circuit needs to be added to return the device to the resting state [50]. In addition, the special electrochemical mechanism in biology also brings a variety of advanced neuronal functions, such as spatiotemporal integration and gain modulation characteristics. A fundamental computation performed by a neuron is to convert incoming synaptic information into a specific spike pattern at output [60]. An important step in this transformation is the neuronal integration, which includes adding simultaneous events through different synapses (spatial summation) and adding non-simultaneous events (temporal summation) [61, 62]. Using the Fig. 1.4a circuit, the spatiotemporal integration capabilities were emulated by NbOx volatile memristor. Figure 1.4b is a schematic diagram of the integration of two pre-synaptic inputs with synchronized stimuli. When only one input is applied to S1 or S2, the firing frequency of neuron is low, but when two pre-synaptic inputs are applied simultaneously, the firing frequency increases significantly, thus achieving spatial summation (Fig. 1.4c). Meanwhile, the spatial summation can be extended to various input strengths, as shown in Fig. 1.4d. Similarly, when the input pulse frequency changes with the pulse interval, the amplitude, width, and number are fixed, and the spatial summation can also be observed (Fig. 1.4e). At the same time, two time-­ dependent pulse sequences are applied to S1 and S2, respectively (Fig. 1.4f), and it finds that the firing frequency is a function of the time interval between the two pulse sequences. These NbOx neurons can also realize the spatiotemporal summation, which is essential for spike time-dependent logic and neural computation emulations. At the same time, individual neurons have more complex nonlinear operations. These nonlinear mechanisms enable neurons to perform a series of arithmetic operations, thus providing powerful computing power for simple neurons. Gain

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Fig. 1.4 (a) The circuit diagram to achieve LIF neuron functions using NbOx device. (b) Schematic diagram of the regulation of spatial summation with different input pulse amplitudes. (c) The firing response of LIF neuron by two input pulses applied on S1 and S2 individually and simultaneously. (d) The spatial summation results plotted as 3D surface by two input pulses applied on S1 and S2 simultaneously with different amplitudes. (e) The spatial summation results plotted as 3D surface by two input pulses applied on S1 and S2 simultaneously with different intervals. (f) The spatial summation results by adjusting the time interval between the two pulse sequences. (g) Schematic diagram of the rate-coded neuronal signaling. The driving input and the modulatory input (shown in red) affect to output firing rate (shown in blue). (h) The firing spikes triggered by only driving input (1.2 V amplitude, 1 μs width, interval 0.4 μs) applied on S1 are shown in the bottom of the figure. The other curve is the firing spikes triggered by the driving input (1.2 V amplitude) and modulatory input (1 μs width, interval 0.4 μs) with different amplitudes of 0.4, 0.5, 0.6, and 0.7 V applied simultaneously. (i) The curve can be multiplicatively tuned by the modulatory input (0.4, 0.5, 0.6, and 0.7 V). (Reproduced with permission [49]. Copyright 2020, Springer Nature)

modulation was demonstrated in a single artificial neuron [49]. The gain modulation of neuron is the approximate multiplicative or divisive change in the tuning curve of a neuron to stimulus parameters, as other parameters or state change [60]. Using the circuit diagram of Fig. 1.4a, a series of pulses are applied on the S1 (amplitude in 1.2 V, width in 1 μs, interval in 0.4 μs, repeat for ten cycles) as the driving input for NbOx neurons, and another series of pulse sequences (amplitude in 0.4, 0.5, 0.6, 0.7 V, width in 1 μs, interval in 0.4 μs, repeat for ten cycles) are applied on the S2 as modulatory input, as shown in Fig. 1.4g. One can see the firing spike count is 0 by

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only applying the driving input, while the firing spike count is 5, 8, 9, and 9 by applying the driving input and modulatory input simultaneously, where the voltages of the modulatory input correspond to m = 0.4 V, 0.5 V, 0.6 V, and 0.7 V, respectively (Fig.  1.4h). Figure  1.4i systematically shows the input-output relationship with the driving input and modulatory input, implying input gain modulation when m is adjusted.

1.3.3 Oscillation Neuron Neural oscillation is a rhythmic or repetitive neuronal activity in the central nervous system. This oscillation is mainly triggered by a single neuron or the interaction between neurons. Meanwhile, it also plays an important role in brain activities, including feature binding, frequency-encoded information transmission mechanisms, and the generation of rhythm [63–65]. Therefore, it is of great significance to realize the emulation of oscillation neurons in hardware in order to build a neuromorphic intelligent hardware system. So far, by connecting a Mott memristor (such as NbOx or VO2) in series with a resistor, the oscillation neurons have been realized by applying a long voltage bias as an input [21, 66, 67]. In addition, the nanoscale magnetic tunnel junction driven by the direct current input uses the mechanism of continuous magnetization precession through the effect of spin torque, thereby constructing a nonlinear self-­ sustaining oscillator that mimics the periodic spike activity of biological neurons [68]. Oscillation neurons can also be used as building blocks for coupled oscillatory networks, as will be described below.

1.3.4 Artificial Dendrites Recent studies in neuroscience have shown that the dendrites in neurons also play a vital role in the processing of information in addition to the simple information transmission function traditionally believed [69–71]. Meanwhile, the  dendrites occupy a large proportion of the volume in the nervous system, and the fact that dendrites themselves can perform calculations, which indicates that our brain’s computing power is hundreds of times stronger than we expected. Therefore, integrating dendritic computing into the neuromorphic system can further greatly increase the computing power of the system. Specifically, the computing of dendrites is reflected in the integration of spatial and temporal information in a nonlinear manner [72, 73] while filtering out noise and background information to avoid the extra energy overhead caused by unimportant information. These functions have been successfully emulated by Pt/TaOx/AlOδ/Al memristors. The conductance state of the device can be reversibly switched by modulating the interfacial Schottky barrier induced by the drift of oxygen ions under the electric field [51]. As shown in

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Fig. 1.4h, the memristor dendrites can filter out small input voltages in the off state while nonlinearly accumulating the signals after switching on by a large stimulus. Further, recognition task from a natural noisy background has been reported. The recognition accuracy of the SVHN dataset is increased from ~79% to more than 87% by incorporating dendritic functions. An extra low power consumption is ~7.84  mW, which is more than 70× lower than that of a typical ASIC chip. Meanwhile, the total energy consumption with artificial dendrites is ~39.2 μJ, more than 1000× lower than that of the CPU (~18 mJ).

1.4 Memristor-Based Neuromorphic Computing Systems 1.4.1 Memristive Reservoir Computing Systems Reservoir computing (RC) is a neuromorphic computing inspired by the biological system. Neurons in the brain generate transient patterns when excited by input sensory signals. By mimicking this operating mode, RC holds extraordinary advantages in processing temporal information [74, 75]. As shown in Fig.  1.5a, a reservoir computing system consists of three parts, namely, input, reservoir, and readout layer. The input signals u(t) are randomly connected to the neurons in the reservoir. The reservoir, containing a large number of neuron nodes, is a recurrent network with feedback loops connected by the nodes. These nodes not only have the ability to process information nonlinearly but also have short-term memory. The input signals u(t) exciting the reservoir to transient state are held by the state of each neuron, denoted as x(t). The neuron states of reservoir x(t) are a high-dimensional space, also known as feature space. The process of input signals exciting the reservoir to transient state can be regarded as projection of u(t) from a low-dimensional space to x(t) in a high-dimensional feature space. Subsequently, these neuron states are read out by a linear weighted sum via the output layer with matrix θ. θ is the only parameter(s) that needs to be determined by training process, which greatly reduces the training workload. The troublesome training procedures of the recurrent network are avoided by keeping the connection strength in the reservoir unchanged during the training process. As previously mentioned, physical implementation of a reservoir requires nonlinear responses and short-term memory features, while these characteristics can be easily found in the family of memristors. For example, a number of redox-based memristors display nonlinear conductance modulations under identical external pulses as well as short-term memory due to spontaneous diffusion of internal ions [42, 43, 78, 79]. Other memristive devices such as phase-change devices [80], spin-­ torque devices [81], as well as leaky ferroelectric devices [54, 55] are utilized as a physical reservoir due to their rich dynamics. As shown in Fig. 1.5b, memristive reservoir computing was realized on a 32 × 32 WOx memristor array by performing a speech recognition task on NIST TI46 dataset and solving a time-series forecasting task [76]. In this implementation, the input

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Fig. 1.5 (a) Schematic of a reservoir computing system which consists of input layer, reservoir, and readout layer. (b) Schematic of the device structure, showing the W bottom electrode, WOx switching layer, SiO2 spacer, and the Pd/Au top electrode. Inset: A zoomed-in scanning electron microscopy image of the 32 × 32 memristor array. Scale bar: 3 μm. (c) Temporal response of WOx memristors to the spike trains. The input is encoded in the spike trains which excite the memristor to different conductance states and realize feature mapping of a reservoir. (d) Temporal response of spintronic memristors to the spike trains. The information is encoded in the voltage amplitude which excites the memristor to oscillate with different amplitudes and realize feature mapping of a reservoir. ((a, b) Reproduced with permission [76]. Copyright 2019, Springer Nature. (c) Reproduced with permission [77]. Copyright 2017, Springer Nature)

data (such as isolated spoken digit “0”) are transformed into digitalized spike trains, which in turn excite the device to separable conductance states (Fig.  1.5c). Nevertheless, because of the limited conductance states of a single device, long temporal sequence may not be distinguishable by a final reading after the pulse train, which can thus degrade the overall performance of the reservoir computing system. A variety of strategies have been proposed to solve this problem, including a segmentation of the long input sequences [76, 82], utilization of devices with various relaxation constants to extract the correlation in different time scales [83, 84],

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and copying the inputs as pulse streams with different frequencies, which significantly improved the ability of hardware reservoir computing system. The features mapped into the device conductance can be read out and processed by a linear classifier for the final classification or synthesis so that the process can also be accelerated by nonvolatile memristor crossbar architecture [82]. Time multiplexing is an important idea to simplify the hardware of the reservoir. Specifically, the spatially interconnected nodes can be replaced by temporally interacted virtual nodes, which can be enabled by a single nonlinear dynamic node with short-term memory [75]. Since the state of a volatile memristor is not only determined by the instantaneous input but also memorized the stimuli in the past, such interactions in time can be equivalent to the connection weights in space, while the outputs of a single device at different moments can be regarded as the outputs of different neurons (virtual nodes). As a result, a high-dimensional reservoir with a very low cost of hardware can be constructed by applying time multiplexing to nonlinear devices, which greatly simplifies the hardware implementation. Based on the time-multiplexing approach, single spintronic oscillator has been used for spoken digit recognition, with an accuracy comparable to that of state-of-the-art neural networks [77]. Herein, the audio waveform is pre-processed and applied to the device as DC current flowing through the junction, as shown in Fig. 1.5d. The resultant oscillating amplitudes with a highly nonlinear relation to input current accompanied by a memory effect are detected at different time steps and exploited as the reservoir states. Similarly, this virtual node strategy has also enhanced the ability of WOx reservoir on delicate forecasting of a chaotic time series [76]. The computing capacity of the reservoir can be further enhanced by optimizing nonlinearity of the device to balance between the effective point-wise separation ability to different inputs and the robustness to noise [85]. Reservoir computing has also been implemented by CMOS analog circuit [86, 87], FPGAs [88, 89], and VLSI circuits [90]. Compared to these implementations, memristive reservoir computing systems offer a much lower energy consumption and compact circuit by replacing the large number of interconnected neuron nodes by time multiplexing.

1.4.2 Memristor-Based Coupled Oscillator Network When a cluster of nonlinear dynamic systems interact with each other, complex and interesting phenomena can be observed such as chaos, bifurcation, fractal, soliton, synchronization, and so on. Given the fact that the human brain consists of ~1011 nonlinear neuron coupled to each other through ~1015 synapses, these nonlinear behaviors are the foundation of the information process in our brain. Among them, synchronization is one of the hottest topics due to its common existing and promising potential applications. Here is a simple example to explain what is synchronization. As shown in Fig. 1.6a, in an all-to-all four-oscillatory neuron network, there are three most commonly observed, rotationally symmetric firing modes including

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Fig. 1.6 (a) The firing modes in an all-to-all four-neuron network including fully synchronous mode, splay mode, and two clusters of 2 mode. The vertical dashed lines indicate the intervals between firing times. (b) A Mott oscillatory network for locomotion control. Four oscillators based on Mott memristors are coupled through capacitances, and the phase order in the synchronization pattern is transformed to footstep sequence. (c) A memristive oscillatory network and its solution for Max-Cut problem. (d) A spintronic oscillatory network for vowel recognition. The schematic illustrates the experimental set-up with four spin-torque nano-oscillators. The oscillators are electrically connected in series and coupled with emitted microwave currents. Two microwave signals encoding information in their frequencies are injected to the system through a strip line. ((a) Reproduced with permission [91]. (b) Reproduced with permission [95]. Copyright 2018, Springer Nature. (c) Reproduced with permission [96]. Copyright 2019, Springer Nature. (d) Reproduced with permission [97]. Springer Nature)

fully synchronous mode (one cluster of four neurons), splay mode in which all neurons fire in a sequential manner, and two clusters of 2 mode in which two clusters of two neurons are in antiphase with each other [91]. Such spontaneously emerging order of nonlinear dynamic systems in time domain is called synchronization. The synchronization of neuron clusters is the underlying mechanism to many complex neuroscience topics, including generating some crucial rhythms, the communication establishment between different brain areas, the neural mechanisms for clinical syndromes of Parkinson’s disease, and so on.

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Memristors can implement coupled oscillator network at a low hardware cost, since only one memristive device is needed to generate oscillations in a simple memristor-based circuit [82]. The lateral dimension of the memristor can be scaled down to nanometers [92]. To implement an oscillatory neuron network, memristive electronic oscillatory neurons have to couple through electrical connections, such as capacitors or resistors. The coupling effect of capacitors and resistors is opposite. When two electronic oscillatory neurons are coupled by a capacitor, they tend to oscillate out-of-phase once the synchronization is achieved. However, resistor coupled oscillatory neurons will join the same pace once the synchronization is established [93, 94]. A capacitor is similar to inhibitory connections between neurons, while a resistor is similar to excitatory connections. Synchronization in memristor-based coupled oscillator network can be used to develop adaptive, low-power, and area-efficient artificial central pattern generator (CPG). CPG, located in the spinal cord of vertebrates and in ganglions of invertebrate, is responsible for the generation of the rhythm patterns for locomotion, breathing, and chewing. Recent studies in neurobiology have discovered that CPG contains a lot of neural oscillators and is based on neuron synchronization [98–100]. The artificial CPG is designed based on VO2 Mott memristor which is in series with a transistor, forming a 1T1R configuration [95]. The natural frequency of such oscillator can be tuned by applying different voltages on the gate of the transistor. In the memristive CPG, four VO2 oscillators are coupled in a ring configuration, where neighboring oscillators are connected by capacitors to achieve interactions. The intrinsic frequencies of individual 1T1R oscillators will change according to the voltages applied to transistors, leading to a changed frequency mismatch among the oscillators, thus generating different synchronization patterns. As shown in Fig. 1.6b, the output waveforms with inconsistent steps in the beginning gradually evolve into a stable synchronization pattern due to the interaction between the oscillators. These different phase patterns could mimic typical locomotion gait patterns of a horse or a quadruped robot, where the order of the limbs is determined by the phase sequence. The artificial CPG could endow the robot with automatic and real-­ time evolution of the control patterns under sensory input signals, allowing an adaptation to the environmental terrain. These oscillatory neuron networks carry rich dynamics, which means memristive coupled oscillator network is very effective in conducting learning/cognitive task. A potential way is to achieve learning by configuring the natural frequencies of the individual neurons. For spin-torque devices, the DC current flowing through the device can be learned to control its oscillation frequency accurately across a wide range [77, 97]. For a Mott oscillator, one can configure its series resistance or adjust the threshold characteristics of the device so as to memorize the knowledge in the oscillation frequency [101]. Another way to achieve learning is to store the training information in the coupling strength, which is similar to the synaptic strength between neurons [102]. A coupled oscillatory network gradually converges to a stationary phase or frequency pattern, which share a similar idea to finding a ground state, analogous to the minimization of the energy function in Hopfield networks [93, 103]. This

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underlying physical process can be exploited to build an Ising machine and solve combinatorial problems. As shown in Fig.  1.6c, an Ising machine based on VO2 oscillators has been demonstrated recently [96]. The building block of Ising machine, i.e., artificial spin, is constructed by a VO2 oscillator and a second harmonic locking signal injected externally, which guarantees a binary phase state (inphase or out-of-phase according to the injection). The interaction between spins is mapped to the properties of coupling, where resistive coupling is equivalent to ferromagnetic interaction, while capacitive coupling emulates anti-ferromagnetic interaction. The input of coupled oscillatory network can be an external frequency information encoded in electrical or magnetic signals, which are unidirectionally coupled with the network [97, 101]. It can also be represented as temporal information, such as the time delay of the supply voltage/current before initiating the oscillation [102]. The output of the network is often provided by the phase information of the steady state, including qualitative synchronization pattern, as shown in Fig. 1.6d. Under this consideration, vowel recognition has been demonstrated using the synchronization of a coupled oscillatory network consisting of four spin-torque oscillators [97]. In this demonstration, two formant frequencies of the vowel are encoded in microwave signals with fixed amplitudes and inject into the network with strip line by generating radiofrequency magnetic field that acts on the spin-torque devices. During training, the DC currents dominating individual oscillating behaviors are modified through a supervised learning procedure. The oscillators in the network talk to each other through millimeter-long wires by microwave currents. The network utilizes the final stable phase pattern as the basis for vowel classification, which is determined not only by the input but also by the network parameters modified through the learning. Compared to CMOS technology, memristor-based oscillatory network systems hold great advantages in area and energy efficiency, thanks to the potential of implementing oscillator in a very simple structure [104, 105]. For example, an oscillator can be realized by a single 10 nm spin-torque device which achieves an ultra-low power consumption of 1 μW [106], comparing to a 10 μm and 8.5 μW CMOS oscillatory neuron [107].

1.4.3 Memristor-Based Continuous Attractor Neural Network In the memory of biological neuron, people think that the brain can temporarily remember the current state during the dynamic assignments process and use this information when you need to use it for computation or memory, which is called working memory and can be realized naturally by continuous attractor neural network (CANN). CANN provides the neural system with  the capacity of tracking time-varying stimuli in real time, so the neural system can easily change its stable state along the attractor space. This mechanism is crucial for the brain to carry out many important computational tasks such as motion control and spatial navigation.

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Fig. 1.7 (a) Descent toward continuous attractors, as well as neutral equilibrium between these attractors. (b) Schematic diagram of continuous attractor network, which has self-sustained activities based on the interaction of positive connection and group inhibition. (c) The influence of weight precision on network activity. (d) The influence of offline write noise on network activity based on weight matrix of full precision. (e) The influence of read noise on network activity based on weight matrix of full precision. (f) The write noise reshapes the pattern of network activity. (g) The read noise sways the pattern of network activity. (h) The influence of read noise on network activity based on single-bit weight matrix. (Reproduced from Ref. [108] with permission. Copyright 2020, John Wiley & Sons)

Wang et al. [108] realized the simulation of CANN based on memristors for the first time, having a vital breakthrough to emulate brain-like memories for future neuromorphic computing systems. As shown in Fig.1.7a, a CANN is endowed with a bunch of continuous attractors, which are neutrally stable. This self-sustained activity of CANN is due to the introducing of positive connection and group inhibition, as shown in Fig. 1.7b. A Oja learning rule is applied to perform working memory based on offline training in CANN by introducing competition and cooperation among neurons. Figure 1.7c verifies that the memristor can easily realize CANN under the weight matrix with different weight accuracies. Even when using the simplest binary devices mapping conductance to +1 and 0, it also can implement CANN

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and further find that the read noise in the memristor array also can generate different effects in CANN with only 1bit weight accuracy, as shown in Fig. 1.7h. Further, they find that the maximum tolerance for write noise based on weight matrix of full precision is 5% (Fig.  1.7d) and the maximum tolerance for read noise based on weight matrix of full precision is 10% (Fig. 1.7e). When the write noise is 0.1, the neuron activity is a sharp single peak. When the write noise is stronger (e.g., 0.3), the neuron activity may be split into multiple peaks (Fig. 1.7f). In contrast, when the read noise is 0.1, the location of peak drift with the overall shape remains almost unchanged (Fig. 1.7g). When the read noise is stronger (e.g., 0.3), the peak value drifts faster in a larger range.

1.4.4 Memristive Spiking Neural Network Spiking neural networks (SNNs) also are inspired by information processing in biology, where information is coded into sparse and asynchronous which are communicated and processed in a massively parallel fashion. The hardware implementation of SNN can exhibit favorable properties such as low power consumption, fast inference, and event-driven information processing. This makes them interesting candidates for the efficient implementation of deep neural networks and many other machine learning tasks. All memristive spiking neural networks can be constructed from the artificial neuron and synapse based on the memristor. Duan et al. [49] developed a rich nonlinear dynamics of the artificial neuron with spatiotemporal integration characteristics and further constructed fully memristive spiking nonlinear system consisting of Pt/Ta/Ta2O5/Pt synapses and Pt/Ti/NbOx/Pt/Ti neurons. Figure 1.8a shows the overview of the structure consisting of synapse crossbar array with NbOx neurons. The structural configurations of the NbOx neurons and Pt/Ta/Ta2O5/Pt synapses were assessed by SEM (Fig. 1.8b, d) and cross-sectional high-resolution TEM (Fig. 1.8c, e). They used a 2 × 1 fully memristive array to achieve the coincidence detection function (Fig. 1.8f). When the two pre-synaptic inputs (1.1 V in amplitude, 1 μs in width, 1.5  μs in interval, for 50  cycles) were simultaneously applied, the output neuron was fired with ~0.3 MHz (Fig. 1.8g). When the two pre-synaptic inputs were asynchronous or randomly arranged in time (where S1 is a periodic input and the timing of S2 is random relative to S1), the neuron cannot fire (Fig. 1.8h, i), which demonstrate the potential of the fully memristive nonlinear system in coincidence detection. Further, they simulated a large-scale spiking neural network with 4000 excitatory and 1000 inhibitory spike trains following Poisson statistics (Fig. 1.8j, k). Simulation results show that the firing rate of the neuron can be increased by over ten times as a result of the synchronous events, as shown in Fig. 1.8l, m. It proves that fully memristive spiking neural network has an extraordinary ability to detect fine correlations in mass signals and small time scale. Recently, Han et al. [109] also implemented the coincidence detection using integrating multistate single-transistor neurons and synapses on the same plane, in which both devices have the same

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Fig. 1.8 (a) The SEM image of fully memristive array. Scale bar, 100 μm. (b) The SEM image (scale bar, 20 μm). (c) The TEM image (scale bar, 50 nm) of Pt/Ti/NbOx/Pt neuron device. (d) The SEM image (scale bar, 10 μm). (e) The TEM image (scale bar, 20 nm) of Pt/Ta/TaOx/Pt synapse device. (f) Schematic diagram of coincidence detection in the fully memristive nonlinear system. (g) The neuronal response by two synchronous input pulse trains (1.1  V in amplitude, 1  μs in width, 1.5 μs in interval, for 50 cycles) applied on S1 and S2. (h) The neuronal response by two asynchronous input pulse trains (1.1 V in amplitude, 1 μs in width, 1.5 μs in interval, for 50 cycles) applied on S1 and S2, where S2 is behind S1 by 1.2 μs. (i) The neuronal response by two asynchronous input pulse trains (1.1 V in amplitude, 1 μs in width, for 50 cycles) applied on S1 and S2, where S1 has an interval of 1.5 μs and S2 is random relative to S2 in timing. (j) The simulated large-scale network with input pulse trains of the neuron from independent 4000 excitatory and 1000 inhibitory random spike trains following Poisson statistics. (k) Introduction of synchronous events following Poisson statistics into the excitatory inputs to network, where the input rates are unchanged and the proportion of synchronous events is 0.3%. (l) The artificial neuron only fires two spikes under (j) inputs in the simulation. (m) The artificial neuron fires 21 spikes under inputs shown in (k). (Reproduced from Ref. [49] with permission. Copyright 2020, Springer Nature)

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homotypic MOSFET structure. Similarly, Wang et  al. [10] successfully demonstrated fully memristive neural networks combining artificial synapses as well as artificial neurons using emerging neuromorphic devices. Specifically, artificial synapses were implemented using nonvolatile Pd/HfO2/Ta synaptic devices and Pt/Ag/ SiOx:Ag/Ag/Pt diffusive memristors used as artificial neurons. The whole system can perform unsupervised learning and patterning classification.

1.4.5 Memristor-Based Chaotic Computing Although many theoretical research results of memristors provide convenience for quantitatively analyzing the complex behavior and computing potential of the memristive oscillatory system [110–116], such as transient chaotic behavior [111, 113], synchronization [112], and anti-synchronization [116] control between memristive chaotic oscillators, it is still a big challenge to experimentally realize these complex chaotic dynamics in devices and implement memristive chaotic computing. Optimization problems are a typical problem and can be solved efferently by memristive chaotic computing. Energy-based networks, for example, Hopfield network, can solve optimization problems by mapping the task to its energy function. By minimizing the energy function through iterations, the network can automatically find optimal solutions. The dynamic neurons built with memristor can be assembled into energy-based networks. Hopfield network usually faces a common problem of being stuck in local minima. This issue becomes more challenging when the task is complicated and hence has a large number of local minima in the solution space. In this case, replacing the threshold function with a chaotic neuron can introduce fluctuations into the evolution process of the network, therefore endowing the network with ability to jump out of local minima. Simulation results in Fig. 1.9a show that better solutions can be found in traveling salesman problem by chaos-­ aided minimization [117]. Figure  1.9b shows the improvement after introducing chaos for a viral quasispecies reconstruction problem in chaotic oscillatory networks [118]. Yang et al. [119] reported a memristive hardware based on Hopfield network to effectively solve the optimization problem. As shown in Fig. 1.9c, by introducing transient chaos to simulated annealing, global optimal solution of continuous and combinatorial optimization problems can be found. To map the algorithm onto the memristor array, they program the devices in the memristor array one by one according to the weight matrix corresponding to the desired optimization task. The conductance of each device represents the synaptic weight through a linear transformation Gij = awij + b. Further, using the write-and-verify strategy program, the selected device and the self-feedback weights of Hopfield neurons are mapped to the diagonal devices in the array to generate transient chaos. Taking the spherical 2 2 function f  x   x1  x2 as an example, it is proved that the transient chaotic memory network can solve continuous function optimization problems. The experimental results of using the transient chaotic network to optimize the spherical function

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Fig. 1.9 (a) Memristive Hopfield network with chaotic neurons and simulation result on traveling salesman problem. (b) Memristive oscillatory network with chaotic oscillators for viral quasispecies reconstruction problem. (c) Transiently chaotic simulated annealing based on intrinsic nonlinearity of memristors and its experimental results on continuous function optimizations and combinatorial optimization problem (Max-Cut problem). ((a) Reproduced with permission [117]. Copyright 2017, Springer Nature. (b) Reproduced with permission [118]. Copyright 2020, Springer Nature. (c) Reproduced with permission [119]. Copyright 2020, American Association for the Advancement of Science)

were shown in Fig. 1.9c. It can be found that the strong self-feedback of the network at the initial state causes the solution space to appear chaotic. As the self-feedback effect of the diagonal memristor continues to decrease after programming, the network begins to converge after hundreds of iterations and finally successfully obtains the solution (0, 0), thus proving the ability to solve continuous optimization problems using this method. This method can also be used to solve the Matyas function f  x1 ,x2   0.26 x12  x22  0.48 x1 x2 , which further proves its universality





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(Fig.  1.9c). In addition to continuous function optimization, they have further expanded to solve combinatorial optimization problems. A 2 × 2 memristor array is used to solve a two-node maximum cut problem. Figure 1.9c shows the results of using a transient chaotic network to solve the maximum cut problem, in which neurons 1 and 2 converge to 1 and 0, respectively, after the chaos. The energy evolution characterizes the state of the network, thus indicating that the network has found the optimal solution. Finally, a large typical combinatorial optimization problem (the ten-city traveling salesman problem (TSP)) was simulated and further proved its universality. At the same time, they have a comparative analysis of three different annealing processes (linear, exponential, and intrinsic long-term depression), and it is found that the inherent nonlinear characteristics of the device are important to effectively solve the optimization problem.

1.5 Conclusions and Outlook Here, we discuss the progress made in emulating synapses and neurons using the rich dynamics of memristive devices and summarize many methods to realize various long-term plasticity and short-term plasticity by using its internal dynamic. Meanwhile, we subsequently showed that different neuronal devices and spiking models, including H-H neuron, LIF neuron, oscillation neuron, and artificial dendrite, can be implemented by memristors by exploiting their internal physics and/or chemistry. It is further discussed that volatile and nonlinear devices can realize the nonlinear mapping function of the characteristics in the reservoir network, which provides a positive hardware solution for processing timing information. In addition, by coupling memristive oscillatory neurons with each other, the resulting oscillatory neural network can be further used in CPG to implement and process various cognitive tasks. The memristive neuron is applied to the spiking neural network, which can perform image recognition, coincidence detection, and other tasks. Finally, we discussed the complex nonlinear dynamics of the memristor, including chaos and local activity, which have been used to efficiently solve optimization problems. For memristive synapses, synaptic plasticity has been successfully emulated. However, there is no device that can contain all synaptic plasticity, and it needs to be achieved by finding a suitable material system. For memristive neurons, some advanced functions such as refractory period are also emulated [54]. However, compared with biological neurons, the functions of artificial neurons are still incomplete. It is also necessary to improve the driving ability of artificial neurons by optimizing the memristor device, so as to realize the application in multilayer neural network hardware. The degree of neuron function in artificial neural network needs to be further discussed in the research community. Although this field has made encouraging progress in recent years, it is still in its infancy. It can be seen that most of the experimental work involved in this chapter is still simple demonstrations at the level of a single device or very small array and

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these demonstrations are still far from the complexity and computing capacity of the brain. The development of practical hardware systems based on these prototypes still requires a lot of scientific and engineering efforts. In addition, it needs to be emphasized that the construction of neuromorphic systems is a highly interdisciplinary task. On the one hand, this is closely related to advances in neuroscience in understanding the detailed working mechanisms of the brain. On the other hand, the joint efforts of physicists, materials scientists, electrical engineers, and computer scientists are essential for further revealing the device mechanism, designing the material structure of the device to control device behavior, and optimizing algorithms based on device characteristics. Therefore, the future development of this field requires close cooperation across fields while relying on mutual inspiration between neuroscience research and artificial neuromorphic systems. We expect that in the next 10 years, there will be more research results on building neuromorphic systems by making full use of the rich dynamic characteristics of memristive devices.

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Chapter 2

Short-Term Plasticity in 2D Materials for Neuromorphic Computing Heejun Yang

2.1 Introduction Neuromorphic computing dreams of human-level artificial general intelligence by emulating the brain, which contrasts the pervasive von Neumann computing architecture. Up to now, artificial synapses have been long and widely adapted to function mostly as signal transmission with a memory effect in neuromorphic computing; significant efforts have been made to mimic mostly the memory function (e.g., memristors). However, emulating synaptic computation, which is vital for information processing, working memory, and decision-making by using short-term plasticity (STP), remains technically challenging to be demonstrated without using numerous CMOS devices. In the human brain, a quadrillion (1015) synapses are present in a massively parallel architecture, which highlights the issue of integration of CMOS devices for an efficient neuromorphic chip. One digital information costs ~1 μJ in current digital computing hardware, while a spike signal (an information unit) in a massively parallel architecture of a neuron-­ synapse system spends only ~1 pJ (106 times lower than the digital hardware). This made a historic and valid result in the “Go” match in March 2016; in an even “AI” match, AlphaGo (artificial intelligence, Google DeepMind) used an energy of 56,000 W with 1200 CPUs, while Lee Sedol (professional GO player) used only 20 W with his brain, which highlights the motivation of neuromorphic technology to mimic ~1012 neurons and ~1015 synapses of the human brain using solid-state devices.

H. Yang (*) Department of Physics, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, South Korea e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 Y. Chai, F. Liao (eds.), Near-sensor and In-sensor Computing, https://doi.org/10.1007/978-3-031-11506-6_2

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H. Yang

In neuroscience, synapses have been long and widely known to function as a memory; many memristors have been developed to mimic the long-term memory function of the synapse. On the other hand, physiologists recently underline the functional role of the numerous (~1015) synapses for various computations, such as temporal signal processing, sensitization/adaptation and gain control, as well as cognitive processes, including working memory and decision-making. But few synaptic devices have been reported to demonstrate the synaptic computation with a small energy consumption for a unit operation (