Memristor‐Based Intelligent Human‐Like Neural Computing

Humanoid robots, intelligent machines resembling the human body in shape and functions, cannot only replace humans to complete services and dangerous tasks but also deepen the own understanding of the human body in the mimicking process. Nowadays, attaching a large number of sensors to obtain more sensory information and efficient computation is the development trend for humanoid robots. Nevertheless, due to the constraints of von Neumann‐based structures, humanoid robots are facing multiple challenges, including tremendous energy consumption, latency bottlenecks, and the lack of bionic properties. Memristors, featured with high similarity to the biological elements, play an important role in mimicking the biological nervous system. The memristor‐based nervous system allows humanoid robots to obtain high energy efficiency and bionic sensing properties, which are similar properties to the biological nervous system. Herein, this article first reviews the biological nervous system and memristor‐based nervous system thoroughly, including the structures and also the functions. The applications of memristor‐based nervous systems are introduced, the difficulties that need to be overcome are put forward, and future development prospects are also discussed. This review can hopefully provide an evolutionary perspective on humanoid robots and memristor‐based nervous systems.


Introduction
Humanoid robots are intelligent robots built to mimic the human motion and human interactions. Recently, multifunctional humanoid robots have illustrated their capabilities in various applications, and related studies are emerging. [1][2][3][4] For example, in the field of servicing robots, more than 10 000 biological-inspired learning algorithms than traditional software neural networks and have been used to implement complex tasks, e.g., perception systems, pattern recognition, image processing, decision-making, classical conditioning, etcetera. Considering the prospect that the memristive nervous system brings to humanoid robotic perception and computational systems, it is urgent to review memristive devices according to the structural hierarchy described above and to provide examples of current memristive bionic applications for the better joint development of both memristors and humanoid robots.
In recent years, boosting a number of studies reviewing memristive systems from the perspectives of material engineering, [9,10] memristive synapses and neurons, [11,12] and applications have been reported. [13][14][15] Our manuscript differs from the existing literature in that we present the first comprehensive overview of the memristor-based nervous system and its correspondence with the biological nervous system, promoting the applications of the memristive nervous system in humanoid robots. Considering the difference between memristors and humanoid robot research, we explain the biological nervous system and how to mimic its functions using memristors from various levels, i.e., synapse, neuron, and central nervous system (Figure 1). In this order, Section 2 to Section 4 construct the memristive nervous system; thus, a better understanding of the memristive nervous system can be obtained. Section 5 then discusses the applications of the memristive nervous system, Figure 1. Schematic diagram of biological and artificial nervous systems. Based on neuromorphic devices, the artificial nervous system can imitate the biological nervous system at the functional level, among which imitating synapses, neurons, neural networks, and the spinal cord is the critical point.

Biological and Memristive Synapses
In the biological nervous system, synapses are specialized junctions between neurons that process and store information simultaneously from a molecular perspective. Thus, synapses are the most important building blocks at the foundation of the biological nervous system, and synaptic plasticity is considered to be the basis for biological learning and memory. When it comes to developing bionic systems such as brain-inspired computing and bionic perception systems, artificial synapses are also undoubtedly the vital building blocks, especially the use of artificial synapses to achieve synaptic plasticity. Memristor-based synapses have been rapidly developed based on the structural and functional similarities between memristors and biological synapses. In this section, we start with the structure of biological synapses and synaptic plasticity and then correspondingly describe how to mimic biological synapses using memristors (Figure 2).

The Basic Structure of Synapses
In the biological nervous system, information transmission mainly occurs in synapses. Depending on the form of information Figure 2. Illustration of the types of biological and memristive synapses and their corresponding synaptic plasticity mechanism. a) Schematics of diverse biological synapse models and synapses' performance when synapses are potentiated or depressed. In biological synapses, there are two main categories of synapses: chemical synapses and electrical synapses, and the two types have different ways of transmitting the information. For chemical synapses, the synaptic weight can be seen as the efficiency of information transmission and is related to the number of receptors and neurotransmitters in the synapse. b) Schematics of diverse memristive synapse models and a typical synaptic plasticity mechanism. After selecting the input and output electrical paraments for memristive synapses, the corresponding conversion relationship between the two can be regarded as the synaptic weight. In the case of a memristive synapse consisting of a single filament-based memristor, the strength of the formed filament represents the conductivity and synaptic weight, and the change of synaptic weight is mainly related to the conductive filament growth.
transmission, there are two main categories of synapses ( Figure 2): chemical synapses and electrical synapses (also called gap junctions). [16] Electrical synapses provide a direct physical connection between presynaptic neurons and post-synaptic neurons and permit the bidirectional transmission of electrical currents, ions, and small molecules. Compared with chemical synapses, electrical synapses have a higher speed of information transfer but lack the flexibility of information processing. The plasticity of electrical synapses has also become an emerging field in neuroscience, but it is still a less understood field.
In chemical synapses, the presynaptic membrane releases neurotransmitters into the synaptic cleft, after which the transmitters then bind to receptors on the postsynaptic membrane. When action potentials arrive, the neurotransmitters can be released from the presynaptic membrane, so the electrical signals have been translated into chemical signals. Then, postsynaptic molecular machinery is required to detect the neurotransmitters, during which the information is converted from the form of chemical signals to postsynaptic potential signals. Unlike electrical synapses, the signal transmission in chemical synapses is unidirectional, and it only transmits from the presynaptic membrane to the postsynaptic membrane. The polarity and magnitude of the potential signals are influenced by the efficiency of neurotransmitter transmission in the synaptic cleft. Moreover, the transmitting efficiency, also called synaptic plasticity, can be flexibly modified through the activities of pre-and postsynaptic neurons. Synaptic plasticity, one of the fascinating properties of the mammalian brain, contributes to the biological basis for the modification of the neural circuit and the complex functions of brains, including learning and memorizing. [17] 2. 1

.2. Synaptic Plasticity
Synaptic plasticity is the ability of synapses to adapt to external stimuli in order to produce different responses, and it is also an essential neural basis for learning and memory ability. Synaptic weight refers to the connection strength between two nodes. According to the duration of this modification, synaptic plasticity is divided into long-term plasticity and short-time plasticity. In addition to neuron activity, synaptic strength can also be affected by the local dynamic at synapses, including membrane voltage and calcium level, which induces some high-order synaptic plasticity, such as spiking time-dependent plasticity (STDP). The following sections will focus on longterm plasticity, short-term plasticity, and STDP, and more synaptic plasticity can be found in these papers. [18][19][20][21] Short-term plasticity is a form of synaptic plasticity that lasts for a short period of time, usually only a few minutes or less, and includes short-term potentiation (STP), short-term depression (STD), pair pulse facilitation (PPF), pair pulse depression (PPD), and post-tetanic potentiation (PTP). [20,[22][23][24][25] When a short sequence of weak stimuli is applied to the presynaptic neuron, the postsynaptic potential will first gradually increase (decrease) and then return to its initial level, which corresponds to the STP (STD). In contrast, after applying a relatively high frequency of external stimuli, the enhancement of excitatory postsynaptic potential can last for a longer time scale of ten seconds to minutes, and PTP occurs. It is most likely due to the Ca 2+ dependent activation of presynaptic protein kinases. PPF (PPD) occurs when two action potentials from the presynaptic neuron arrive at the exact same synapse in a short interval. This type of synaptic plasticity usually lasts for tens to hundreds of milliseconds, and the interval determines the magnitude of the enhancement (decrease). A shorter interval between two spikes will lead to a more considerable current enhancement or a smaller current decrease. It is associated with the increase (decrease) in presynaptic Ca 2+ concentration after the first spike. The increase or decrease in presynaptic Ca 2+ concentration results in more (fewer) neurotransmitters being released when the second spike arrives. In terms of biological functions, it is found that short-term plasticity plays an essential role in performing critical functions, such as fast response and information filtering. The formation of short-term memory is also related to it.
In contrast with short-term plasticity, long-term plasticity can last for hours or even days, which is usually triggered by repetitive activities. [26][27][28][29] Similarly, long-term plasticity contains two main types, long-term potentiation (LTP) and long-term depression (LTD), with different alterations in synaptic weight. LTP and LTD were first observed in the hippocampus, which is related to the frequency of stimuli. After experiencing high-frequency repetitive activation of electrical stimuli, the synaptic connection was strengthened for hours to days (LTP). However, the synaptic connection was decreased under low-frequency stimulus for long periods (LTD). For the hippocampus, NMDAR, a special ligand-gated ion channel on the postsynaptic membrane, would be activated to permit the influx of Ca 2+ to the postsynaptic cell. Whether LTP or LTD occurs seems to be dependent on the calcium ion concentration. In fact, mechanisms of long-term plasticity formation vary at different synapses, but it is widely believed that long-term plasticity plays a critical role in the foundation of memory. It is noted that the synaptic connection is not fixed in long-term plasticity and will decay over time but with a longer course of time than short-term plasticity.
Spike-timing-dependent plasticity (STDP) is a far-reaching synaptic plasticity that has been proved by many biological experiments. [30,31] STDP refers to the ability of the temporal sequencing of presynaptic and postsynaptic neuronal activity to influence the form and magnitude of long-range synaptic modulation. In biological synapses, divergent plasticity outcomes completely depend on the timing of the presynaptic and postsynaptic activity, which highlights the significance of the STDP pairing relationship. In conclusion, the changes in synaptic weight are time-dependent; the synaptic weight increases when the presynaptic membranes receive a spike earlier than the postsynaptic membranes; conversely, the synaptic weight reduces. As an essential method of updating weights in neuromorphic computing, the implementations of STDP using memristors can be found in Section 2.3.

Memristor-Based Synapse Models
In building memristor-based synapse models, we primarily focused on how to exhibit synaptic plasticity using memristors, which requires us to abstract the biological synapse characteristics into the actual electrical model. From the current perspective, the conductance or current of the memristive device is usually regarded as the synaptic weight, and the external stimuli, such as voltage pulses, are treated as nerve spikes. A comparison of different memristive synapse models is shown in Table 1 below.
Considering simplicity and integration, most memristorbased synapse models propose to use a single memristor as the synapse. [32][33][34][35][36] The conductance of the memristor usually represents the synaptic weight when external stimuli are applied to it in terms of voltage pulses. The response current and external voltage stimuli are in accordance with Ohm's law, i.e., if the conductance increases, the response increases. However, this model also has three limitations, namely the symbolic limitation, the sneak path problem, and the synaptic weight update asymmetry. First, the sign of synaptic weight is constrained to a positive value according to Ohm's law; therefore, the negative response cannot be expressed. Secondly, current can sneak through other cells in memristor crossbar arrays, which is defined as sneak path problems. This problem can be solved by connecting the single memristor with some selective devices, such as the transistor, diodes, etcetera. [37][38][39] Besides, Rao et al. proposed and demonstrated a timing selector, and the sneak path issue was addressed using a voltage-dependent delay time of its transient switching behavior. [40] Third, due to the nonlinearity and variability characteristics of the memristors, synaptic devices based on a single memristor always suffer from a mismatch between the expected synaptic weight change and the actual synaptic weight change.
Owing to the synaptic weight restriction of a single memristor, the synapses with two memristors would become the alternative. [35,41,42] One of the memristors is considered as a positive weight, and the other is considered as a negative weight; this produces a difference between the two output currents by an external circuit. As shown in Table 1 above, input voltage pulses are applied to the column of the crossbar and form a differential current output signal by subtracting currents flowing in the adjacent columns. Thus, the synapse weight can be expressed as the equation below; this design doubles the size of the crossbar and requires complex postsynaptic neurons.
The ± G ij is the conductance of a memristor in Table 1. Another kind of synaptic weight implementation is a bridge arrangement. [43,44] Similar to the structure of the Wheatstone bridge-like circuit, the bridge synapse mainly consists of four memristors placed. When an input signal voltage is applied to the memristor bridge, the output voltage V out can be represented as the equation below. We define the synaptic weight as an equation that reflects the ratio of output to input; thus, the synaptic weight of the bridge circuit is indicated below, which can either be positive, negative or zero.
The V in and V out represent the input and output voltage, and M represents the resistance of memristor in the bridge.

Realization of Synaptic Plasticity
In the imitation of biological synapses, synaptic plasticity is usually achieved by applying DC voltage and electric pulses to the memristive synapse, and the change of synaptic weight would be observed as shown in Figure 3a. The biological synaptic weight modulation is simulated and conveniently translated into the incremental conductance switching in memristive synapses, and the type of synaptic plasticity achieved is closely related to the properties of memristors and applied pulses. An overview of the various type of synaptic plasticity is provided before describing them in detail. Majumdar et al. demonstrated some key functions including short-term plasticity, long-term plasticity and STDP based on their organic FTJ memristor Figure 3b. [45] To implement LTP and LTD, the memristor is first set to the low resistance state and high resistance state respectively. Then a series of voltage pulses with a duration of 100 ms and an amplitude of +3 V (potentiation) and -2 V (depression) is applied to the memristor. After repeated application of voltage pulses at a 3 s interval, LTP and LTD can be observed as shown in Figure 3c,d. However, if the interval between two pulses is extended, long-term plasticity will convert into shortterm plasticity (Figure 3e,f). Otherwise, PPD and PPF behaviors can be demonstrated using two consecutive voltage pulses (Figure 3g,h).
The different timescales between distinct forms of synaptic plasticity demand the conductance retention characteristics of memristors. The implementation of short-term plasticity is usually demonstrated by memristive devices with volatile switching behaviors. [46][47][48][49][50] In contrast, long-term plasticity is usually demonstrated by utilizing nonvolatile memristors. [49,51] Note that some memristors may have these two behaviors in different states, and long-term plasticity and short-term plasticity can be demonstrated on the same device. [52][53][54] Taking memristors based on Ag conductive filaments as an example, Ohno et al. fully demonstrated both short-term plasticity and long-term plasticity with an Ag 2 S inorganic memristor. When a burst of spikes with a low frequency was applied to this device, the conductance of the memristor increased temporarily and decayed automatically, which corresponded to the forming and automatic weakening of short-term plasticity. This conductance change phenomenon is primarily related to the formation and rupture of the Ag conductive filament. The increase in conductance is due to the formation of conductive filaments in the initial phase. In contrast, the rupture of conductive filaments resulted in the decay of conductance; when increasing the repetition frequency, the full formation of conductive filament would result in long-term plasticity. [53] Similarly, Hu et al. converted the short-term plasticity into long-term plasticity by raising the amplitude of applied voltage pulses, as shown in Figure 4a,b. [55] In addition to the implementation of synaptic plasticity in the time scale, the strengthening or weakening of synaptic plasticity is controlled primarily through the polarity of the applied pulses. [56][57][58] Jo and coworkers demonstrated a nanoscale memristor based on Ag/Si mixture and emulated LTP and LTD by applying electrical pulses. The current of this device was regarded as synaptic weight; the synaptic weight is increased to achieve LTP by applying positive pulses. The device current could be increased by applying positive pulses, which would V. e,f) Emulation of STD and STP in short-term plasticity. The time delay between consecutive voltage pulses is 153 s. The currents and conductance states in (c-f) are recorded at V m = 0.1 V. g,h) Emulation of g) PPD and h) PPF using two consecutive voltage pulses of g) −2 V and h) +2 V with a time interval of Δt = 10 ms. The duration of individual pulses is 12 ms. Reproduced with permission. [45] Copyright 2019, Wiley-VCH. be translated to LTP. In comparison to LTP, the implementation of LTD only required changing the polarity of the applied pulses. [59] By comparing a single IGZO with IGZO/ZnO memristors, Choi et al. found that the oxide bi-layer memristor has better electrical properties and can be utilized to achieve synaptic devices with highly linear LTP and LTD characteristics. [60] The nonlinearity of the LTP and LTD characteristics in a bi-layer IGZO/ZnO memristor was 6.77% and 11.49%, respectively, compared to those of 20.03% and 51.1% in a single IGZO memristor, respectively.
PPF is a significant short-term synaptic function that intervenes in simple learning and information processing, which can help to solve temporary memory tasks and information processing. PPF has been demonstrated in many memristive devices made of different materials. [48,61,62] In contrast with the response to the single pulse stimulation, one of the most striking features of PPF is the gain of the response. As mentioned in short-term plasticity, there is an attenuation effect of the current response. When a pair of positive pulses with intervals shorter than the forgetting time, the conductance gradually increases due to the first positive pulse, and the maximum responding current of the second pulse is much larger than the first pulse. Moreover, the smaller the pulse interval is, the larger the PPF index is. Zhou et al. demonstrated an organic synapse, which is made of monochloro copper phthalocyanine with high-temperature resilience, and their memristive switching originates from the migration of oxygen ions under an electrical field. PPF/PPD can be demonstrated by applying the pulses of the same polarity (positive/negative) with a short interval. [63] Wang et al. demonstrated both PPF and PPD in their diffusive SiO x N y :Ag memristive devices based on the Ag dynamics (Figure 4d). The Ag dynamics of their devices are functionally similar to the biological synaptic Ca 2+ behavior, and the Ag cluster is driven to form conductive filaments under an external electrical field. However, the filament spontaneously ruptures after removing the electrical field. Note that PPD can be demonstrated using low-frequency pulses, while highfrequency pulses can trigger PPF. When applying pulses with a short time interval (high-frequency), the memristor conductance increases (facilitation) as the number of pulses increases (Figure 4d). More interestingly, the inflection from facilitation to inhibition in biological synapses, induced by a series of stimuli at the same frequency, is also demonstrated on their device. As shown in Figure 4e, the conversion from PPF to PPD can be realized by increasing the number of electrical pulses at a fixed frequency (5000 Hz). [58] STDP, a critical function in constructing brain-inspired computing systems (Figure 5a), was earlier demonstrated with Ag/Si mixture memristors. In their device, a two-terminal memristor connects CMOS-based pre and postsynaptic neurons in a crossbar structure. A time-division multiplexing approach is utilized to convert the spiking time difference into a pulse width, and then the neuron circuits generate the pulse across the memristive synapse. The synaptic changes versus the spike time difference and the modification of synaptic weight are similar to the STDP in biological synapses. [59] Lu et al. demonstrated a self-adaptive STDP behavior based on metal-oxide memristors and mitigated the effect of initial conductance on the synaptic weight adjustment. [64] The central operation of this form of completion is to encode the spiking time difference in the amplitude or width of the externally applied pulses, and STDP can be demonstrated through applying or overlapping manually and carefully designed programming pulses across the artificial synapse. [33] There are some closely related comparative . Schematic illustration of the transformation from short-term plasticity to long-term plasticity and synaptic PPF and PPD behavior. a) Schematic of the two-layer structure of the memristor. b) Implementation of short-term plasticity and long-term plasticity using the memristive synapse in (a). In biological synapses, high action potentials are more likely to induce long-term plasticity, thus short-term plasticity may be converted to long-term plasticity. Similarly, long-term plasticity has been demonstrated by raising the amplitude of voltage pulses. a,b) Reproduced with permission. [55] Copyright 2017, Wiley-VCH. c) Schematic illustration of the analogy between Ca 2+ and Ag dynamics. d) Experimental demonstration of PPF and PPD behavior. e) Simulation of synaptic PPF and PPD behaviors, as well as PPD following PPF behavior. c-e) Reproduced with permission. [58] Copyright 2017, Springer Nature. studies. [64][65][66] Kim et al. demonstrated a second-order memristor, and designed the voltage applied to its top electrode (TE) and bottom electrode (BE). The equivalent pulses formed by the presynaptic voltage and postsynaptic voltage together enable the memristor resistance to change in accordance with the STDP learning rule (Figure 5b-d). [67] Using a comparable pulse application, as shown in Figure 5e, STDP is realized by Wang et al. in their diffusive memristive synapse (Figure 5f). [58] The long lowvoltage pulse in each spike turns the diffusive memristor ON, and the short high-voltage pulse switches the drift memristor.
When the post-spike precedes or follows the pre-spike, the device is depressed or potentiated. The time difference between the two spikes will determine the voltage drop across the synapse.
The realization of synaptic plasticity can be considered a modulation process of the memristive device resistance value using electrical stimuli. In contrast, the measurement of synaptic plasticity is the reading process of the resistance value of the memristive synapse model. [67][68][69] Alternating current (AC) and direct current (DC) are the two types of electrical signals that can be used to realize and measure synaptic plasticity. The synaptic weight increases when the spike timing difference is positive; conversely, the synaptic weight reduces. b) Experimental set up: a pair of spikes (V pre--V post-) applied to TE is equivalent to a pair of spikes V pre-and V post-applied to the presynaptic and postsynaptic side, respectively. c) The equivalent pulses applied to the top electrode and the corresponding synaptic weight change. d) Comparison between the measured STDP results (symbols) and the simulated STDP results (solid lines) demonstrated on the second-order memristor in (b). b-d) Reproduced with permission. [67] Copyright 2015, ACS. e) Electrical implementation of a biological synaptic junction. f) Schematic of voltage pulses applied to the memristive synapse and STDP response. e,f) Reproduced with permission. [58] Copyright 2017, Springer Nature.
For the realization process, it is worth noting that AC specifically refers to electrical pulses. Some use the term "AC voltage" to describe their synaptic plasticity realization but actually use electrical pulses. [70][71][72] Electrical pulses are applied to the memristive synapse to modify its resistance value, and its change is related to the pulse parameters, including amplitude, duration, and interval. Jo et al. use a series of 100 identical positive pulses (3.2 V, 300 µS) followed by a series of 100 identical negative pulses (−2.8 V, 300 µS) to realize LTP and LTD on their memristive synapse, respectively. [59] Zhang et al. realize the transformation between short-term plasticity and long-term plasticity by changing the pulse amplitude and pulse number. [73] DC usually refers to DC voltage sweeps, [59,[74][75][76] and memristive synapse resistance changes continuously under voltage sweeps. Jo et al. also realize LTP and LTD on the same memristive device using DC voltage sweeps, and the synapse resistance decreases or increases with the positive or negative voltage sweeps. [59] In comparison, synaptic weights and the type of synaptic plasticity can be adjusted by adjusting the parameters of the electrical pulses. The use of DC voltage sweeps to achieve synaptic plasticity cannot precisely modulate synaptic weights like electrical pulses, although the U-I characteristics of the memristor can be obtained simultaneously. Besides, the mainstream synaptic plasticity is based on the Hebbian learning rule, in which the stimuli are in the form of pulses. [21,30,77] Therefore, using electrical pulses to achieve synaptic plasticity is more consistent with Hebb learning rules than using DC voltage sweeps.
There are two methods for memristive synaptic plasticity measurements: the first method, where the state of the memristive synapse is obtained when achieving the synaptic plasticity simultaneously, and the second method, where additional read electrical stimuli are applied for measurement. For the first method, the response current of the memristive synapse under DC voltage sweeps or electrical pulses is generally recorded. [66,67,75] Measurements based on the first method require a high degree of device and array stability and a high degree of mastery of device performance. For the second method, weak electrical stimuli are used to obtain the resistance or responding current of the memristive synapse while ensuring that the memristive synapse state is unchanged. [49,78,79] Therefore, small-amplitude DC voltages or small-amplitude short-duration read pulses are used to obtain the memristive synaptic weights. Other types of electrical stimuli, such as sinusoidal voltage, are more likely to alter the current memristive synaptic weight and, therefore, are not used. Wang et al. measured the response current of their memristive synapse for over 1000 s using a DC voltage at a bias of 0.1 V after implementing long-term plasticity on it. [80] Lee et al. demonstrated LTP, LTD, and STDP based on the KN memristor, and read pulses (0.1 V/10 µs) were used to obtain the response current. [66] Yin et al. realized and measured the synaptic plasticity on homogenous bilayer memristor using writing pulses followed by reading pulses. [81] Since the first method is related largely to electrical stimuli used for realizing synaptic plasticity, only the second method is compared. The detection of synaptic plasticity based on electrical pulses is more flexible than DC voltage. By adjusting the pulse parameters appropriately, multiple resistance measurements can be made without changing the state of the memristive synapse. DC voltages are suitable for longterm measurements, and the amplitude and duration need to be taken into account in the measurement, neither of which should be too large.
In recent years, there has been a proliferation of studies on memristive synapses and their synaptic plasticity, and more studies and comparisons can be found in Table 2. Before reading the table, understanding the mechanism and the dynamics of resistance switching is very critical for the memristive nervous system modeling and other applications. Hence, we will briefly describe the mechanism and switching type of memristors in advance, and the differences and commonalities in intrinsic characteristics can be better understood. More detailed reviews can be found in these papers. [82][83][84][85] The switching type of the memristors can be classified into bipolar and unipolar, according to the polarity of the external electric field. The bipolar resistance switching effect is related to the polarity of the electric field, while the unipolar memristive resistance changes independently of voltage polarity. Further, after removing the electric field, the switching type of the memristor can be divided into two categories: volatile and nonvolatile, according to its subsequent resistance transformation. Nonvolatile memristors have a strong state retention capability, and it is usually difficult for volatile memristors to maintain their resistance after removing the electric field. The following mechanisms usually drive the resistive switching in memristors: electrochemical redox reactions (including electrochemical metallization and valence change mechanism), phase changes, magnetic tunneling, or ferroelectric polarization.
When dielectrics such as transition metal oxides and perovskites are electrically activated for redox-based devices, anions such as oxygen ions are driven towards the anode by an electric field. [34,41,[86][87][88][89] The migrated anions induce the reduction of metal cations, which in turn form conductive filaments and set the device into a low resistance state (LRS). Applying a reverse electric field, the conductive filaments dissolve, resetting the device back to a high resistance state (HRS). The resistive switching of phase-change memory is mainly driven by Joule heating. The bias of the applied programming current can generate Joule heat, thereby changing the crystallinity of the material. Phase change materials (e.g., GST and Te-free SiSb) typically have at least one crystalline phase and one amorphous phase. [90][91][92] When the temperature reaches the crystallization temperature, the phase change material will transform from the amorphous phase to the crystalline phase, shifting the resistive state of the device. Memristive devices driven by magnetic tunneling are usually called magnetic tunnel junctions (MTJ). [93][94][95][96] The switching mechanism of MTJs is the spin-dependent tunneling effect. The tunneling conductance depends on the magnetization direction of the ferromagnetic layer. When the magnetization is saturated, the magnetization directions of the two ferromagnetic layers are parallel, and the tunneling conductance is high. When the magnetization is reversed, the magnetization directions of the two ferromagnetic layers are antiparallel, and the tunneling conductance is small. The ferroelectric tunneling junction (FTJ) generally refers to a metal/ferroelectric/metal junction of ferroelectric thin films with two polarization directions. [97,98] The resistive state of the device depends on the Nonvolatile, bipolar STP, PPF, PPD, LTP, LTD, STDP [112] ferroelectric polarization. The polarization direction of the ferroelectric tunneling barrier can be reversed by adjusting the bias voltage, thereby changing the tunneling barrier and electron tunneling resistance.

Biological and Memristive Neurons
In the biological nervous system, neurons are the fundamental information processing and transmission units, and their function is to produce the corresponding electrical signals in response to external excitatory or inhibitory signals. Thus, artificial neurons are critical computational units in neuromorphic computing, and the main functional requirements for artificial neurons are to achieve the integration and firing dynamics in biological neurons. Currently, artificial neurons have covered a wide range of materials and devices; among these devices, memristors have gained significant attention for constructing electronic equivalents of biological neurons. In contrast with traditional artificial neurons based on CMOS transistors only, memristive neurons have a higher level of integration as well as energy efficiency. We first explain the typical dynamic properties in biological neurons and then describe how to mimic their properties using a memristor as the core. The typical dynamic properties of neurons and the corresponding memristive neurons can be seen in the following Figure 6. In the case of LIF neurons, memristive neurons have structures similar to dendrites to collect various input stimuli, structures similar to the soma (capacitor) to accumulate potentials and compare them with thresholds, and finally, corresponding output structures similar to the axon. The neuronal dynamics are also highly similar, with the membrane potential accumulating after integrating external pulses, producing a neural spike when the threshold is reached, after which the membrane potential resets to resting potential. It is worth noting that there are also leaky channels in the cell membrane, so the membrane potential decreases in the absence of external stimuli, defined as leakage.

The Basic Structure of Neurons
Neurons are the highly specialized cells for perceiving stimuli and transmitting nerve excitation, which are considered to be the basic units of the nerve system. A neuron usually connects with thousands of neurons via synapses in our brain, and they together form a large and complicated neural network that supports various functions such as vision, audition, emotion, etcetera.
A typical neuron consists of three parts: dendrites, a soma, and an axon ( Figure 6). [117] Dendrites, the branches of a neuron, act as the input part to receive the spikes from other neurons. Soma, or the cell body of a neuron, can sum the external signal from dendrites and compare the sum with a certain threshold. [118] When the threshold is exceeded, the neuron is activated into a state of excitement, and potential action pulses appear in the axonal hillock. The action potentials cause the axon facilitation, whose main manifestation is an increase in the concentration of calcium ions at the axon terminal. The axon acts as the part of the output and releases neurotransmitter molecules into the intersynaptic cleft. Therefore, the information can be passed to downstream neurons through the axon terminal. Note that the more pronounced the facilitation is, the more neurotransmitters the axon will release into the synaptic cleft. [119]

The Typical Behaviors of Neurons
For biological neurons, whose natural dynamic properties are highly complicated, several models have been proposed to describe their spiking feature, and these models can be compartmentalized into two main categories: i) biologically plausible neurons that use particularly modeling to achieve similar complex behaviors to biological neurons and ii) biologically inspired neurons that use simplified models designed to replicate key features of biological neurons. The representative biologically plausible neuron is Hodgkin-Huxley (H-H) model, and the representative biologically inspired neurons are integrateand-fire (IF) model and leaky integrate-and-fire (LIF) model. Biologically plausible neurons are superior in mimicking the abundant properties of biological neurons and undoubtedly contain critical features of neurons, while biologically inspired neurons are more suitable for neuromorphic computing due to their ease of implementation and computational efficiency. Thus, we will focus on a few key dynamic features of the neuron in this section, and more detailed dynamic properties can be found in the references cited herein. [120,121] In the biological nervous system, there are three main behaviors in neurons, as shown in (Figure 6). [122][123][124][125][126] First, accumulate charge to generate action potentials based on external excitatory and inhibitory signals (integrate). Second, the soma generates an action potential (fire). Third, the membrane potential of soma reduces to the resting potential. Current research and artificial implementation of neurons also focus on these behaviors. The soma sums the input signals from dendrites, which corresponds to the process of integrating electrical potentials on the cell membrane. When the total potential from dendrites exceeds the neuron activation threshold, action potentials will be generated from the axonal hillock. This process is further defined as integrate-and-fire. In addition to the integration of ions, there are also leaky channels in the cell membrane, and the ions (Na + , K + ) could inflow and outflow simultaneously as neurons process information. Thus, the membrane potential difference between intracellular and extracellular decreases, and the membrane potential decreases to the resting potential; this process is defined as leakage.

Memristor-Based Neuron Models
The H-H model is a well-known biologically plausible neuron model for emulating the electrical properties of neurons, especially the biophysical dynamic details of ion channels in the neuron membranes. [127] Moreover, the dynamic properties in the H-H model contain properties that IF and LIF can achieve. However, the high degree of bionics poses difficulties in implementation; IF and LIF biologically inspired neuron models are more prevalent in neuromorphic computing systems with less biological realistic but computational efficiency. We will mainly introduce the IF and LIF models and their implementations based on memristors.
The IF model was first proposed by Lapicque to mimic the simplest spiking behaviors in neurons, including integrate and fire functions. [128] However, the original idea did not account for the dynamics of neuron membrane potential, such as the decay of membrane potential over time.
After combining with the leakage of membrane potential, the LIF model has been proposed to enhance the model's biomimetic. [129] Currently, LIF models are playing an important role in brain-inspired computing; [130][131][132][133] to achieve different spiking behaviors, IF models have been continuously improved in different aspects, and several relevant models have been derived so far. [134,135] The common focus in IF and LIF models is integrating inputs, boosting the membrane potential, and spiking when the membrane potential reaches the threshold. There are two main methods based on the switching characteristics of memristors; one is composed of hybrid CMOS and memristive devices, [130,133,136] and the other is based on a simple memristor with particular threshold switching characteristics. [58,137] In hybrid circuits, the device composition is related to the threshold behaviors of memristors. For the memristors with a threshold, a capacitor is usually connected in parallel with the memristors, and the capacitor, regarded as the neuron membrane, performs the function of integrating the inputs and boosting the potential (Figure 7a); whereas for the memristors without a threshold, a comparator is used to set the switching threshold. When a memristor is able to achieve the integration effect and has a stable switching behavior at the same time, integration and fire functions can be emulated in a single memristor. In comparison to the IF model, the LIF model has the additional feature of leaking charge in the absence of input spikes. In practical implementations, we usually utilize the volatile property of the memristor or control the capacitor to achieve the "leaky" function.

Implementation of Neuronal Functions
Following the models introduced in the previous section, the current representative work on memristive neurons will be discussed and analyzed in this section.
In the implementations of artificial neurons, whether a memristor has an obvious threshold value is of great concern; this feature influences the device structure directly. For memristors with a certain threshold, LIF neuron can be implemented in conjunction with a capacitor as shown in Figure 7b,c. [138] Yang et al. demonstrated a LIF neuron based on a Pt/SiO x N y : Ag/Pt diffusive memristor with a certain threshold value as shown in Figure 7d. [139] The neuron consists of three parts: an axial resistor (R a ), a diffusive memristor (functions as an ion channel), and a capacitor (C m ). The diffusive memristor, with the initial HRS, can switch to the LRS owing to the formation of the Ag conductive filament driven by the electric field. However, a single voltage pulse does not reach the switching threshold. When external stimuli (voltage pulses) are applied to the neuron, the capacitor is charged with a time constant of R a C m . This charging process can be considered as an accumulation of potential on the neuron membrane, and the charging time can be adjusted by changing the element parameters (Figure 7e). Once the voltage across the capacitor exceeds the switching threshold of the memristor, it switches from HRS to LRS with the discharge of the capacitor, which can be counted as the  [138] Copyright 2020, Wiley-VCH. d) Illustration of an ion channel embedded in the cell membrane near the soma of a biological neuron and the analogous electrical integrate-and-fire circuit of the artificial neuron. e) Response of integrated-and-fire circuits to multiple continuous pulses and the effect of different membrane capacitance C m and axial resistance R a on the neuronal dynamics. d,e) Reproduced with permission. [139] Copyright 2018, Springer Nature. f) Schematic of the IF circuit. g) Input voltage pulses and voltage at node A as a function of time. When voltage pulses are applied as input to the circuit, the capacitor starts charging and the voltage at node A increases as the black line. h) Output spikes of the artificial neuron showing the integration time. f-h) Reproduced under the terms of the CC-BY license. [119] Copyright 2019, Springer Nature. spiking process. The leakage function is mainly implemented through the volatile conductance change of the diffusive memristor. This LIF model provides a complete description of the dynamic change in neurons, and the spiking neurons can be modulated by the RC constant of the circuit flexibly. Such electrical circuits can also be used to realize IF neuron (Figure 7f), and the dynamics of membrane potential is also largely resembling that of LIF neuron (Figure 7g,h). [119] Similarly, Zhang and co-workers performed an IF model based on an Ag/SiO 2 /Au threshold switching memristor. [130] Tian et al. demonstrated neural state machines based on weight tunable synapses, and LIF neurons with a similar structure to the previous work. [140] Fu et al. demonstrated an artificial neuron fabricated from the protein nanowires with tunable integrate-and-fire functions. The spiking process is made to be dependent on the external signal frequency by connecting a capacitor in parallel with the memristive device. Besides, this device has the potential to process bio-signals due to its material and highly biological similarly dynamic properties. [141] For a memristive device without an obvious threshold value, a comparator is needed to achieve the threshold spiking process. Yang et al. demonstrated a LIF neuron model as shown in Figure 8a below; [142] Memristor 1 represents the synapse receiving input spikes with nonvolatile switching characteristics. Then, the adder OP 1 performs the integration function, and the input spikes temporarily and spatially integrate as V add ; after applying V add to the Memristor 2, its resistance decreases, which results in the increase of V out . Once the V out is larger than the reference voltage of OP 2 (V R ), a spike bursts, which can be defined as "fire." The implementation of the leaky function is mainly based on the volatile property of Memristor 2. In contrast with the threshold switching memristor, this form of neuron circuit is more complex, which brings additional difficulty to the high-destiny integration. The conductance evolution when changing the applied stimuli can be found in Figure 8b,c.
Some memristors possess both the threshold switching characteristics and the integration effect; thus, an artificial neuron can be realized by a single memristor that has this kind of characteristic (Figure 9a). Mehonic and Kenyon implemented a LIF neuron model based on a TiN/SiO x /TiN memristor. [143] When the membrane potential induced by a train of closely spaced current pulses reaches the threshold, the neuron generates a spike. Through integrating a memristor with a series capacitor physically, Wang et al. demonstrated a LIF model. [144] Pablo et al. demonstrated a LIF neuron model based on a single Mott-based memristive device, and this "leaky integrateand-fire" functionality is related to the resistance transition in narrow-gap Mott insulators (Figure 9b,c). [146] The applied voltage pulses have a cumulative influence on the state switching of the memristor, and the memristor exhibits a spontaneous relaxation behavior without an external electric field. Note that the working process of an artificial neuron using a single memristor resembles the neuron implemented with hybrid circuits. Zhang et al. demonstrated a rich dynamics-driven artificial neuron and the Ag movements in the memristive device can be utilized to mimic the biological membrane potential (Figure 9d,e). [137] Furthermore, the response current is also consistent with typical LIF neuronal dynamics (Figure 9f). Chen et al. performed an artificial neuron based on a new 2D material named MXene. [145] The energy consumption per spike is projected to 2 × 10 −8 J. When positive pulses with short intervals are applied to the Cu/MXene/Cu memristor, Cu atoms are injected from the top electrode into MXene flakes with a slight increase of conductance. The process is equivalent to making integration for the subsequent "fire"; afterwards, Cu atoms will accumulate between the two electrodes. The complete formation of conductive filament will cause a significant increase in conductance, which can be defined as "fire." The leaky function mainly corresponds to the relaxation behavior during the pulse interval. The memristive neuron is undoubtedly very important as an essential component and basic computational unit for implementing hardware neural networks, and more relevant studies and comparisons about IF and LIF models can be found in Table 3.
As a complement, Yi et al. have demonstrated a biologically plausible memristive neuron with twenty-three types of biological neuronal behaviors, and the neuronal circuit has the same dimensionality as the H-H model. [133] By customizing passive resistor and capacitor elements (and circuit topology), a variety of neuronal dynamics can be achieved without changing the parameters of the memristor, thus promoting the development of memristor-based biologically plausible models.

Biological and Memristive Central Nervous System
At the top of the pyramid of all biological nervous systems, the central nervous system is composed of the spinal cord and the brain (Figure 10). [151] The spinal cord plays an essential role in different aspects of the body's functioning, including movement, sensation, and more. In the human brain, various neural networks are organized by hierarchy to achieve complex functions, including memorizing, learning, etcetera. [152] By collaborating synapses with different forms of synaptic plasticity and neurons with different functions, biological neural networks proved to process information and implement complex works efficiently at a low cost. Inspired by biological neural networks, neural networks are a powerful system of tools for data analysis tasks in an expansive area of practical applications, which is expected to mimic the structure and function of biological neural networks. However, neural networks are mainly constructed by software models under the von Neumann structure, which prevents neural networks from achieving brain-like extreme efficiency. Based on the memristive synaptic elements and neuronal circuits above, memristive neural networks can directly use physical laws to achieve high computational speed and energy efficiency. [153] For specific applications, memristive neural networks need to be adjusted in terms of structure and internal network parameters through learning algorithms. Taking the structure and learning methods of biological neural networks as a reference, we analyze the two main memristive neural networks and the corresponding learning algorithms. Finally, for the completeness of the memristive central nervous system, we would introduce a memristor-based simulation of the spinal cord functions.

Neural Networks in Brains
Biological neural networks are networks of neurons connected through synapses. Under the external stimulus, the axon of a neuron transports chemicals that induce transmitters to be released onto the dendrite, and other neurons could receive the excitatory or inhibitory signals via the electrochemical exchange of neurotransmitters. Information processing occurs Figure 9. a) Schematic of memristive neurons based on a single memristor. b) The hardware implementation of a LIF model based on a Mott memristor and its dynamic behaviors. c) The input pulses applied to the memristor in (b) and its LIF behavior owing to the accumulation of correlated metallic sites. b,c) Reproduced with permission. [146] Copyright 2017, Wiley-VCH. d) Memristive device structure and its electrical characteristics. e) Schematic diagram of artificial neuron and the emulation of membrane dynamics using memristive device in (d). f) The demonstration of integrateand-fire behavior under continuous voltage pulses applied to the memristive device (d-f) Reproduced with permission. [137] Copyright 2018, Wiley-VCH. mainly in the neurons and synapses. In the brain, the synaptic weight, and the structure of neural networks, i.e., the network topology has a specific initial state, which is in part genetically derived. The neural network can perform new functions with a learning process by making minor tweaks both in topology and weights. During learning and information processing, the brain performs tasks using layers of hierarchical and parallel neural circuits, which provide better computational efficiency than traditional artificial neural networks (ANNs). There is variability among these neural networks depending on the responsible function. To clarify this point, we take the visual system as a typical example to introduce the structure of biological neural networks and the typical working principles. [154]   From the acquisition of external visual information, the retina is a remarkable sensor which receives light that the lens has focused on and converts the light into neural signals. Initially, two main types of photoreceptors, rods and cones, transform the visual information into electrical signals. Observing the principle of parallel processing, the former is sensitive to light, and the latter is responsible for the perception of color. The previously processed electrical signals are transmitted to bipolar cells and eventually transmitted to vertically oriented ganglion cells. Each ganglion cell responds to luminance contrast within its receptive field. Besides, photoreceptors are also cross-linked by horizontal and anaplastic cells, which modify the electrical signals before they reach the ganglion cells. These cells work together to form an edge map. The lateral geniculate nucleus then relays the visual signals from the retina to the primary cortex or V1 area to achieve more complex information processing. There are two main categories of neurons in the V1 area. One being, called simple cells, responds to lightdark edges with a particular direction, not the light spot in the center. The other being, called complex cells, can be activated by light-dark edges in an extensive range of its receptive field, which is more positional invariant. While both types of cells work together, it is possible to maintain the invariance of target appearance and high selectivity in object recognition, which can also be seen as parallel processing. Overall, these neurons process information hierarchically and contribute differently, intended for excellent information processing.

The Learning Rules
Hebbian learning is a biologically plausible and ecologically valid learning mechanism, which wants to explain the synaptic plasticity and the adaptation of biological neurons during the learning process. [155][156][157] Hebbian claimed that the synaptic efficiency increases under the presynaptic cell's repeated and sustained activation of a postsynaptic cell. The basic mathematical description of the Hebbian learning rule takes the following form.
where Δw ij donates the change in connection strength between neurons i and j, ε donates the learning rate, which reflects the rate of response to external activation. f i (a i ) and f j (a j ) are functions on presynaptic activity (a i ) and postsynaptic activity (a j ), and reflect the activation level of neurons i and j respectively. When neurons i and j fire together, the corresponding function values are large, thus the weight increase will also be large. As mentioned above, STDP is a form of synaptic plasticity that supports Hebbian learning rules with strong evidences. [30,59] However, the neurons that are already connected together will bind with a stronger link owing to the continuous stimuli in Hebbian learning rules, which is a positive feedback process. Besides, the relationship between firing and wiring causes the neurons in a circuit to be cyclically connected to each other, reducing the possibilities of variability. Hence, homeostatic plasticity, a negative feedback process, is used to maintain the normal activation level of neurons. [158] The defining feature of homeostatic plasticity is the ability to drive synaptic strength, consequently ensuring a homeostatic set point. Several theories have been proposed to explain homeostatic plasticity, including synaptic scaling, the shift of excitation and inhibition ratio, the sliding threshold for LTP and LTD, etcetera.

The Basic Structure of Memristive Artificial Neural Networks
There is a basic set of structures and functional implementations in memristor-based ANNs. It is worth pointing out that ANNs here include convolutional neural networks, Hopfield neural networks, etcetera.
From the perspective of composition structure, the mainstream design of ANNs (Figure 11a) consists of three types of layers: an input layer, one or more middle/hidden layer(s) formed of neurons, and an output layer. [161][162][163] The input variables for the network are contained in the input layer, and the calculated results are contained in the output layer. In the middle/hidden layers, these neurons connect each other by weighted synapses as an interconnected group of biological neurons, which transforms the input variables into output results.
From the perspective of functional implementations, ANNs need to map one numerical vector space to another, by means of vector-matrix multiplication, weight matrix updating, and nonlinear activation functions. In a certain layer, the potential energy obtained by a neuron is equal to the sum of the outputs of the corresponding neurons on the previous layer multiplied by their weights. This weighted sum is then passed through an activation function (usually non-linear) to produce the output. Based on these synapses being connected, ANNs map one numerical vector space to another using vector-matrix multiplication. Mentioning a specific application, synaptic weights are updated through training.
In terms of hardware implementation, the memristor is generally integrated into the crossbar structure easily where each cross-point acts as the synapse which is introduced before, and the peripheral neuron circuits will be purchased to match the construction of non-linear activation functions. [42,164,165] The whole of the memristor crossbar can be considered as a layer, the input voltage (current) is applied to the row of the memristor crossbar, which acts as the input of ANN, and the corresponding output current will be detected at every column. [76,166,167] More details can be found in Figure 12. The vector-matrix multiplication is naturally implemented in the layer to achieve the mapping of numerical vector space. When the inputs in the form of voltages are driven to the rows of the memristor in parallel, the output current at every column is determined by the total current of all memristors connected to the input vector voltage via Ohm's law and Kirchhoff's law (Figure 11a). [168] In contrast with software neural networks, the vector-matrix multiplication can be implemented as a single-analog computational step instead of weight update and transfer, reducing the time and energy consumption. Thus, most of the neural networks can be accelerated in memristor crossbars owing to the parallel, analog, and in-memory characteristics of memristors. [41,42,139] As mentioned above, the synaptic matrix of the neural network can be directly mapped to a memristor crossbar in the hardware whereas memristors store synaptic weights and simplify the computation. Usually, a single memristor crossbar can only implement a single layer in ANN. When implementing a deep neural network, a multi-hidden layer neural network, more memristor crossbars are needed, and the output of the previous memristor crossbar acts as the input of the next memristor crossbar. The output neuron based on the memristor with a settable threshold and dynamic regulation ability is also needed, such as the LIF neuron. A large number of hidden layers make the advantages of memristors more obviously shown, simplifying the computation and reducing energy consumption.
Except for matrix multiplication and activation functions, weight updating is majorly related to learning rules which will be introduced in the next section. The conductance of the memristor is adjusted to the target value during training, which corresponds to adjusting the cells' connections between each other. By tuning multiple cells individually or simultaneously in parallel, the memristive synaptic weight would be adjusted to match the need for specific tasks.

The Learning Algorithms for ANNs
The structure of hardware neural networks and the training methods are equally crucial in applying memristive neural networks. We will analyze two typical categories of learning algorithms in neural networks: unsupervised and supervised learning. Figure 11. Comparisons of ANNs and spiking neural networks (SNNs) in terms of neuron, neural network abstraction and hardware implementation. Reproduced with permission. [159] Copyright 2018, Wiley-VCH. Reproduced under the terms of the CC-BY license. [160] Copyright 2018, Springer Nature.
Supervised learning utilizes the labeled dataset to learn the mapping function between inputs and outputs, which can be thought of as studying from a teacher figuratively. By analyzing the training dataset, the function of input and output can be inferred and used for mapping new examples. [169] Generally, the principle of supervised learning is to introduce feedback progress to lower the difference between the inferred outputs and the desired outputs. Therefore, the synaptic weight can be progressively adapted to reduce errors. When the training inputs are transmitted to the preneuron layer, the neural network can arise the corresponding inferred outputs through the feed-forward process, and the supervised learning algorithms will configure the network. In multi-layers neural networks, backpropagation learning is widely used and particularly popular. [170] In hardware implementations, Alibart and co-workers demonstrated the pattern classification with a single-layer perceptron neural network based on the memristive crossbar. [42] In particular, the perceptron learning rule was implemented by both ex-situ and in situ methods. For in situ approach, four specific pulse sequences are applied to the inputs and outputs of the crossbar circuit to strengthen or weaken the synaptic weight. Here are some similar examples (Figure 12c). [41,165,[171][172][173][174] Recently, Cai et al. fabricated a complete, integrated memristor/CMOS system, and a supervised classification layer can be achieved based on a passive memristor crossbar array integrated with all the necessary interface circuity, digital buses, and an Open-RISC processor. They demonstrated some widely used models on the same chip. A feed-forward single-layer perceptron (SLP) network is demonstrated to verify the operation of the integrated chip, and the SLP can already achieve 100% classification accuracy for both the training and testing sets after five online training epochs. They also demonstrated a two-layer network used to analyze and classify data obtained from breast cancer screening, [172] and 94% and 94.6% classification accuracy during training and testing can be realized.
In contrast to supervised learning, unsupervised learning utilizes the training data without assigned labels or scores in order to learn the relations between the elements in the dataset. The main idea of the algorithm is to find the hidden structures, patterns, or features in training data so that the incoming data can be analyzed. For example, K-means, a representative unsupervised learning algorithm, partitions the input data into K clusters according to the hidden similarity among the input data. [175] Related hardware implementations can be found in these works. [57,176] Jeong et al. demonstrated the K-means algorithms using a 16 × 3 crossbar array in which an additional row can represent the Euclidean distance. After identifying the nearest centroid, the conductance states are updated to stabilize the centroids of the K clusters. Furthermore, unsupervised learning has been widely used in data clustering, pattern classification, etcetera. These hardware implementations show great potential in ultra-dense, low-power computing systems. [57,139,[177][178][179] Moreover, a diffusive memristor is implanted as a neuron that can utilize the integrate-and-fire functions independently. Therefore, it is able to achieve the unsupervised synaptic weight updating and pattern classification without additional circuits. Wang et al. demonstrated a LIF neuron-based diffusive memristor, which has similar dynamic properties to ion channels. Subsequently, synaptic weight updating and pattern classification of convolutional neural networks were implemented using the learning rules of STDP. [139]

The Basic Structure of Spiking Neural Networks
In the real biological nervous system, neurons contact each other in terms of "spiking." Spiking neural networks (SNNs) employ spiking neurons as computing units, as shown in Figure 11b, in which the information is transmitted and processed in terms of sparse and spatiotemporal binary signals (Figure 13a). [181][182][183][184] We can conclude by comparison that ANNs used currently are inconsistent with the working mechanism of biological neurons. Besides, the necessary conditions for SNNs are mainly three parts, the data-to-spike encoder, the neuron model, and more biological learning rules than ANNs. The special component among these is the data-to-spike encoder. Because SNNs perform calculations using spikes, the data-to-spike encoder needs to map the real-valued dataset to the sequence of spikes.
Distinguished from ANNs that use real-valued dataset elements directly, SNNs need to encode the information into binary spike trains. A detailed introduction to neural encoding can be found in Schliebs et al. [185] However, the encoding schemes of spikes used currently are all special cases of fully temporal cases. One of them is a special binary encoding which is all-or-nothing coding. It ignores time properties, and the spikes are presented as digital sequences (0 or 1). Another kind Figure 13. Memristor-based spiking neural networks (SNN). a) Structure and principle of multiple SNN. Reproduced with permission. [182] Copyright 2009, Elsevier. b) Scanning electron top-view image of a SNN and implementation of its LIF neurons. Reproduced under the terms of the CC-BY license. [160] Copyright 2018, Springer Nature. c) Spatiotemporal patterns recognition based on single layer SNN. Reproduced with permission. [197] Copyright 2018, AAAS. d) Training of SNN based on multi-memristive synapses. The time detection task was completed by unsupervised learning, and the weight was updated by STDP rules. Reproduced under the terms of the CC-BY license. [192] Copyright 2018, Springer Nature. e) A SNN implemented by capacitances coupling memristor-based synapses. Reproduced with permission. [188] Copyright 2019, Wiley-VCH. of abstraction of the timing properties of spikes is rate coding, and only the rate of spikes in the interval is recorded as information. The firing rate of spike trains is positively related to the strength of the input signal. [186] Except for these two schemes, real-valued datasets can be encoded into the spatial and temporal firings of spikes in the spatiotemporal-coding scheme. In the spatiotemporal-coding scheme, data is encoded into the spatial and temporal firings of the spikes corresponding to the strength of input signals (stimulus), and neurons that receive stronger signals would spike earlier. [10] After receiving input signals via synapses, neurons demonstrate abundant spike characteristics in SNNs. In comparison to the neuron model in ANNs, neurons in SNNs send nerve spikes in response to signals instead of continuous values. Therefore, these neurons often have complex dynamic properties, and the models commonly used are the H-H model, IF model, LIF model, etcetera. Among these, the LIF model with a certain threshold is widely used. As introduced before, the LIF model transmits a pulse forward only when the membrane potential threshold is exceeded; after firing, the potential of the membrane will be reset to the original state and waiting for the next spike. Prezioso et al. implemented coincidence detection with passively integrated memristive circuits, in which 20 input neurons are connected to a single silicon-based LIF neuron via memristive crossbar-integrated synapses (Figure 13b). [160] The updating of synaptic weight is based on the STDP learning rule. Zhang et al. demonstrated a one-layer SNN based on LIF Mott spiking neurons and RRAM synapses to classify the MNIST datasets with high recognition accuracy. The different digital patterns can be presented in terms of different spiking rates. [187] Except for the basic structure of SNN, it is also essential to choose the appropriate learning algorithms to implement specific functions and improve performance. Consequently, biologically plausible learning approaches are adopted to change synaptic weights, which will be introduced in more detail in the following section.
In the hardware implementation of SNNs, encoding and decoding the pulses is still a challenge to overcome. As the implementation of ANNs is relatively more straightforward for both hardware and software, a popular approach to developing SNNs is the ANN-to-SNN conversion, whose core is to convert the spike rates of neurons in SNNs into the value of neurons in ANN. Rivu et al. built compact oscillatory neurons made of diffusive memristors and shunt capacitors and mapped the weights of a pre-trained ANN to neurons in SNNs. Thus, the spike rates of neurons in SNNs are proportional to the amplitude of the current applied to them (Figure 13c). [188] Based on the ANN-SNN conversion scheme proposed by Diehl et al., [189] Sengupta et al. proposed a weight-normalization technique to balance sequentially for each layer, and the SNN operation is in the loop during the conversion phase. The accuracy loss during the ANN-SNN conversion process is minimized by a margin of 0.57% by considering SNN-model based weight-normalization scheme. [190]

The Learning Algorithms for SNNs
In SNNs, a representative unsupervised learning algorithm is STDP, in which the modification of synaptic weight is related to the time difference between the pre-and postsynaptic spike. Currently, the main approach for hardware implementation of STDP is to utilize memristors as synapses matched with additional neuron circuits, and the STDP rule can be attained using the gradual and probabilistic switching characteristic of memristive synapses. Serb et al. demonstrated weight-dependent STDP in an individual TiO 2 -based memristor. [57] Chu et al. demonstrated an SNN for pattern recognition, and a modified STDP rule was used to adjust the synaptic weight. [191] A multimemristive synaptic SNN architecture was proposed by Boybat et al. In their experiment (Figure 13d), [192] the synaptic weight of a single synapse was represented as the combined conductance of multiple PCM devices, whose synaptic weights were updated using the STDP rule. Moreover, the IF model can be simplified based on the intrinsic accumulation effect of PCMs. Some common non-ideal effects in a single memristor, such as nonlinearity, conductance drift, and read noise were mitigated, and equivalent accuracies could be calculated. In addition to STDP, SNNs can also use other unsupervised learning rules. Similar to a human brain, the strength of the interaction between neurons changes during the learning process. Zhang et al. implemented an emerging in silico neuron that communicated and modulated each other's membrane potential by event-driven spikes instead of adjustable synaptic weight. [193] Compared to unsupervised learning, supervised learning algorithms remain to be further investigated. On the one hand, the plasticity of memristive devices makes it easy to exhibit STDP-like weight adaption, which is more bio-plausible. [67,194] On the other hand, the network should fire spikes at the accurate time in response to the input according to the definition of supervised learning, which is a challenging task. Currently, there are several supervised learning algorithms for SNNs. In the process of implementing supervised learning algorithms in SNN neural networks, the backpropagation algorithm in ANNs is a vital reference object. However, due to the non-differentiability of the spikes, much work was carried out to investigate how to adapt the backpropagation algorithm to make it suitable for SNNs, including the surrogate gradient method. [195] Multi-SpikeProp, akin to traditional error-backpropagation (gradients of postsynaptic potential), has demonstrated the ability to perform complex learning tasks. [182] In the remote supervised method (ReSuMe), the synaptic weight can be updated based on STDP and anti-STDP rules. [196] Both of these rules are more sophisticated than traditional supervised learning in ANN; regardless of this fact, they still did not provide us with better performances (Figure 13e). [197]

Comparisons between Memristor-Based ANNs and SNNs
Having introduced ANNs and SNNs separately, it is necessary to compare them for a clear understanding and to guide their future development ( Table 4). Inspired by the human brain, SNN is the third generation of neural networks, which is believed to hold promise for energy-efficient computing and remarkable cognitive performance. [181,198] It encodes information into sparse and spatiotemporal binary spikes; in other words, it introduces the concept of time when operating on discrete spikes. In contrast, ANNs originate from mathematical derivation, and the information is transmitted and processed in terms of continuous analog value. [161,162] The differences in theoretical source and information flow also result in the differences in the essential components of neural networks. Synapses in ANNs are primarily responsible for the vector-matrix multiplication. Neurons integrate the weighted-sum from synapses and apply non-linear activation functions to determine its output signal. The numerical matrix is usually implemented with a memristor crossbar; thus, the performance of memristor-based ANN is tightly related to the stability and analog switching behavior of the memristive synapse. Since SNNs treat data as a time series and the output of SNN neurons needs to encode the time domain information, SNNs usually have a critical requirement on the dynamics of synapses and neurons. [199] Memristive devices with synaptic plasticity provide the condition for implementing bio-plausible learning rules in SNNs. [200,201] The memristors' switching behavior and relaxation dynamic are utilized to implement the neuronal function of threshold logic. For the same neuron model, it simply uses its weight to calculate forward in ANNs, while in SNNs, it only switches to the working mode when the nerve spike received exceeds its spike threshold, then an output pulse will be sent out. As a result, the neuronal dynamics will directly affect the transmission and process of the spike (information). Besides, owing to the difference in information flow, backpropagation, one of the most used algorithms in ANNs, cannot be used to train SNNs as the spike cannot be differentiated. The STDP and surrogate gradient descent learning rules are commonly used in SNNs. [195,202] Overall, ANNs are data-and math-intensive, and high accuracy for specific tasks can be obtained through layer-by-layer computation, which results in high power consumption at the same time. In contrast, SNNs are math-light, and their information flow and working modes are more bio-realistic than ANNs. The combination of spatial and temporal information helps them compute faster and more energy-efficient. [203,204] Besides, switching from standby to working mode also reduces unnecessary energy consumption. In noise immunity, SNNs usually perform better than ANNs. [205] On the one hand, hardware-based SNNs take into account the intrinsic stochasticity of the device, which increases SNNs' noise immunity.
On the other hand, information is contained in presence or absence of a spike in SNN, thus usually the frequency (the number of pulses during a set sampling time) of spikes is used to represent information. As the sampling time gets longer, the noise effect is attenuated. As a result, SNNs have better noise immunity than ANNs. However, there are some tricky issues for SNNs, including the lack of comprehensive benchmark data sets, the lack of satisfactory general learning rules, the immaturity of the information coding framework, etc. Thereby, it is feasible and practical to use ANNs in a mathintensive computing system and SNNs are often difficult to achieve the same level of accuracy. SNNs have a unique advantage in processing spatiotemporal data, allowing for faster and more energy-efficient computing, and demonstrating strong competence in low-power edge employment. [206,207] Thus, it is feasible to combine the advantages of these two types of networks and consolidate their development, and there are some studies available. Xu et al. propose a brain-inspired perceptroninception-based neural network (CSNN) consisting of a partial CNN and an SNN. This combination results in better performance compared to other cognitive models with fewer neurons and training samples, and brings more biological realism into the explanation of image classification models. [208] Yang et al. designed the ANN-SNN converter based on diffusion memristors and shunt capacitors to improve SNN performance. [188]

Memristor-Based Spinal Cord
From a functional point of view, the spinal cord is an essential conduit where motor and sensory information travel between the brain and other parts of the body. The spinal cord receives messages from the brain to control body movement, breathing, and other bodily functions; the spinal cord sends messages from the skin and other sensory organs to keep the brain informed about the rest of the human body. Besides, the spinal cord may also function independently from the brain in conducting motor reflexes, including patellar reflex, tendon reflex, etcetera. However, there is no mature architecture for a memristive manual spinal cord, and we will report some current achievements related to the emulation of the spinal cord. Throughout the body, the spinal cord serves as a sensory-motor interface with its environment, and the vast majority part of the memristor-based spinal cord implementations mainly focused on the neural pathways via the spinal cord. From receiving stimulus to acting on the impulse, the memristive device would be responsible for processing the sensory information during these processes.
Until now, work and research on the neural pathway have focused on the perceptual part, i.e., receiving external information and performing initial processing. Straight after transforming external sensory signals into electrical signals, the conductance change of the memristor can be considered an adaptive response to the stimulus based on the memristor's switching characteristics. The whole process is similar to emulating synaptic functions using memristors. Usually, the response is expressed in the form of voltage or current; note that the response refers specifically to the initial processing of the spinal cord in receiving a perceptual signal rather than motor actions. Among these, most studies are related to the sensory receptors, including rapidly adapting receptors, slowly adapting receptors, and nociceptors. [209][210][211][212][213] Jung et al. demonstrated the spinal cord perception of temperature signals with a thermoelectric module, a memristor, and a resistor in series with the memristor. The thermoelectric module acts as the external signal source to generate voltage pulses of different amplitudes depending on external thermal stimuli. The conductance of the memristor changes with the voltage pulses, and the voltage changes of different characteristics observed from the resistor are defined as the key functions of the biological nociceptor, including "threshold," "relaxation," "no adaptation," "sensitization" and "cure" (Figure 14a). [209] Similarly, Kim et al. demonstrated a solid-state nociceptor based on a Pt/HfO 2 /TiN memristor with the functions of threshold, relaxation, allodynia, and hyperalgesia. [210] In particular, a p-type enhancement-mode field effect transistor (p-FET) was considered the spinal cord, and its gate is connected to the output of the memristive nociceptor. Under external stimuli, the output voltage of the nociceptor increases, and p-FET starts to be turned off owing to the increase of gate voltage in the positive direction. As a result, the p-FET current decreases violently, and p-FET mimics the amplification of the output signal of the nociceptor by the spinal cord. Furthermore, Song et al. demonstrated several different receptors based on their diffusive memristors, including rapidly adapting receptors, slowly adapting receptors, and nociceptors. The switching mechanism of their memristive device is related to the formation of the Ag conductive filament, and the shape of the conductive filament can be controlled through the injected amount of Ag in the device. The shape of the conductive filament affects the device's response to electrical stimuli, and memristor-based receptors with different adaptive characteristics have been realized by changing the amount of Ag embedded in the device (Figure 14b). [212] Recently, Wang et al. demonstrated a closed-loop system consisting of an MXene/thermoplastic polyurethane (TPU) tensile sensor, an Ag ionic polymer-metal composite (IPMC) actuator, and a novel flexible threshold-switching memristor. Based on this system, they constructed an unconditional reflex arc system. In contrast with the previous work, this system contains the perceptual part and the motor part. The addition of the IPMC actuator emulates the motor signals sent from the spinal cord. The whole reflex arc exploits the bionic characteristics of memristors and provides a potential prospect of applications in soft robots and health monitoring. [214] It is expected that the sensing part of the memristor will be combined with the actuator in the future to provide more practical value. Figure 14. Emulation of spinal cord functions using memristors. a) Implementation of the nociceptor using a diffusive memristor. Reproduced under the terms of the CC-BY license. [209] Copyright 2018, Springer Nature. b) The sensory receptor that can demonstrate adaptive and maladaptive behaviors simultaneously. Reproduced with permission. [212] Copyright 2021, Wiley-VCH.

Application
Based on the neural system of memristors, and the primary application needs of humanoid robots, we will present three aspects of the application of memristor neural systems (Figure 15), including perception systems, brain-inspired computing systems, and etcetera.

Perception Systems Based on Memristors
Perception systems are the medium of communication between us and the external environment, and commonly recognized perception systems include vision, hearing, touch, taste, and so on. Recently, demonstrations of perception systems using memristors are concentrated on hearing, vision and touch.
In the tactile sensory systems, various kinds of sensors are connected to memristors (Figure 16a), among which piezoresistive films are very common. After transducing external pressure information into electrical signals, the state of memristors changes accordingly. In response to varying degrees of external stimuli, memristors respond differently due to their threshold switching behaviors and richly dynamic properties. [215,216] As the stimulus reached a certain threshold, the state of the memristor changed. Zhang et al. connected a piezoresistive film with a memristor as shown in Figure 16b, and the conductance of the memristor changed with the external pressure ( Figure 16c). As the external force increases, the response current of the device increases. They attached their sensing system to a pen, and different characters were written, which can be characterized owing to the different strokes using KNN algorithms (Figure 16d,e). [216] Furthermore, Tan et al. realized a tactile sensing and processing system which consists of a pressure sensor, the ADC-LED circuit and memristors as shown in Figure 16f. [217] Once external pressure has been applied to the pressure sensor, ADC-LED circuits will initiate the optical spike based on the voltage signal sent by the pressure sensor. Following this, the memristor processes the pressure information, and the corresponding current response can be observed. Intriguingly, the system can process multiple stimulus inputs simultaneously by setting up multiple branches (Figure 16g). By attaching multiple sensing points, this tactile sensing system can sense movement and the response currents vary significantly from one movement to another (Figure 16h,i). Similarly, Xia et al. demonstrated an artificial tactile perception system with additional memory properties. While the CNT/PDMS sensor transforms the pressure information into electrical signals, the memristor serves as a synapse, and the pressure information can be retained in the memristor element. [215] In terms of visual perception systems, memristors can map external image information to its conductance. Similar to the tactile perception system, the visual perception systems can be demonstrated by connecting light-sensitive devices to ordinary memristors. Light-sensitive devices convert optical signals to electrical signals, which can motivate the switching of memristors. Jiang et al. displayed a novel high-performance dual-excited pressure memory (DPM) device consisting of a piezo-OLED array and the piezo-memristor array, which could receive the potential excitation. The resistance of the DPM pixel could be modified by ultraviolet illumination of the piezo-OLED and piezo-potential of the piezo-memristor with the applied force. Thus, this DPM device exhibits the ability of pressure or vision sensing and memory functions in a system (Figure 17a). [218] The specific mechanism of the device and the effect of the light intensity on the response current of the memristor can be found in Figure 17b,c. Chen et al. integrated ultraviolet image sensor arrays and the memristive device in series; thus, image information would be obtained in terms of conductance values at various points in the memristor arrays (Figure 17d-f). [219] Another type of implementation is based on memristors, which can be motivated by optical signals. Similar to human eyes, Kim et al. demonstrated an artificial photonic nociceptor, and the memristor-based on ZnO/ATO/FTO structure can receive and respond to external optical stimuli. [220] Zhu et al. developed a CH 3 NH 3 PbI 3 (MAPbI 3 )-based memristor that exhibits light-tunable synaptic behavior. The V I · /V I × concentration in MAPBI 3 film increases under electrical stimulation, and spontaneously decays after removing the electrical stimulation. Besides, the increase/decrease of V I · /V I × concentration results in the increase/decrease of device conductance. Light illumination increases the formation energy of V I · /V I × (Figure 17g-i); thus, light can be used to control the V I · /V I × generation and annihilation dynamics. [221] Based on this feature, the device can be used to detect the coincidence of electrical and light stimulations. As shown in Figure 17j, when a nonlight pulse is applied between t 1 and t 2 and the electrical pulse is applied between t 3 and t 4 , the distribution of the current response is related to the position of the applied nonlight and electrical pulses. The device current is an essential parameter in detecting whether electrical and optical pulses overlap. Only when the nonlight pulse and the electrical pulses were partially or fully overlapped, the device current significantly increased to a value higher than 3 µA. In contrast, the response current is weak. In the auditory perception systems, researchers have demonstrated memristors in sound azimuth detection and speech recognition. Azimuth detection is usually different from the speech recognition in that the former is more concerned with location information, while the latter is more concerned with speech content. Thus, the sound signal is usually divided into a left signal and a right signal to be processed in azimuth detection, and most implementations rely on interaural time difference (ITD) theory, i.e., using the difference between the sound reaching two ears to determine the direction of the sound source. [222] Wang et al. demonstrated a 2 × 2 SNN to detect the sound location based on ITD theory as shown in Figure 18a. The acoustic signals detected in the left and right ears serve as inputs to the neural network and result in the different voltages in POST1 and POST2. The different ΔV int between POST1 and POST2 is a function of the interaural time difference, so azimuth detection has been eventually achieved. The specific composition of the memristive synapse can be found in Figure 18b-d. [197] Furthermore, Hu et al. demonstrated braininspired sound localization based on the integrated 1 K HfO xbased memristor array (Figure 18e,f). After training in situ using Head Related Transformation Function dataset, sound Figure 16. Tactile perception systems based on memristive devices. a) Schematic of perception systems based on memristive device. b) The artificial haptic perception system consisting of a pressure sensor and Nafion-based memristor. c) Current response to the different pressure applied to the perception system. d) Framework for sensing pressure information. When applying the perception system to the pen, different responses corresponding to various written letters can be detected, thus characters can be recognized using KNN algorithms in (e). a-e) Reproduced with permission. [216] Copyright 2019, Wiley-VCH. f) Schematic diagram of the biological and artificial pressure sensing systems. In the memristive pressure perception systems, external pressure can change the resistance of MXene in the pressure sensor, then the ADC-LED circuit receives the voltage signal from the sensor and initiates the optical spike based on the pressure information, so the pressure information can be processed using photomemristor device where they induce post-synaptic current (PSC). g) Schematic diagram of an optoelectronic pressure perception system with two branches. h) Schematic diagram of a 2 × 2 optoelectronic pressure perception system for motion detection. i) PSCs and frequencies detected when touching the sensor array from 1a to 2a (red). PSCs and frequencies were detected when moving a finger from sensor 1a to 2b (green). f-i) Reproduced under the terms of the CC-BY license. [217] Copyright 2020, Springer Nature.
localization can be realized in the auditory perception system. A notable aspect of their work is that they further analyzed the balance between training effectiveness and hardware overhead with different training protocols and hardware platforms. [222] Unlike the simpler pressure signals and varying degrees of optical stimuli, acoustic signals related to spatiality and temporality tend to be more complex to process. Therefore, a neural network consisting of memristive synapses and neurons has been used to complete auditory perception systems. For specific sound processing, the common workflow is as follows. First, the cochlear implant encodes sound samples into signals that serve as inputs to the neural network. In Figure 17. Visual perception systems based on memristive devices. a) Bio-inspired pressure or vision memory system integrated by the piezo-memristors and the piezo-OLEDs. b) Analytical mechanism of the UV-excited conversion of the piezo-memristor with the valence state change between Mo 6+ and Mo 5+ in the MoO x layer. The resistance of the DPM pixel could be modified by ultraviolet illumination of the piezo-OLED. c) Retention time for the piezomemristor from high resistance state to low resistance state with various UV-excitation intensities. a-c) Reproduced with permission. [218] Copyright 2020, Elsevier. d) Schematic of human visual perception system (taking butterfly observation by human eye as an example). e) Schematic illustration of memristive visual perception and memory system consisting of image sensor and UV-motivated memristors. f) Imaging and memorizing behaviors of the visual perception system. d-f) Reproduced with permission. [219] Copyright 2018, Wiley-VCH. g) Schematic of the CH 3  . j) Coincidence detection of electrical and light stimulations using the memristive device. When a nonlight pulse is applied between t 1 and t 2 , the current response of the device is related to the coincidence between the nonlight pulse and the electrical pulse applied between t 3 and t 4 . g-j) Reproduced with permission. [221] Copyright 2018, ACS.   works, the encoding of the cochlear implant is mostly based on software simulation. The core of the simulation is to convert time-domain signals to frequency domain signals through the Fourier transform and then feed them into a neural network after some filtering operations. Secondly, train the neural network until sound samples can be classified. [223,224] Lately, Seo et al. displayed a hardware neural network consisting of artificial hybrid synapses based on WSe 2 and MoS 2 memristor (Figure 18g). After Fourier transforms, they translate the sound sample to the specific acoustic pattern and directly use these patterns to train the neural network (Figure 18h). [225] Details of the hardware implementation of the neural network can be found in Figure 18i.
In conjunction with the external signal conversion system, the switching characteristics of the memristor allow for a certain degree of processing of external stimuli, which lays a solid foundation for a more bionic artificial perception system.

Brain-Inspired Computing Systems
Due to the switching dynamics and in-memory computing capabilities, memristors become promising candidates for implementing massive parallel and energy-efficient braininspired computing systems such as a biological neural network. Currently, abundant brain-inspired computing systems based on memristors have been demonstrated to complete complex tasks, such as pattern recognition (object classification, object recognition, etcetera.), sequence recognition (speech, handwritten recognition), image processing, and so on.
In brain-inspired computing systems, information processing normally occurs in ANNs, which is usually a large crossbar constructed by memristors. In pattern recognition, Joeng et al. applied the memristor-based ANN to analyze three kinds of flowers in IRIS flower data using K-means algorithms. In this algorithm, the conductance state of each memristor is directly mapped into the location of K centrioles. They also showed that the Euclidean distance comparisons could easily be obtained by expanding the crossbar array to an additional row. [175] In a single-layer perception network, Prezioso et al. mapped a 3 × 3 image into V1-V9 as the input signal of the neural network; synaptic weights, which correspond to the difference between the conductance of two memristors, can be adjusted by a specific error matrix. [41] Furthermore, Li et al. demonstrated a multilayer neural network using a 128 × 64 memristor array (Figure 19a), and the hardware implementation process can be referred to Figure 19b. After training the network using backpropagation algorithms in situ (Figure 19c), handwritten digits can be recognized by recording the currents of output layer neurons. As shown in Figure 19d, the neuron representing digit "9" has the highest output current compared to other output neurons, and the classification result is in accordance with the input digit. [174] Yao et al. demonstrated a neural network for face classification where the architecture of one transistor and one memristor was used to achieve this (Figure 19e). [180] Furthermore, both with and without writeverify operation schemes are studied, and the write-verify scheme shows a better performance in converging speed, recognition accuracy, and energy consumption. However, the scheme without write-verify simplifies the operation to a great degree. Similarly, Jang et al. reported a two layer ANN for face classification where every pixel in the picture is connected to the input layer neuron as shown in Figure 19f. [226] Sun et al. implemented a sequence module through the design of a fully memristive neural network that can converge 24 sorting cases to one case. Hence, the neural network can recognize and sequence four characters simultaneously. [227] In image processing, Sheridan et al. implemented a sparse-coding system constructed by a memristor crossbar. Based on pattern matching and lateral neuron inhibition, they demonstrated image construction successfully, and the performance can be further improved with image pre-processing techniques (Figure 20a). [228] Yao et al. demonstrated a five-layer convolutional neural network (CNN) consisting of eight 128 × 16 memristor crossbars, which is the first hardware implementation of CNN using memristor crossbars. A hybrid-training method was then proposed to accommodate non-ideal device properties. [229] Besides, some memristors, as the basic units of memristive neural networks, have highly dynamic properties and short-term memory functions, which are similar to the properties of the high-dimensional and dynamic reservoir. Therefore, the "echo state" and "separation" functions can be demonstrated naturally in the memristor crossbar. The echo state corresponds to the fading of the former state with time passing, and separation corresponds to the different outputs of different input sequences. Hence, the projected features of different sequences in high dimensional feature space can be learned and analyzed by supervised learning algorithms such as backpropagation. In general, reservoir computing allows more complex tasks to be accomplished with simple networks, and the basic structure of reservoir computing can be found in Figure 20b. Du et al. demonstrated a small reservoir consisting of 88 memristor devices that can directly process information in the temporal domain, such as handwriting recognition as shown in Figure 20c-e. The performance was comparable to those achieved in large networks. [230] Midya et al. performed a memristive reservoir equipped with memristor-based read-out layer. They trained the read-out system in situ to recognize the temporal version of MNIST and received an accuracy of 83%. [231] Furthermore, Moon et al. increased the dimensionality of the reservoir space presynaptic neurons (PREs), postsynaptic neurons (POST) and synapses. c) Typical current-voltage curves of the RARM device in (b). d) Schematic diagram of the memristive synapse based on one transistor and one memristor structure. a-d) Reproduced with permission. [197] Copyright 2018, AAAS. e) Implementation of sound localization based on memristors. f) Mechanism of human brain sound localization and realization of binaural sound signal processing by memristor crossbar array. In this system, memristor array acts as synapses to process sound signal. e,f) Reproduced under the terms of the CC-BY license. [222] Copyright 2022, Springer Nature. g) Functional and structural comparison of the biological synapse with the memristive device. h) Working flow of acoustic pattern recognition. In this working flow, the sound wave is first recorded as a function of time or frequency and the sound signals are sampled. Finally, an acoustic image can be obtained based on the discrete sound information. i) Hardware neural network used for acoustic recognition task. g-i) Reproduced under the terms of the CC-BY license. [225] Copyright 2020, Springer Nature. using virtual nodes, which in turn significantly improved the accuracy of speech recognition. [232] Recently, Wang et al. demonstrated spoken-digit recognition based on a memristor-based reservoir computing system as shown in Figure 20f. [233] In this system, the input vector is transformed into a temporal signal through a mask and sent to the reservoir consisting of a memristor and a resistor. The memristor response in a duration time is chosen as the virtual nodes, and the mask and recording processes are repeated N times to mimic an N-parallel reservoir computing system, where the N time memristor responses form the reservoir state together for subsequent classification. The specific audio waveform, time multiplexing process, and memristor response can be found in Figure 20g. When the total reservoir size is constant at 400, and the mask length is set to 10, the word error of predicted results is as low as 0.4%, achieving a good recognition result (Figure 20h).
The application of SNNs in brain-like computing is more concentrated on the recognition of spatiotemporal patterns. Prezioso et al. demonstrated an SNN consisting of memristorbased synapses and LIF neurons. In the coincidence detection task, the STDP rule was adopted to fire a spike when receiving correlated spikes from several input neurons. [160] Similarly, Wang et al. demonstrated a memristor-based SNN which can learn and recognize spatiotemporal patterns. [197]

Other Bionic Applications
Memristive circuits can also be utilized to perform other bionic functions. Among these, classical conditioning and brainmachine interface have developed rapidly and are significant for the integrity of the memristor-based neuromorphic system.
Classical conditioning, also known as Pavlovian conditioning, is a kind of associative learning and memory in which an association between unconditioned stimulus (US) and neutral stimulus (NS) has been established. Thus, the Figure 19. Brain-inspired computing systems for pattern recognition. a) Photograph of the integrated 128 × 64 1T1M (one transistor and one memristor) array. b) Schematic of fully connected neural networks and corresponding hardware implementation. c) Flow chart of the backpropagation algorithm for in situ training. d) Demonstration of handwritten digit recognition based on the memristive neural networks in (b). The raw current measured from the output layer neurons depends on the input digit. a-d) Reproduced under the terms of the CC-BY license. [174] Copyright 2018, Springer Nature. e) A memristor-based neural network in which one memristor is the basic unit for face classification. Reproduced under the terms of the CC-BY license. [180] Copyright 2017, Springer Nature. f) A two-layer ANN for face recognition. The input neurons are connected to the pixels of the input image. Reproduced with permission. [226] Copyright 2019, ACS.
single NS can elicit a conditioned response (CS) which is similar to the unconditioned response (UR) elicited by the US. In fact, the formation of classical conditioning is related to the coupled stimuli, i.e., coupled signals, which is similar to the STDP learning rule as depicted in Figure 21a. The mechanism behind the formation of classical conditioning is also the resistance plasticity of the memristor. [234][235][236][237][238][239] Wu et al. demonstrated classical conditioning with an Ag-filament Figure 20. a) Natural image processing using the sparse coding algorithm. Reproduced with permission. [228] Copyright 2017, Springer Nature. b) Schematic diagram of reservoir computing systems. c) Network for digit recognition based on the reservoir computing system based on memristive devices with short-term plasticity. d) Working flow of the reservoir computing system in (c) for handwritten digit recognition. e) Reservoir states corresponding to the three examples. b-e) Reproduced under the terms of the CC-BY license. [230] Copyright 2017, Springer Nature. f) Schematic of a dynamic memristor-based parallel reservoir computing system, where the mask sequences are different for every single memristor reservoir computing unit. g) Illustration of the procedure of feature extraction of digit 9 based on the reservoir computing system in (f). h) Comparison of predicted and correct digits obtained from memristor-based reservoir computing systems. The color depth is proportional to the number of correctly classified digits, and the word error rate decreases with the reservoir size. f-h) Reproduced under the terms of the CC-BY license. [233] Copyright 2021, Springer Nature. flexible memristor, and several vital characteristics of classical conditioning can be observed based on the switching properties of the memristor, including acquisition, extinction, and recovery. Positive pulses, negative pulses, and output current are defined as US, NS, and the response strength, respectively. Only after applying enough pairing positive and negative pulses to the memristor directly does its conductance increase. Therefore, when negative pulses are applied individually, a sufficient current through the memristor can be observed. The whole training process is defined as acquisition. When NS is applied for a long time without accompanying CS, the memristor conductance decreases. Thus, the output current becomes negligible, which can be defined as extinction. Classical conditioning can be recovered after the training process. [235] Similarly, Li et al. demonstrated classical conditioning based on an Ag/AgInSbTe/Ta memristor, and the memristive device could be modified by CS-US spiking pair based on the STDP learning rule (Figure 21b). [238] Brain-machine interfaces (BMI) construct new paths between the human brain and target effectors, including robots, in which the memristor in BMI is mainly responsible for translating neural signals into control commands as shown in Figure 21c,d. [240][241][242] Liu et al. demonstrated a neural signal analysis system based on memristor arrays (Figure 21d). [240] There are two crucial parts to this system: the memristor-based filter bank and the single-layer perceptron neural network. The latter could filter the neural signals into several frequency bands, which are related to the brain states. Then the singlelayer neural network is trained offline to identify the brain states from filtered signals. Finally, the identification of the neural signals reached an accuracy of 93.46% and showed the feasibility of memristor to be used in brain interfaces. Further work is required to integrate a multifunctional memristorbased signal processing unit with neural probes monolithically, and the validity and robustness of memristor-based BMI can be tested.

Conclusion Challenge and Outlook
Although different materials and stimulus conditions make the integration of memristive systems difficult, existing work suggests these systems can still be integrated.
Let us start with the internal compatibility between memristor-based systems. Various materials have been applied to construct the memristors, and most materials and processes are compatible with the CMOS. The neuromorphic systems based on these memristors are similarly compatible with CMOS; thus, CMOS can bridge these systems together despite different materials. Besides, the inputs and outputs of these systems are mainly in the form of electrical pulses, thus integrating memristive nervous systems is also feasible in terms of stimulus conditions. Yi et al. have simulated a one-neuron one-synapse circuit using a VO 2 memristor neuron and a TaO x passive memristor synapse, and the synaptic weight can be continuously increased or decreased by the spikes sent from the VO 2 neuron without adjusting the VO 2 and TaO x model parameters. [133] For large memristive neural networks, the work of Figure 21. Other bionic applications based on memristors including classical conditioning and brain-machine interface. a) STDP-like learning memristive Pavlov's dog implementation. Reproduced under the terms of the CC-BY license. [234] Copyright 2019, Springer Nature. b) An associate learning model and the demonstration of Pavlovian conditioning based on it. Reproduced with permission. [238] Copyright 2015, Wiley-VCH. c) A multichannel parallel neural signal processing system based on memristor arrays. Reproduced with permission. [242] Copyright 2020, AAAS. d) Memristor-based neural signal analysis system for brain-machine interfaces. Reproduced under the terms of the CC-BY license. [240] Copyright 2020, Springer Nature.
Yang et al. also demonstrates the feasibility of integration. [139] In their fully memristive neural network, they interfaced the Pd/HfO 2 /Ta memristive synapse crossbar with SiO x N y :Ag memristive neuron to achieve pattern classification.
When integrating memristor-based systems into humanoids, the primary consideration is similarly their hardware compatibility. Current technologies related to sensing, processing, and control in humanoid robots are also based on CMOS. Although there are no practical applications of memristive nervous systems (including synapses and neurons) in humanoid robots, the memristive nervous systems are compatible with humanoid robot systems in terms of hardware.
So far, we have reviewed biological nervous systems and memristive nervous systems in hierarchical correspondence, including synapses, neurons, and the central nervous system. Starting with a brief introduction to biological systems, we focus on the basic construction of memristive neuromorphic devices and how to perform these biological functions. In particular, the memristive synapses and neurons are introduced in detail with their corresponding biological functions implemented within the memristors. Based on this knowledge, we explain the structure and learning algorithms of the highdimensional memristive central nervous system. The bionic nature of memristor brings new possibilities in humanoid research, and we further discuss several application fields. In summary, this paper covers most of the biological and memristive nervous systems, which makes it a very practical guide for bionic researchers or those who want to learn more about the functions and applications of memristors.
Despite the encouraging progress so far, the memristive nervous system is still in its infancy stage, and there are still many obstacles that must be tackled.

Non-Idealities of Memristors
The limitations for recent neuromorphic devices mainly derive from the nonidealities of memristors, such as the drift and nonlinearity of the conductance update, device variations, and etcetera. In particular, the drift and nonlinearity of conductance conflict with the ideal artificial synaptic weight modulation with high accuracy, which directly harms the learning effectiveness of memristive nervous systems.
Device to device and cycle to cycle variations is another significant nonideality issue for quick and accurate computations. The former leads to different electrical characteristics between memristors, while the latter leads to temporal stochasticity. Such spatial and temporal stochasticity have a direct impact on the information stored in memristors.

The Lack of the Modeling of Memristor-Based Neural Circuits
The gap between the biological nervous system and the memristive nervous system is still significant, in which the lack of neuronal circuits is the vital barrier, including artificial synapses and neurons. The main neuronal models currently used in the memristive nervous system are homogeneous and lack biological details, which is in contrast to the diversity in biological nervous systems. Thus, the lack of functional specialization of neural models blocks the memristive nervous system from processing information as efficiently as the brain. With the natural bio-realistic properties of memristors, considerable effort should be devoted to modeling neuronal circuits which can specifically mimic biological behaviors with little or no added cost. Thus, the memristive nervous system would possess more capacities similar to the biological nervous system.

Undeniably, with Challenges Comes Opportunities
The development of the memristive nervous system makes robots more human-like. The human-like characteristics here include not only bionic perception but also learning styles. As mentioned before, many attempts have been made from the acquisition to the processing of external information. We look forward to further integrating a neuromorphic system, which can be applied to humanoid robots. This neuromorphic system will significantly contribute to the operational security of humanoid robots in close vicinity of humans. Control schemes that support the body dynamics are expected to replace the traditional trajectory imposition scheme based on the bionic sensory system. Meanwhile, robots deal with realworld data most of the time, which is consistent with the spatiotemporal-coding characteristics of SNNs. SNNs have been commonly used for the functional implementation of robots to enhance their learning ability in recent years. [243][244][245] This aspect has rarely been emulated using memristor-based SNNs yet. Based on the convenience of biological-like learning algorithms and online learning achieved by memristors, the robots' learning ability and self-adaptive capability will be significantly improved.
Memristors not only bring us "a machine man" but also help us better understand ourselves from the neuroscientific perspective. From the fantastic analogies between biological neural dynamics and memristor switching mechanisms to simulating biological brain network activity at the scale of billions of neurons in the future, we can better understand the principles of brains and the treatment of many brain disorders like epilepsy and Parkinson's diseases. Not only that, but we can also explore the mechanisms behind memory and emotion with the memristive circuits. Recent advances in neuroscience techniques allowed us to observe and manipulate memory engrams, [246] which then enables us to investigate the memory in the cell population and circuitry level. The storage and memory characteristics of memristors allow us to emulate the memory engrams, thus driving our understanding of memory. In contrast, emotion is similar to associate memory due to its connection with news notifications. Several memristive circuits and neural networks have been proposed based on achieving associative memory, but the models are homogeneous. [247,248] Future research should focus primarily on the mutually reinforcing and diverse development of biological models and practical implementations of emotions.