Neuromorphic computing using spike-based learning has broad prospects in reducing computing power. Memristive neurons composed with two locally active memristors have been used to mimic the dynamical behaviors of biological neurons. In this work, the dynamic operating conditions of NbO2-based memristive neurons and their transformation boundaries between the spiking and the bursting are comprehensively investigated. Furthermore, the underlying mechanism of bursting is analyzed and the controllability of the number of spikes during each burst period is demonstrated. Finally, pattern classification and information transmitting in a perceptron neural network by using the number of spikes per bursting period to encode information is proposed. The results show a promising approach for the practical implementation of neuristor in spiking neural networks.
Neuromorphic computing based on artificial neural network (ANN) has received extensive attention due to its low energy consumption. The high-power consumption in the conventional CMOS hardware based on the von Neumann framework limits the use for data-driven machine learning tasks. [1] From a software perspective, the energy consumed for training an ANN can be reduced by optimizing the algorithm. However, brain-inspired neuromorphic hardware has demonstrated promising potential for energy efficient computation. Replacing a portion of the CMOS components with emerging devices can implement an artificial neural network circuit using fewer components and lower power consumption than conventional CMOS. [2][3] Artificial neuron is one of the most important elements in artificial neural networks. [4] Memristor is one of the promising candidates because of its low power consumption, plasticity and compatibility with conventional CMOS. [5,[6][7] Pickett et al. [8][9] demonstrated a memristive neuron by using two Mott memristors and realized the four basic neuronal functions, including: all-or-nothing spiking of an action potential, a bifurcation threshold to a continuous spiking regime, signal gain and a refractory period. Yi et al. [10] achieved 23 types of biological neuronal behaviors in memristive neurons, which possessed most of the known biological neuronal dynamics. Furthermore, Cassidy et al. [11] demonstrated the potential of achieving thousands of logic gates in neurons. Comparing to the traditional CMOS based artificial neurons, memristive neurons greatly reduce the power consumption and the number of components. However, there is still a lack of research on the state dynamics and operational window of the neuronal behaviors in relation to the input signals which limits the use of the rich dynamics of the memristive neuron. Comprehensive understanding of the memristive neurons is crucial for the practical implementation in artificial neural networks.
In this work, we report the spiking dynamics of NbO2-based memristive devices that exhibit insulator-metal transition (IMT). The transformation conditions and operational boundary of NbO2based memristive neurons are investigated. The effect of input resistance and capacitance on the bursting behavior of the memristive neuron is studied. Furthermore, the memristive neurons are incorporated into a 9×1 array perceptron to demonstrate the potential for neuromorphic computing.
Potential information spreading between neurons with different layers is also demonstrated.
Figure 1a shows a biological neuron that generates an action potential in the direction of an output synapse after receiving sufficient stimulus from dendrites. Lim et al. [12] approximated the resistance of the memristor to a hard switching between two preset resistance values of Ron and Roff, and calculated the boundaries A and B of the memristive neuron that can generate spike when one of the memristors X1 or X2 is in the critical state of switching, as shown in Figure 1c,d. However, memristor is a non-linear resistor, and the memristor resistance at the critical state is different from Ron and Roff, which results in inaccurate theoretical boundaries.
A resistor Rth at the threshold voltage and a resistor Rh at the hold voltage are introduced, as shown in Figure 1e. Figure 1f shows the operational window Rin-Vin of the simulated (see the parameters used for simulation and calculation are shown in Table S1 and S2 in the supplementary material 1). The operational window diagram is divided into three main areas: failure to fire (white), continuous spike (blue), bursting spike (green). The theoretical boundaries after the introduction of Rh and Rth are optimized from A (or B) to A’ (or B’), which are consistent with the simulated window diagram (see Equations S3, S4, S7 and S8 in the supplementary material 2).
Interestingly, a new boundary C’ for the two dynamic transformations between continuous spike and bursting spike is theoretically introduced considering that X1 and X2 are simultaneously in the critical state of transition (see Equations S5 and S6 in the supplementary material 2), and the calculated boundary is consistent with the simulated boundary. According to the calculation formula of the three boundary lines, we can design the desired window size of the continuous spike and the bursting spike.
Generally, every bursting spike possesses two oscillations components: one is the inter-spike oscillation which is a fast spiking oscillation within a single burst, the other is inter-burst oscillation which is modulated by a slow oscillation between the bursts (see Figure S2a in the supplementary material 3). [13] In memristive neuron, VK represents fast spiking oscillation and VNa represents slow oscillation. Figure 2a-e are the waveforms of VNa and VK when the capacitance C1 is in the range between 2 nF and 5 nF and C2 is between 0.2 nF and 0.5 nF. Equation 1 and 2 describe the charging an
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