Neuromorphic computing with multi-memristive synapses

Abstract

Neuromorphic computing has emerged as a promising avenue towards building the next generation of intelligent computing systems. It has been proposed that memristive devices, which exhibit history-dependent conductivity modulation, could efficiently represent the synaptic weights in artificial neural networks. However, precise modulation of the device conductance over a wide dynamic range, necessary to maintain high network accuracy, is proving to be challenging. To address this, we present a multi-memristive synaptic architecture with an efficient global counter-based arbitration scheme. We focus on phase change memory devices, develop a comprehensive model and demonstrate via simulations the effectiveness of the concept for both spiking and non-spiking neural networks. Moreover, we present experimental results involving over a million phase change memory devices for unsupervised learning of temporal correlations using a spiking neural network. The work presents a significant step towards the realization of large-scale and energy-efficient neuromorphic computing systems.

Fig. 1

The multi-memristive synapse concept. a The net synaptic weight of a multi-memristive synapse is represented by the combined conductance $\left(\sum G_n\right)$ of multiple memristive devices. To realize synaptic efficacy, a read voltage signal, V, is applied to all devices. The resulting current flowing through each device is summed up to generate the synaptic output. b To capture synaptic plasticity, only one of the devices is selected at any instance of synaptic update. The synaptic update is induced by altering the conductance of the selected device as dictated by a learning algorithm. This is achieved by applying a suitable programming pulse to the selected device. c A counter-based arbitration scheme is used to select the devices that get programmed to achieve synaptic plasticity. A global selection counter whose maximum value is equal to the number of devices representing a synapse is used. At any instance of synaptic update, the device pointed to by the selection counter is programmed. Subsequently, the selection counter is incremented by a fixed amount. In addition to the selection counter, independent potentiation and depression counters can serve to control the frequency of the potentiation or depression events

Fig. 2

Synapses based on phase change memory. a A PCM device consists of a phase-change material layer sandwiched between top and bottom electrodes. The crystalline region can gradually be increased by the application of potentiation pulses. A depression pulse creates an amorphous region that results in an abrupt drop in conductance, irrespective of the original state of the device. b Evolution of mean conductance as a function of the number of pulses for different programming current amplitudes (I_prog). Each curve is obtained by averaging the conductance measurements from 9700 devices. The inset shows a transmission electron micrograph of a characteristic PCM device used in this study. c Mean cumulative conductance change observed upon the application of repeated potentiation and depression pulses. The initial conductance of the devices is ∼5 μS. d The mean and the standard deviation (1σ) of the conductance values as a function of number of pulses for I_prog = 100 μA measured for 9700 devices and the corresponding model response for the same number of devices. The distribution of conductance after the 20th potentiation pulse and the corresponding distribution obtained with the model are shown in the inset. e The left panel shows a representative distribution of the conductance change induced by a single pulse applied at the same PCM device 1000 times. The pulse is applied as the 4th potentiation pulse to the device. The same measurement was repeated on 1000 different PCM devices, and the mean (μ) and standard deviation (σ) averaged over the 1000 devices are shown in the inset. The right panel shows a representative distribution of one conductance change induced by a single pulse on 1000 devices. The pulse is applied as the 4th potentiation pulse to the devices. The same measurement was repeated for 1000 conductance changes, and the mean and standard deviation averaged over the 1000 conductance changes are shown in the inset. It can be seen that the inter-device and the intra-device variability are comparable. The negative conductance changes are attributed to drift variability (see Supplementary Note 4)

Fig. 3

Multi-memristive synapses based on phase change memory. a The mean cumulative conductance change is experimentally obtained for synapses comprising 1, 3, and 7 PCM devices. The measurements are based on 1000 synapses, whereby each individual device is initialized to a conductance of ∼5 μS. For potentiation, a programming pulse of I_prog = 100 μA was used, whereas for depression, a programming pulse of I_prog = 450 μA was used. For depression, the conductance response can be made more symmetric by adjusting the length of the depression counter. b Distribution of the cumulative conductance change after the application of 10, 30, and 70 potentiation pulses to 1, 3, and 7 PCM synapses, respectively. The mean (μ) and the variance (σ²) scale almost linearly with the number of devices per synapse, leading to an improved weight update resolution

Fig. 4

Applications of multi-memristive synapses in neural networks. a An artificial neural network is trained using backpropagation to perform handwritten digit classification. Bias neurons are used for the input and hidden neuron layers (white). A multi-memristive synapse model based on the nonlinear conductance response of PCM devices is used to represent the synaptic weights in these simulations. Increasing the number of devices in multi-memristive synapses (both in the differential and the non-differential architecture) improves the test accuracy. Simulations are repeated for five different weight initializations. The error bars represent the standard deviation (1σ). The dotted line shows the test accuracy obtained from a double-precision floating-point software implementation. b A spiking neural network is trained using an STDP-based learning rule for handwritten digit classification. Here again, a multi-memristive synapse model is used to represent the synaptic weights in simulations where the devices are arranged in the differential or the non-differential architecture. The classification accuracy of the network increases with the number of devices per synapse. Simulations are repeated for five different weight initializations. The error bars represent the standard deviation (1σ). The dotted line shows the test accuracy obtained from a double-precision floating-point implementation

Fig. 5

Experimental demonstration of multi-memristive synapses used in a spiking neural network. a A spiking neural network is trained to perform the task of temporal correlation detection through unsupervised learning. Our network consists of 1000 multi-PCM synapses (in hardware) connected to one integrate-and-fire (I&F) software neuron. The synapses receive event-based data streams generated with Poisson distributions as presynaptic input spikes. 100 of the synapses receive correlated data streams with a correlation coefficient of 0.75, whereas the rest of the synapses receive uncorrelated data streams. The correlated and the uncorrelated data streams both have the same rate. The resulting postsynaptic outputs are accumulated at the neuronal membrane. The neuron fires, i.e., sends an output spike, if the membrane potential exceeds a threshold. The weight update amount is calculated using an exponential STDP rule based on the timing of the input spikes and the neuronal spikes. A potentiation (depression) pulse with fixed amplitude is applied if the desired weight change is higher (lower) than a threshold. b The synaptic weights are shown for synapses comprising N = 1, 3, and 7 PCM devices at the end of the experiment (5000 time steps). It can be seen that the weights of the synapses receiving correlated inputs tend to be larger than the weights of those receiving uncorrelated inputs. The weight distribution shows a clearer separation with increasing N. c Weight evolution of six synapses in the first 300 time steps of the experiment. The weight evolves more gradually with the number of devices per synapse. d Synaptic weight distribution of an SNN comprising 144,000 multi-PCM synapses with N = 7 PCM devices at the end of an experiment (3000 time steps) (upper panel). 14,400 synapses receive correlated input data streams with a correlation coefficient of 0.75. A total of 1,008,000 PCM devices are used for this large-scale experiment. The lower panel shows the synaptic weight distribution predicted by the PCM device model