Memristor-enabled neuromorphic computing systems provide a fast and energy-efficient approach to training neural networks1,2,3,4. However, convolutional neural networks (CNNs)—one of the most important models for image recognition5—have not yet been fully hardware-implemented using memristor crossbars, which are cross-point arrays with a memristor device at each intersection. Moreover, achieving software-comparable results is highly challenging owing to the poor yield, large variation and other non-ideal characteristics of devices6,7,8,9. Here we report the fabrication of high-yield, high-performance and uniform memristor crossbar arrays for the implementation of CNNs, which integrate eight 2,048-cell memristor arrays to improve parallel-computing efficiency. In addition, we propose an effective hybrid-training method to adapt to device imperfections and improve the overall system performance. We built a five-layer memristor-based CNN to perform MNIST10 image recognition, and achieved a high accuracy of more than 96 per cent. In addition to parallel convolutions using different kernels with shared inputs, replication of multiple identical kernels in memristor arrays was demonstrated for processing different inputs in parallel. The memristor-based CNN neuromorphic system has an energy efficiency more than two orders of magnitude greater than that of state-of-the-art graphics-processing units, and is shown to be scalable to larger networks, such as residual neural networks. Our results are expected to enable a viable memristor-based non-von Neumann hardware solution for deep neural networks and edge computing.
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The simulator XPEsim used here is publicly available39. The codes used for the simulations described in Methods are available from the corresponding author upon reasonable request.
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This work is supported in part by the National Natural Science Foundation of China (61851404), the Beijing Municipal Science and Technology Project (Z191100007519008), the National Key R&D Program of China (2016YFA0201801), the Huawei Project (YBN2019075015) and the National Young Thousand Talents Plan.
The authors declare no competing interests.
Peer review information Nature thanks Darsen Lu and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.
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Extended data figures and tables
Extended Data Fig. 1 Cumulative probability distribution of memristor conductance for the remaining seven 2,048-cell arrays.
The red circles highlight abnormal data points, which deviate from their target conductance ranges owing to device variations. a, The 32-level conductance distribution on an entire 2,048-cell array. b–g, Conductance distributions for the first 32 rows of memristors (namely, 512 devices) for each of the remaining 2,048-cell arrays. A small number of writing errors were observed during the programming procedure (red circles), which could be attributed to device variations. These results show good consistency with Fig. 1c.
Extended Data Fig. 2 Input patch set generated during the sliding process and input waveforms during the convolution.
a, Input nine-dimensional vectors unrolled from the input 3 × 3 patch set. xm_n indicates the relevant pixel at the crossing of row m and column n. The input patches are generated during the sliding convolutional process over the input feature planes and are subsequently injected into the memristor weight array. For a specific input vector, each element is encoded as the corresponding input pulse applied on the associated bit line. The red box indicates the current input vector, in agreement with the case illustrated in b. b, Input waveform sample in a memristor-based convolutional operation. Each element (an 8-bit binary number) in the input vector is encoded as sequential pulses over eight time intervals (t1, t2, …, t8). For a particular period tk, bit k determines whether a 0-V pulse or a 0.2-V pulse is used. Each ‘1’ at a certain bit location implies the existence of a 0.2-V read pulse in the corresponding time interval, and a ‘0’ indicates a 0-V read pulse. The corresponding output current Ik is sensed, and this quantized value is then left-shifted by k – 1. Finally, the quantized and shifted results with respect to the same source line over the eight time intervals are summed together (ISL in the inset equation). The difference between every two ISL values from a pair of differential source lines is considered to be the expected weighted-sum result.
Extended Data Fig. 3 Drift of conductance weights in time and associated degradation in system accuracy.
a, Changes in the conductance weights with time, over 30 days after the transfer. The grey lines present the changing traces of all the cell weights, and the three coloured lines depict representative evolution trends. b, Mean weight value for the cells that belong to each of the 15 levels according to a. The 15 coloured traces show the 15 mean-value evolution traces as a function of time. c, Profile of accuracy loss during the experiment. The overall trend of the accuracy loss indicates how the conductance weight drifts deteriorate the recognition accuracy over time after hybrid training. Compared with the initial state, the recognition accuracy increases by 0.37% at t = 10 min, owing to random device-state fluctuations. d, Evolution of the weights of the weight cells considered in c over 2 h. t0 denotes the moment when the hybrid training is completed. The grey lines show the changing traces of the states of the cells, and the three coloured lines depict representative evolution trends.
Extended Data Fig. 4 Experimental accuracy of parallel memristor convolvers after hybrid training, and simulated training efficiency of different combinations of tuning layers.
a, The error rate on the entire training set after hybrid training drops substantially compared with that achieved after weight transfer for any individual convolver group. The error rates with respect to the G1, G2 and G3 groups decrease from 4.82%, 6.43% and 5.85% to 2.89%, 4.22% and 3.40%, respectively, after hybrid training. b, Simulation results for all combinations of tuning weights for different layers using hybrid training and the five-layer CNN.
Architecture of the simulated memristor-based neural processing unit and relevant circuit modules in the macro core.
The joint strategy combines the hybrid training method and the parallel computing technique of replicating the same kernels. We show that a small subset of training data is sufficient for hybrid training. a, Recognition accuracies at different stages of the simulation process. During the simulation with ResNET-56, the kernel weights of the first convolutional layer are replicated to four groups of memristor arrays. b, After hybrid training the error rate on the test set drops substantially compared with that obtained immediately after weight transfer using each convolver group. c, The error rates drop considerably after hybrid training using 10% of the training data in the experiment with the five-layer CNN.The three experimental results show good consistency. d, Recognition accuracies at different stages of the simulation with ResNET-56. A high level of accuracy is achieved even when using 3% of the training data (1,500 training images) to update the weights of the FC layer. The mean accuracy for 10 trials is 92.00% after hybrid training, and the standard deviation is 0.8%.
To investigate this effect, we set up this experiment by writing all the convolutional kernel weights to two memristor PEs. After programming all the conductance weights smoothly, we physically apply 1,000,000 read pulses (0.2 V) on all weight cells to see how the read operations disturb the weight states. a, Changes in the states of the 936 conductance weightswhile cycling read operations. The grey lines give the changing traces of the states of all cells, and the three coloured lines depict representative evolution trends. b, Conductance evolution of eight memristor states during 106 read cycles. c, Distributions of weight states after 1, 105, 5 × 105 and 106 read cycles.
Extended Data Fig. 8 Test results of the required programming pulse number and programming currents.
a, Average pulse number required to reach each target conductance state. All the initial states were programmed to >4.0 μA. b, Stacked histogram distribution corresponding to the data in a. c, Current–voltage curve obtained during a d.c. voltage sweep. RESET and SET currents are measured at points #1 and #3, respectively. The conditions of RESET and SET pulses in this study are marked by points #2 and #4, respectively. Point #5 labels the read current at the low-resistance state (LRS) and point #6 labels the read current at the high-resistance state (HRS). d, Typical programming parameters. The programming current is 60 μA at 1.5 V during the SET process and 45 μA at −1.2 V during RESET.
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Yao, P., Wu, H., Gao, B. et al. Fully hardware-implemented memristor convolutional neural network. Nature 577, 641–646 (2020). https://doi.org/10.1038/s41586-020-1942-4
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