Area-Efficient Mapping of Convolutional Neural Networks to Memristor Crossbars Using Sub-Image Partitioning

Memristor crossbars can be very useful for realizing edge-intelligence hardware, because the neural networks implemented by memristor crossbars can save significantly more computing energy and layout area than the conventional CMOS (complementary metal-oxide-semiconductor) digital circuits. One of the important operations used in neural networks is convolution. For performing the convolution by memristor crossbars, the full image should be partitioned into several sub-images. By doing so, each sub-image convolution can be mapped to small-size unit crossbars, of which the size should be defined as 128 × 128 or 256 × 256 to avoid the line resistance problem caused from large-size crossbars. In this paper, various convolution schemes with 3D, 2D, and 1D kernels are analyzed and compared in terms of neural network's performance and overlapping overhead. The neural network's simulation indicates that the 2D + 1D kernels can perform the sub-image convolution using a much smaller number of unit crossbars with less rate loss than the 3D kernels. When the CIFAR-10 dataset is tested, the mapping of sub-image convolution of 2D + 1D kernels to crossbars shows that the number of unit crossbars can be reduced almost by 90% and 95%, respectively, for 128 × 128 and 256 × 256 crossbars, compared with the 3D kernels. On the contrary, the rate loss of 2D + 1D kernels can be less than 2%. To improve the neural network's performance more, the 2D + 1D kernels can be combined with 3D kernels in one neural network. When the normalized ratio of 2D + 1D layers is around 0.5, the neural network's performance indicates very little rate loss compared to when the normalized ratio of 2D + 1D layers is zero. However, the number of unit crossbars for the normalized ratio = 0.5 can be reduced by half compared with that for the normalized ratio = 0.

Memristor-CMOS Hybrid Neuron Circuit with Nonideal-Effect Correction Related to Parasitic Resistance for Binary-Memristor-Crossbar Neural Networks

Voltages and currents in a memristor crossbar can be significantly affected due to nonideal effects such as parasitic source, line, and neuron resistance. These nonideal effects related to the parasitic resistance can cause the degradation of the neural network’s performance realized with the nonideal memristor crossbar. To avoid performance degradation due to the parasitic-resistance-related nonideal effects, adaptive training methods were proposed previously. However, the complicated training algorithm could add a heavy computational burden to the neural network hardware. Especially, the hardware and algorithmic burden can be more serious for edge intelligence applications such as Internet of Things (IoT) sensors. In this paper, a memristor-CMOS hybrid neuron circuit is proposed for compensating the parasitic-resistance-related nonideal effects during not the training phase but the inference one, where the complicated adaptive training is not needed. Moreover, unlike the previous linear correction method performed by the external hardware, the proposed correction circuit can be included in the memristor crossbar to minimize the power and hardware overheads for compensating the nonideal effects. The proposed correction circuit has been verified to be able to restore the degradation of source and output voltages in the nonideal crossbar. For the source voltage, the average percentage error of the uncompensated crossbar is as large as 36.7%. If the correction circuit is used, the percentage error in the source voltage can be reduced from 36.7% to 7.5%. For the output voltage, the average percentage error of the uncompensated crossbar is as large as 65.2%. The correction circuit can improve the percentage error in the output voltage from 65.2% to 8.6%. Almost the percentage error can be reduced to ~1/7 if the correction circuit is used. The nonideal memristor crossbar with the correction circuit has been tested for MNIST and CIFAR-10 datasets in this paper. For MNIST, the uncompensated and compensated crossbars indicate the recognition rate of 90.4% and 95.1%, respectively, compared to 95.5% of the ideal crossbar. For CIFAR-10, the nonideal crossbars without and with the nonideal-effect correction show the rate of 85.3% and 88.1%, respectively, compared to the ideal crossbar achieving the rate as large as 88.9%.

Towards spike-based machine intelligence with neuromorphic computing

Guided by brain-like 'spiking' computational frameworks, neuromorphic computing-brain-inspired computing for machine intelligence-promises to realize artificial intelligence while reducing the energy requirements of computing platforms. This interdisciplinary field began with the implementation of silicon circuits for biological neural routines, but has evolved to encompass the hardware implementation of algorithms with spike-based encoding and event-driven representations. Here we provide an overview of the developments in neuromorphic computing for both algorithms and hardware and highlight the fundamentals of learning and hardware frameworks. We discuss the main challenges and the future prospects of neuromorphic computing, with emphasis on algorithm-hardware codesign.

Hybrid Circuit of Memristor and Complementary Metal-Oxide-Semiconductor for Defect-Tolerant Spatial Pooling with Boost-Factor Adjustment

Hierarchical Temporal Memory (HTM) has been known as a software framework to model the brain's neocortical operation. However, mimicking the brain's neocortical operation by not software but hardware is more desirable, because the hardware can not only describe the neocortical operation, but can also employ the brain's architectural advantages. To develop a hybrid circuit of memristor and Complementary Metal-Oxide-Semiconductor (CMOS) for realizing HTM's spatial pooler (SP) by hardware, memristor defects such as stuck-at-faults and variations should be considered. For solving the defect problem, we first show that the boost-factor adjustment can make HTM's SP defect-tolerant, because the false activation of defective columns are suppressed. Second, we propose a memristor-CMOS hybrid circuit with the boost-factor adjustment to realize this defect-tolerant SP by hardware. The proposed circuit does not rely on the conventional defect-aware mapping scheme, which cannot avoid the false activation of defective columns. For the Modified subset of National Institute of Standards and Technology (MNIST) vectors, the boost-factor adjusted crossbar with defects = 10% shows a rate loss of only ~0.6%, compared to the ideal crossbar with defects = 0%. On the contrary, the defect-aware mapping without the boost-factor adjustment demonstrates a significant rate loss of ~21.0%. The energy overhead of the boost-factor adjustment is only ~0.05% of the programming energy of memristor synapse crossbar.

Partial-Gated Memristor Crossbar for Fast and Power-Efficient Defect-Tolerant Training

A real memristor crossbar has defects, which should be considered during the retraining time after the pre-training of the crossbar. For retraining the crossbar with defects, memristors should be updated with the weights that are calculated by the back-propagation algorithm. Unfortunately, programming the memristors takes a very long time and consumes a large amount of power, because of the incremental behavior of memristor’s program-verify scheme for the fine-tuning of memristor’s conductance. To reduce the programming time and power, the partial gating scheme is proposed here to realize the partial training, where only some part of neurons are trained, which are more responsible in the recognition error. By retraining the part, rather than the entire crossbar, the programming time and power of memristor crossbar can be significantly reduced. The proposed scheme has been verified by CADENCE circuit simulation with the real memristor’s Verilog-A model. When compared to retraining the entire crossbar, the loss of recognition rate of the partial gating scheme has been estimated only as small as 2.5% and 2.9%, for the MNIST and CIFAR-10 datasets, respectively. However, the programming time and power can be saved by 86% and 89.5% than the 100% retraining, respectively.

Asymmetrical Training Scheme of Binary-Memristor-Crossbar-Based Neural Networks for Energy-Efficient Edge-Computing Nanoscale Systems

For realizing neural networks with binary memristor crossbars, memristors should be programmed by high-resistance state (HRS) and low-resistance state (LRS), according to the training algorithms like backpropagation. Unfortunately, it takes a very long time and consumes a large amount of power in training the memristor crossbar, because the program-verify scheme of memristor-programming is based on the incremental programming pulses, where many programming and verifying pulses are repeated until the target conductance. Thus, this reduces the programming time and power is very essential for energy-efficient and fast training of memristor networks. In this paper, we compared four different programming schemes, which are F-F, C-F, F-C, and C-C, respectively. C-C means both HRS and LRS are coarse-programmed. C-F has the coarse-programmed HRS and fine LRS, respectively. F-C is vice versa of C-F. In F-F, both HRS and LRS are fine-programmed. Comparing the error-energy products among the four schemes, C-F shows the minimum error with the minimum energy consumption. The asymmetrical coarse HRS and fine LRS can reduce the time and energy during the crossbar training significantly, because only LRS is fine-programmed. Moreover, the asymmetrical C-F can maintain the network's error as small as F-F, which is due to the coarse-programmed HRS that slightly degrades the error.

Toward Fast Neural Computing using All-Photonic Phase Change Spiking Neurons

The rapid growth of brain-inspired computing coupled with the inefficiencies in the CMOS implementations of neuromrphic systems has led to intense exploration of efficient hardware implementations of the functional units of the brain, namely, neurons and synapses. However, efforts have largely been invested in implementations in the electrical domain with potential limitations of switching speed, packing density of large integrated systems and interconnect losses. As an alternative, neuromorphic engineering in the photonic domain has recently gained attention. In this work, we propose a purely photonic operation of an Integrate-and-Fire Spiking neuron, based on the phase change dynamics of Ge₂Sb₂Te₅ (GST) embedded on top of a microring resonator, which alleviates the energy constraints of PCMs in electrical domain. We also show that such a neuron can be potentially integrated with on-chip synapses into an all-Photonic Spiking Neural network inferencing framework which promises to be ultrafast and can potentially offer a large operating bandwidth.