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The design of balanced ternary digital logic circuits based on memristors and conventional CMOS devices is proposed. First, balanced ternary minimum gate TMIN, maximum gate TMAX and ternary inverters are systematically designed and verified by simulation, and then logic circuits such as ternary encoders, decoders and multiplexers are designed on this basis. Two different schemes are then used to realize the design of functional combinational logic circuits such as a balanced ternary half adder, multiplier, and numerical comparator. Finally, we report a series of comparisons and analyses of the two design schemes, which provide a reference for subsequent research and development of three-valued logic circuits., Comment: 15 pages, 30 figures

We present MEMprop, the adoption of gradient-based learning to train fully memristive spiking neural networks (MSNNs). Our approach harnesses intrinsic device dynamics to trigger naturally arising voltage spikes. These spikes emitted by memristive dynamics are analog in nature, and thus fully differentiable, which eliminates the need for surrogate gradient methods that are prevalent in the spiking neural network (SNN) literature. Memristive neural networks typically either integrate memristors as synapses that map offline-trained networks, or otherwise rely on associative learning mechanisms to train networks of memristive neurons. We instead apply the backpropagation through time (BPTT) training algorithm directly on analog SPICE models of memristive neurons and synapses. Our implementation is fully memristive, in that synaptic weights and spiking neurons are both integrated on resistive RAM (RRAM) arrays without the need for additional circuits to implement spiking dynamics, e.g., analog-to-digital converters (ADCs) or thresholded comparators. As a result, higher-order electrophysical effects are fully exploited to use the state-driven dynamics of memristive neurons at run time. By moving towards non-approximate gradient-based learning, we obtain highly competitive accuracy amongst previously reported lightweight dense fully MSNNs on several benchmarks.

We present a fully memristive spiking neural network (MSNN) consisting of novel memristive neurons trained using the backpropagation through time (BPTT) learning rule. Gradient descent is applied directly to the memristive integrated-and-fire (MIF) neuron designed using analog SPICE circuit models, which generates distinct depolarization, hyperpolarization, and repolarization voltage waveforms. Synaptic weights are trained by BPTT using the membrane potential of the MIF neuron model and can be processed on memristive crossbars. The natural spiking dynamics of the MIF neuron model are fully differentiable, eliminating the need for gradient approximations that are prevalent in the spiking neural network literature. Despite the added complexity of training directly on SPICE circuit models, we achieve 97.58% accuracy on the MNIST testing dataset and 75.26% on the Fashion-MNIST testing dataset, the highest accuracies among all fully MSNNs.

We present a fully memristive spiking neural network (MSNN) consisting of physically-realizable memristive neurons and memristive synapses to implement an unsupervised Spiking Time Dependent Plasticity (STDP) learning rule. The system is fully memristive in that both neuronal and synaptic dynamics can be realized by using memristors. The neuron is implemented using the SPICE-level memristive integrate-and-fire (MIF) model, which consists of a minimal number of circuit elements necessary to achieve distinct depolarization, hyperpolarization, and repolarization voltage waveforms. The proposed MSNN uniquely implements STDP learning by using cumulative weight changes in memristive synapses from the voltage waveform changes across the synapses, which arise from the presynaptic and postsynaptic spiking voltage signals during the training process. Two types of MSNN architectures are investigated: 1) a biologically plausible memory retrieval system, and 2) a multi-class classification system. Our circuit simulation results verify the MSNN's unsupervised learning efficacy by replicating biological memory retrieval mechanisms, and achieving 97.5% accuracy in a 4-pattern recognition problem in a large scale discriminative MSNN.

The search for a compatible application of memristor-CMOS logic gates has remained elusive, as the data density benefits are offset by slow switching speeds and resistive dissipation. Active microdisplays typically prioritize pixel density (and therefore resolution) over that of speed, where the most widely used refresh rates fall between 25-240 Hz. Therefore, memristor-CMOS logic is a promising fit for peripheral IO logic in active matrix displays. In this paper, we design and implement a ternary 1-3 line decoder and a ternary 2-9 line decoder which are used to program a seven segment LED display. SPICE simulations are conducted in a 50-nm process, and the decoders are synthesized on an Altera Cyclone IV field-programmable gate array (FPGA) development board which implements a ternary memristor model designed in Quartus II. We compare our hardware results to a binary coded decimal (BCD)-to-seven segment display decoder, and show our memristor-CMOS approach reduces the total IO power consumption by a factor of approximately 6 times at a maximum synthesizable frequency of 293.77MHz. Although the speed is approximately half of the native built-in BCD-to-seven decoder, the comparatively slow refresh rates of typical microdisplays indicate this to be a tolerable trade-off, which promotes data density over speed.

Deep neural network inference accelerators are rapidly growing in importance as we turn to massively parallelized processing beyond GPUs and ASICs. The dominant operation in feedforward inference is the multiply-and-accumlate process, where each column in a crossbar generates the current response of a single neuron. As a result, memristor crossbar arrays parallelize inference and image processing tasks very efficiently. In this brief, we present a 3-D active memristor crossbar array `CrossStack', which adopts stacked pairs of Al/TiO2/TiO2-x/Al devices with common middle electrodes. By designing CMOS-memristor hybrid cells used in the layout of the array, CrossStack can operate in one of two user-configurable modes as a reconfigurable inference engine: 1) expansion mode and 2) deep-net mode. In expansion mode, the resolution of the network is doubled by increasing the number of inputs for a given chip area, reducing IR drop by 22%. In deep-net mode, inference speed per-10-bit convolution is improved by 29\% by simultaneously using one TiO2/TiO2-x layer for read processes, and the other for write processes. We experimentally verify both modes on our $10\times10\times2$ array., Comment: 5 pages, 4 figures

Artificial neural networks have become ubiquitous in modern life, which has triggered the emergence of a new class of application specific integrated circuits for their acceleration. ReRAM-based accelerators have gained significant traction due to their ability to leverage in-memory computations. In a crossbar structure, they can perform multiply-and-accumulate operations more efficiently than standard CMOS logic. By virtue of being resistive switches, ReRAM switches can only reliably store one of two states. This is a severe limitation on the range of values in a computational kernel. This paper presents a novel scheme in alleviating the single-bit-per-device restriction by exploiting frequency dependence of v-i plane hysteresis, and assigning kernel information not only to the device conductance but also partially distributing it to the frequency of a time-varying input. We show this approach reduces average power consumption for a single crossbar convolution by up to a factor of x16 for an unsigned 8-bit input image, where each convolutional process consumes a worst-case of 1.1mW, and reduces area by a factor of x8, without reducing accuracy to the level of binarized neural networks. This presents a massive saving in computing cost when there are many simultaneous in-situ multiply-and-accumulate processes occurring across different crossbars., Comment: 2019 IEEE International Conference on Artificial Intelligence Circuits and Systems, 5 pages, 4 figures

Large-capacity Content Addressable Memory (CAM) is a key element in a wide variety of applications. The inevitable complexities of scaling MOS transistors introduce a major challenge in the realization of such systems. Convergence of disparate technologies, which are compatible with CMOS processing, may allow extension of Moore's Law for a few more years. This paper provides a new approach towards the design and modeling of Memristor (Memory resistor) based Content Addressable Memory (MCAM) using a combination of memristor MOS devices to form the core of a memory/compare logic cell that forms the building block of the CAM architecture. The non-volatile characteristic and the nanoscale geometry together with compatibility of the memristor with CMOS processing technology increases the packing density, provides for new approaches towards power management through disabling CAM blocks without loss of stored data, reduces power dissipation, and has scope for speed improvement as the technology matures., Comment: 10 pages, 11 figures