4K-memristor analog-grade passive crossbar circuit.

The superior density of passive analog-grade memristive crossbar circuits enables storing large neural network models directly on specialized neuromorphic chips to avoid costly off-chip communication. To ensure efficient use of such circuits in neuromorphic systems, memristor variations must be substantially lower than those of active memory devices. Here we report a 64 × 64 passive crossbar circuit with ~99% functional nonvolatile metal-oxide memristors. The fabrication technology is based on a foundry-compatible process with etch-down patterning and a low-temperature budget. The achieved <26% coefficient of variance in memristor switching voltages is sufficient for programming a 4K-pixel gray-scale pattern with a <4% relative tuning error on average. Analog properties are also successfully verified via experimental demonstration of a 64 × 10 vector-by-matrix multiplication with an average 1% relative conductance import accuracy to model the MNIST image classification by ex-situ trained single-layer perceptron, and modeling of a large-scale multilayer perceptron classifier based on more advanced conductance tuning algorithm.

Combinatorial optimization by weight annealing in memristive hopfield networks.

The increasing utility of specialized circuits and growing applications of optimization call for the development of efficient hardware accelerator for solving optimization problems. Hopfield neural network is a promising approach for solving combinatorial optimization problems due to the recent demonstrations of efficient mixed-signal implementation based on emerging non-volatile memory devices. Such mixed-signal accelerators also enable very efficient implementation of various annealing techniques, which are essential for finding optimal solutions. Here we propose a "weight annealing" approach, whose main idea is to ease convergence to the global minima by keeping the network close to its ground state. This is achieved by initially setting all synaptic weights to zero, thus ensuring a quick transition of the Hopfield network to its trivial global minima state and then gradually introducing weights during the annealing process. The extensive numerical simulations show that our approach leads to a better, on average, solutions for several representative combinatorial problems compared to prior Hopfield neural network solvers with chaotic or stochastic annealing. As a proof of concept, a 13-node graph partitioning problem and a 7-node maximum-weight independent set problem are solved experimentally using mixed-signal circuits based on, correspondingly, a 20 × 20 analog-grade TiO2 memristive crossbar and a 12 × 10 eFlash memory array.

Versatile stochastic dot product circuits based on nonvolatile memories for high performance neurocomputing and neurooptimization.

The key operation in stochastic neural networks, which have become the state-of-the-art approach for solving problems in machine learning, information theory, and statistics, is a stochastic dot-product. While there have been many demonstrations of dot-product circuits and, separately, of stochastic neurons, the efficient hardware implementation combining both functionalities is still missing. Here we report compact, fast, energy-efficient, and scalable stochastic dot-product circuits based on either passively integrated metal-oxide memristors or embedded floating-gate memories. The circuit's high performance is due to mixed-signal implementation, while the efficient stochastic operation is achieved by utilizing circuit's noise, intrinsic and/or extrinsic to the memory cell array. The dynamic scaling of weights, enabled by analog memory devices, allows for efficient realization of different annealing approaches to improve functionality. The proposed approach is experimentally verified for two representative applications, namely by implementing neural network for solving a four-node graph-partitioning problem, and a Boltzmann machine with 10-input and 8-hidden neurons.

Spike-timing-dependent plasticity learning of coincidence detection with passively integrated memristive circuits.

Spiking neural networks, the most realistic artificial representation of biological nervous systems, are promising due to their inherent local training rules that enable low-overhead online learning, and energy-efficient information encoding. Their downside is more demanding functionality of the artificial synapses, notably including spike-timing-dependent plasticity, which makes their compact efficient hardware implementation challenging with conventional device technologies. Recent work showed that memristors are excellent candidates for artificial synapses, although reports of even simple neuromorphic systems are still very rare. In this study, we experimentally demonstrate coincidence detection using a spiking neural network, implemented with passively integrated metal-oxide memristive synapses connected to an analogue leaky-integrate-and-fire silicon neuron. By employing spike-timing-dependent plasticity learning, the network is able to robustly detect the coincidence by selectively increasing the synaptic efficacies corresponding to the synchronized inputs. Not surprisingly, our results indicate that device-to-device variation is the main challenge towards realization of more complex spiking networks.

Prevalence of zinc deficiency in junior high school students of Tehran City.

Zinc deficiency is a health problem in many communities especially among adolescents because of pubertal growth sprout. This investigation was carried out to determine the epidemiology of zinc deficiency in junior high school students in Tehran City in 1997. This cross-sectional study was performed on 881 students (452 males and 429 females) with the mean age of 13.2+/-1.0 yr, who were selected by multistage random sampling method. Plasma, erythrocyte, and hair zinc levels were assayed by flame atomic absorption spectrophotometry. Anthropometric and demographic characteristics were measured and recorded on a questionnaire. Dietary intakes were evaluated by a 24-h recall method. Zinc deficiency was defined as having at least two indices from indices of erythrocyte, plasma, and hair zinc below 10 microg/mL, 100 microg/dL, and 125 microg/g of hair, respectively. The results showed that zinc deficiency prevalence was 31.1% (confidence interval: 28-34.4%). Zinc deficiency was 65%, 49%, and 1.3% based on plasma, erythrocyte, and hair zinc levels, respectively. The mean +/- SD for plasma, erythrocyte, and hair zinc concentration, height-for-age, as well as weight-for-age Z scores were 95.2+/-17.7 microg/dL, 10.3+/-2.3 microg/mL, 239.4+/-54.4 microg/g, -0.40+/-0.92, and 0.12+/-0.91, respectively. As for dietary intake compared with the RDA, 50% of the subjects consumed less than 50% of their requirement for zinc RDA based on a 24-h dietary recall. Zinc intake in subjects was 7.5+/-3.7 microg, that in boys was higher than in girls. Correlation coefficients between zinc status indices were very weak. There was neither a linear nor nonlinear relationship between biochemical parameters and nutritional zinc intake. It is concluded that almost one-third to one-half of the subjects would be considered zinc deficient.