Research on the Impact of Data Density on Memristor Crossbar Architectures in Neuromorphic Pattern Recognition.

Binary memristor crossbars have great potential for use in brain-inspired neuromorphic computing. The complementary crossbar array has been proposed to perform the Exclusive-NOR function for neuromorphic pattern recognition. The single crossbar obtained by shortening the Exclusive-NOR function has more advantages in terms of power consumption, area occupancy, and fault tolerance. In this paper, we present the impact of data density on the single memristor crossbar architecture for neuromorphic image recognition. The impact of data density on the single memristor architecture is mathematically derived from the reduced formula of the Exclusive-NOR function, and then verified via circuit simulation. The complementary and single crossbar architectures are tested by using ten 32 × 32 images with different data densities of 0.25, 0.5, and 0.75. The simulation results showed that the data density of images has a negative effect on the single memristor crossbar architecture while not affecting the complementary memristor crossbar architecture. The maximum output column current produced by the single memristor crossbar array decreases as data density decreases while the complementary memristor crossbar array architecture provides stable maximum output column currents. When recognizing images with data density as low as 0.25, the maximum output column currents of the single memristor crossbar architecture is reduced four-fold compared with the maximum currents from the complementary memristor crossbar architecture. This reduction causes the Winner-take-all circuit to work incorrectly and will reduce the recognition rate of the single memristor crossbar architecture. These simulation results show that the single memristor crossbar architecture has more advantages compared with the complementary crossbar architecture when the images do have not many different densities, and none of the images have very low densities. This work also indicates that the single crossbar architecture must be improved by adding a constant term to deal with images that have low data densities. These are valuable case studies for archiving the advantages of single memristor crossbar architecture in neuromorphic computing applications.

Noise and Memristance Variation Tolerance of Single Crossbar Architectures for Neuromorphic Image Recognition.

We performed a comparative study on the Gaussian noise and memristance variation tolerance of three crossbar architectures, namely the complementary crossbar architecture, the twin crossbar architecture, and the single crossbar architecture, for neuromorphic image recognition and conducted an experiment to determine the performance of the single crossbar architecture for simple pattern recognition. Ten grayscale images with the size of 32 × 32 pixels were used for testing and comparing the recognition rates of the three architectures. The recognition rates of the three memristor crossbar architectures were compared to each other when the noise level of images was varied from -10 to 4 dB and the percentage of memristance variation was varied from 0% to 40%. The simulation results showed that the single crossbar architecture had the best Gaussian noise input and memristance variation tolerance in terms of recognition rate. At the signal-to-noise ratio of -10 dB, the single crossbar architecture produced a recognition rate of 91%, which was 2% and 87% higher than those of the twin crossbar architecture and the complementary crossbar architecture, respectively. When the memristance variation percentage reached 40%, the single crossbar architecture had a recognition rate as high as 67.8%, which was 1.8% and 9.8% higher than the recognition rates of the twin crossbar architecture and the complementary crossbar architecture, respectively. Finally, we carried out an experiment to determine the performance of the single crossbar architecture with a fabricated 3 × 3 memristor crossbar based on carbon fiber and aluminum film. The experiment proved successful implementation of pattern recognition with the single crossbar architecture.

Compensating Circuit to Reduce the Impact of Wire Resistance in a Memristor Crossbar-Based Perceptron Neural Network.

Wire resistance in metal wire is one of the factors that degrade the performance of memristor crossbar circuits. In this paper, an analysis of the impact of wire resistance in a memristor crossbar is performed and a compensating circuit is proposed to reduce the impact of wire resistance in a memristor crossbar-based perceptron neural network. The goal of the analysis is to figure out how wire resistance influences the output voltage of a memristor crossbar. It emerges that the wire resistance on horizontal lines causes the neuron's output voltage to vary more than the wire resistance on vertical lines. More interesting, the voltage variation caused by wire resistance on horizontal lines increases proportionally to the length of metal wire. The first column has small voltage variation whereas the last column has large voltage variation. In addition, two adjacent columns have almost the same amount of voltage variation. Under these observations, a memristor crossbar-based perceptron neural network with compensating circuit is proposed. The neuron's outputs of two columns are put into a subtractor circuit to eliminate the voltage variation caused by the wire resistance. The proposed memristor crossbar-based perceptron neural network is trained to recognize the 26 characters. The proposed memristor crossbar shows better recognition rate compared to the previous work when wire resistance is taken into account. The proposed memristor crossbar circuit can maintain the recognition rate as high as 100% when wire resistance is as high as 2.5 Ω. By contrast, the recognition rate of the memristor crossbar without the compensating circuit decreases by 1%, 5%, and 19% when wire resistance is set to be 1.5, 2.0, and 2.5 Ω, respectively.

Comparative Study on Statistical-Variation Tolerance Between Complementary Crossbar and Twin Crossbar of Binary Nano-scale Memristors for Pattern Recognition.

This paper performs a comparative study on the statistical-variation tolerance between two crossbar architectures which are the complementary and twin architectures. In this comparative study, 10 greyscale images and 26 black-and-white alphabet characters are tested using the circuit simulator to compare the recognition rate with varying statistical variation and correlation parameters.As with the simulation results of 10 greyscale image recognitions, the twin crossbar shows better recognition rate by 4 % on average than the complementary one, when the inter-array correlation = 1 and intra-array correlation = 0. When the inter-array correlation = 1 and intra-array correlation = 1, the twin architecture can recognize better by 5.6 % on average than the complementary one.Similarly, when the inter-array correlation = 1 and intra-array correlation = 0, the twin architecture can recognize 26 alphabet characters better by 4.5 % on average than the complementary one. When the inter-array correlation = 1 and intra-array correlation = 1, the twin architecture is better by 6 % on average than the complementary one. By summary, we can conclude that the twin crossbar is more robust than the complementary one under the same amounts of statistical variation and correlation.

Neuromorphic crossbar circuit with nanoscale filamentary-switching binary memristors for speech recognition.

In this paper, a neuromorphic crossbar circuit with binary memristors is proposed for speech recognition. The binary memristors which are based on filamentary-switching mechanism can be found more popularly and are easy to be fabricated than analog memristors that are rare in materials and need a more complicated fabrication process. Thus, we develop a neuromorphic crossbar circuit using filamentary-switching binary memristors not using interface-switching analog memristors. The proposed binary memristor crossbar can recognize five vowels with 4-bit 64 input channels. The proposed crossbar is tested by 2,500 speech samples and verified to be able to recognize 89.2% of the tested samples. From the statistical simulation, the recognition rate of the binary memristor crossbar is estimated to be degraded very little from 89.2% to 80%, though the percentage variation in memristance is increased very much from 0% to 15%. In contrast, the analog memristor crossbar loses its recognition rate significantly from 96% to 9% for the same percentage variation in memristance.