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Analog computing based on memristor technology is a promising solution toaccelerating the inference phase of deep neural networks (DNNs). A fundamentalproblem is to map an arbitrary matrix to a memristor crossbar array (MCA) whilemaximizing the resulting computational accuracy. The state-of-the-art mappingtechnique is based on a heuristic that only guarantees to produce the correctoutput for two input vectors. In this paper, a technique that aims to producethe correct output for every input vector is proposed, which involvesspecifying the memristor conductance values and a scaling factor realized bythe peripheral circuitry. The key insight of the paper is that the conductancematrix realized by an MCA is only required to be proportional to the targetmatrix. The selection of the scaling factor between the two regulates theutilization of the programmable memristor conductance range and therepresentability of the target matrix. Consequently, the scaling factor is setto balance precision and value range errors. Moreover, a technique ofconverting conductance values into state variables and vice versa is proposedto handle memristors with non-ideal device characteristics. Compared with thestate-of-the-art technique, the proposed mapping results in 4X-9X smallererrors. The improvements translate into that the classification accuracy of aseven-layer convolutional neural network (CNN) on CIFAR-10 is improved from20.5% to 71.8%.

Representable Matrices: Enabling High Accuracy Analog Computation for Inference of DNNs using Memristors