Software and Hardware Techniques for Reducing the Impact of Quantization Errors in Memristor Crossbar Arrays

Abstract

Matrix-vector multiplication is the dominating computational workload in the evaluation of neural networks. It has recently been demonstrated that memristor crossbar arrays (MCAs) can perform matrix-vector multiplication with small power consumption and low latency. However, the computational accuracy may be degraded by quantization errors. The quantization errors of mapping a matrix to an MCA are proportional to the the number of distinguishable states of each memristor and the difference between the largest and smallest element in the matrix. In this paper, we propose a framework for mapping an arbitrary matrix A to a grid of MCAs (or a single MCA) while minimizing the negative impact of quantization errors. The framework is guided by a total quantization error bound (TQEB) metric, which is an upper bound on the total quantization errors (TQE). Using the proposed TQEB metric, three techniques of reducing TQE are proposed. The first method is based on scaling and shifting the rows in A with different factors to improve the memristor conductance band utilization. The second technique is based on representing a single column in a matrix A using multiple columns in an MCA, to reduce the magnitude of the smallest and largest elements in A. The third technique is based on permuting the order of the columns in A when the matrix A is required to be mapped to a grid of MCAs. The quantization errors are reduced by assigning matrix values of similar magnitude to the same MCAs in the grid. The experimental results demonstrate that the proposed metric and techniques are capable of greatly reducing the negative impact of quantization errors.