XMAP: Programming Memristor Crossbars for Analog Matrix-Vector Multiplication: Toward High Precision Using Representable Matrices

Necati Uysal, Baogang Zhang, Sumit Kumar Jha, Rickard Ewetz

Abstract: Linear transformations are the dominating computation within many important applications. The natural multiply-and-accumulate feature of memristor crossbar arrays promise unprecedented processing capabilities to resistive dot-product engines (DPEs), which can accelerate approximate matrix–vector multiplication (MVM). Unfortunately, the precision of the analog computation may be degraded by parasitics, nonlinear device characteristics, and variations. In this article, we propose a framework, called XMAP, for mapping an arbitrary matrix into appropriate memristor conductance values (or state variables for nonlinear devices). The specified conductance values are next programmed to the memristor hardware using accurate closed-loop tuning. XMAP is based on formulating the mapping problem as a mathematical optimization problem, which can be elegantly minimized using the concept of representable matrices, i.e., the matrices that can be represented on a crossbar. Compared to the state-of-the-art conversion algorithm, the computational accuracy is improved with up to $3.29 \times $ at the expense of overhead in runtime. The precision improvements translate into noteworthy application-level benefits within signal compression and neural network inference.