Tutorial: Analog Matrix Computing (AMC) with Crosspoint Resistive Memory Arrays

TL;DR

This tutorial introduces analog matrix computing circuits using crosspoint resistive memory arrays, enabling efficient matrix operations like multiplication and inversion with potential applications in machine learning and scientific computing.

Contribution

It presents the design principles, mapping strategies, and stability analysis of AMC circuits based on resistive memory arrays, highlighting their capabilities for various matrix computations.

Findings

AMC circuits perform matrix multiplication, inversion, and eigenvector computation in a single operation.

Mapping strategies effectively handle matrices with negative values.

Transfer function analysis defines circuit stability and time complexity.

Abstract

Matrix computation is ubiquitous in modern scientific and engineering fields. Due to the high computational complexity in conventional digital computers, matrix computation represents a heavy workload in many data-intensive applications, e.g., machine learning, scientific computing, and wireless communications. For fast, efficient matrix computations, analog computing with resistive memory arrays has been proven to be a promising solution. In this Tutorial, we present analog matrix computing (AMC) circuits based on crosspoint resistive memory arrays. AMC circuits are able to carry out basic matrix computations, including matrix multiplication, matrix inversion, pseudoinverse and eigenvector computation, all with one single operation. We describe the main design principles of the AMC circuits, such as local/global or negative/positive feedback configurations, with/without external inputs. Mapping strategies for matrices containing negative values will be presented. The underlying requirements for circuit stability will be described via the transfer function analysis, which also defines time complexity of the circuits towards steady-state results. Lastly, typical applications, challenges, and future trends of AMC circuits will be discussed.