Learning in memristive electrical circuits

TL;DR

This paper investigates how to determine and control resistance states in memristive crossbar arrays, enabling their use in hardware-based learning tasks like linear least squares.

Contribution

It provides methods to infer and steer memristor resistances in crossbar circuits, advancing their application in neuromorphic computing and hardware learning.

Findings

Resistance values can be inferred from voltage and current measurements.

Resistances can be controlled by applying external voltages.

The approach enables solving linear least squares problems in hardware.

Abstract

Memristors are nonlinear two-terminal circuit elements whose resistance at a given time depends on past electrical stimuli. Recently, networks of memristors have received attention in neuromorphic computing since they can be used as a tool to perform linear algebraic operations, like matrix-vector multiplication, directly in hardware. In this paper, the aim is to resolve two fundamental questions pertaining to a specific, but relevant, class of memristive circuits called crossbar arrays. In particular, we show (1) how the resistance values of the memristors at a given time can be determined from external (voltage and current) measurements, and (2) how the resistances can be steered to desired values by applying suitable external voltages to the network. The results will be applied to solve a prototypical learning problem, namely linear least squares, by applying and measuring voltages and currents in a suitable memristive circuit.