# Learning in memristive electrical circuits

arXiv: https://arxiv.org/abs/2409.15136 · HTML: https://mlsanity.com/paper/2409.15136/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Sep 2024.

## Built on by (most cited first, 2 of 2)

- [Convergence of energy-based learning in linear resistive networks](https://mlsanity.com/paper/2503.00349/) (2025)
- [Circuit realization and hardware linearization of monotone operator equilibrium networks](https://mlsanity.com/paper/2509.13793/) (2025)

## Abstract (arXiv)

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.