Associative Memories Using Complex-Valued Hopfield Networks Based on Spin-Torque Oscillator Arrays

TL;DR

This paper demonstrates that complex-valued Hopfield networks built from spin-torque oscillator arrays can effectively store and recover phase-encoded images, with energy efficiency depending on error tolerance.

Contribution

It introduces a novel implementation of complex-valued Hopfield networks using spin-torque oscillators and memristor-augmented inverters for tunable weights, enabling image storage and retrieval.

Findings

Able to store at least 12 images in 192 oscillators

Image recovery with 5% RMS deviation takes about 5 μs and 130 nJ

Network performance depends on oscillator frequency tuning within a fractional spread of 10^{-3}

Abstract

Simulations of complex-valued Hopfield networks based on spin-torque oscillators can recover phase-encoded images. Sequences of memristor-augmented inverters provide tunable delay elements that implement complex weights by phase shifting the oscillatory output of the oscillators. Pseudo-inverse training suffices to store at least 12 images in a set of 192 oscillators, representing 16$\times$12 pixel images. The energy required to recover an image depends on the desired error level. For the oscillators and circuitry considered here, 5 % root mean square deviations from the ideal image require approximately 5 $\mu$s and consume roughly 130 nJ. Simulations show that the network functions well when the resonant frequency of the oscillators can be tuned to have a fractional spread less than $10^{-3}$, depending on the strength of the feedback.