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

arXiv: https://arxiv.org/abs/2112.03358 · HTML: https://mlsanity.com/paper/2112.03358/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 11 references that are in the map.
- First posted on arXiv 6 Dec 2021.

## Builds on (most cited first, 2 of 2)

- [Hopfield Networks is All You Need](https://mlsanity.com/paper/2008.02217/) (2020)
- [Large Associative Memory Problem in Neurobiology and Machine Learning](https://mlsanity.com/paper/2008.06996/) (2020)

## Abstract (arXiv)

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 16×12 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 μs 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.