Associative Memories Using Complex-Valued Hopfield Networks Based on Spin-Torque Oscillator Arrays
This work addresses efficient associative memory for image recovery in neuromorphic computing, but it is incremental as it builds on existing Hopfield networks with hardware-specific adaptations.
The paper tackled the problem of recovering phase-encoded images using complex-valued Hopfield networks based on spin-torque oscillator arrays, achieving storage of at least 12 images in 192 oscillators with 5% error requiring about 5 μs and 130 nJ.
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 $μ$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.