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

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.