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Associative memories using complex-valued Hopfield networks based on spin-torque oscillator arrays



Nitin Prasad, Prashansa Mukim, Advait Madhavan, Mark Stiles


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 is sufficient to store at least twelve images in a set of 192 oscillators, representing the $16\times 12$ pixel images. The energy to recover an image depends on the desired error level. For the oscillators and circuitry considered here, 1\% root mean square deviations from the ideal image require approximately 5$\mu$s and consumes roughly 465nJ. Simulations show that the network functions well when the resonant frequency of the oscillators has a fractional spread less than $10^-3}$ depending on the strength of the feedback.
Neuromorphic Computing and Engineering


Spin-torque oscillators, magnetic tunnel junctions, Hopfield networks, CMOS delay circuits, memristor, image reconstruction, associative memory, spin-transfer torque, oscillators, synchronization, image reconstruction


Prasad, N. , Mukim, P. , Madhavan, A. and Stiles, M. (2022), Associative memories using complex-valued Hopfield networks based on spin-torque oscillator arrays, Neuromorphic Computing and Engineering, [online],, (Accessed May 24, 2024)


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Created July 14, 2022, Updated November 29, 2022