Hopfield neural networks (HNNs) have proven useful in solving optimization problems that require fast response times. However, the original analog model has an extremely high implementation complexity, making discrete implementations more suitable. Previous work has studied the convergence of discrete-time and quantized-neuron models but has limited the analysis to either two-state neurons or serial operation mode. Nevertheless, two-state neurons have poor performance, and serial operation modes lose fast convergence, which is characteristic of analog HNNs. This letter is the first in the field analyzing the convergence and stability of quantized Hopfield networks (QHNs)—with more than two states—operating in fully parallel mode. Moreover, this letter presents some further analysis on the energy minimization of this type of network. The main conclusion drawn is that QHNs operating in fully parallel mode always converge to a stable state or a cycle of length two and any stable state is a local minimum of the energy.

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