We introduce and analyze an open quantum generalization of the q-state Potts-Hopfield neural network, which is associative memory model based on multi-level classical spins. The dynamics this many-body system formulated in terms a Markovian master equation Lindblad type, allows to incorporate both probabilistic coherent processes equal footing. By employing mean field description we investigate...

We propose answers to four open problems listed recently by Koiran on the dynamics of discrete-time, continuous-state Hopfield neural networks.

Due to feedback connections, recurrent neural networks (RNNs) are dynamic models. RNNs can provide more compact structure for approximating dynamic systems compared to feedforward neural networks (FNNs). For some RNN models such as the Hopfield model and the Boltzmann machine, the fixed-point property of the dynamic systems can be used for optimization and associative memory. The Hopfield model...