Theoretical analysis of hysteresis quantized Hopfield networks for integer programming

Quantized Hopfield networks (QHNs), each neuron of which takes quantized values (e.g. integers), need fewer neurons and connections than the binary or continuous Hopfield networks (BHNs or CHNs), when applied to integer optimization problems, so they can obtain feasible solutions more quickly than BHNs or CHSs. Furthermore, hysteresis quantized Hopfield networks (HQHNs), which are the generalizations of QHNs, have been shown through simulations to obtain optimal or nearly optimal solutions more frequently than BHNs, CHSs, or QHSs and as quickly as QHSs. Although the dynamics of QHNs have been theoretically explored, those of HQHNs have not. In this paper we analyze the dynamics of HQHNs to show their good performance theoretically, and illustrate these theoretical conclusions through simulations