A neural network unification

We study the relation between the asymptotic behaviour of synchronous Boltzmann machines and synchronous Hopfield networks. More specifically, we consider the relation between the pseudo consensus function that is used in analyzing Boltzmann machines and the energy function that is used in the study of Hopfield networks. We show that for small values of the control parameter, synchronous Boltzmann machines and synchronous Hopfield networks compute global respectively local maxima of the same function.