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We study Generalised Restricted Boltzmann Machines with generic priors forunits and weights, interpolating between Boolean and Gaussian variables. Wepresent a complete analysis of the replica symmetric phase diagram of thesesystems, which can be regarded as Generalised Hopfield models. We underline therole of the retrieval phase for both inference and learning processes and weshow that retrieval is robust for a large class of weight and unit priors,beyond the standard Hopfield scenario. Furthermore we show how the paramagneticphase boundary is directly related to the optimal size of the training setnecessary for good generalisation in a teacher-student scenario of unsupervisedlearning.

Phase transitions in Restricted Boltzmann Machines with generic priors