  We consider restricted Boltzmann machines with a binary visible layer and a
Gaussian hidden layer trained by an unlabelled dataset composed of noisy
realizations of a single ground pattern. We develop a statistical mechanics
framework to describe the network generative capabilities, by exploiting the
replica trick and assuming self-averaging of the underlying order parameters
(i.e., replica symmetry). In particular, we outline the effective control
parameters (e.g., the relative number of weights to be trained, the
regularization parameter), whose tuning can yield qualitatively-different
operative regimes. Further, we provide analytical and numerical evidence for
the existence of a sub-region in the space of the hyperparameters where
replica-symmetry breaking occurs.
