Restricted Boltzmann Machines (RBMs) are generative models designed to learn from data with a rich underlying structure. In this work, we explore a teacher-student setting where a student RBM learns from examples generated by a teacher RBM, with a focus on the effect of the unit priors on learning efficiency. We consider a parametric class of priors that interpolate between continuous (Gaussian) and binary variables. This approach models various possible choices of visible units, hidden units, and weights for both the teacher and student RBMs. By analyzing the phase diagram of the posterior distribution in both the Bayes optimal and mismatched regimes, we demonstrate the existence of a triple point that defines the critical dataset size necessary for learning through generalization. The critical size is strongly influenced by the properties of the teacher, and thus the data, but is unaffected by the properties of the student RBM. Nevertheless, a prudent choice of student priors can facilitate training by expanding the so-called signal retrieval region, where the machine generalizes effectively.

Restricted Boltzmann machines (RBM) are generative models capable to learn data with a rich underlying structure. We study the teacher-student setting where a student RBM learns structured data generated by a teacher RBM. The amount of structure in the data is controlled by adjusting the number of hidden units of the teacher and the correlations in the rows of the weights, a.k.a. patterns. In the absence of correlations, we validate the conjecture that the performance is independent of the number of teacher patters and hidden units of the student RBMs, and we argue that the teacher-student setting can be used as a toy model for studying the lottery ticket hypothesis. Beyond this regime, we find that the critical amount of data required to learn the teacher patterns decreases with both their number and correlations. In both regimes, we find that, even with an relatively large dataset, it becomes impossible to learn the teacher patterns if the inference temperature used for regularization is kept too low. In our framework, the student can learn teacher patterns one-to-one or many-to-one, generalizing previous findings about the teacher-student setting with two hidden units to any arbitrary finite number of hidden units.