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.

翻译：受限玻尔兹曼机（RBMs）是一种生成模型，旨在从具有丰富底层结构的数据中学习。本研究探讨了一种师生学习场景，其中学生RBM从教师RBM生成的样本中学习，重点关注单元先验分布对学习效率的影响。我们考虑了一类参数化的先验分布，其在连续（高斯）变量与二元变量之间连续过渡。该方法为教师和学生RBM的可见单元、隐藏单元及权重建模了多种可能的选择。通过分析贝叶斯最优与失配机制下后验分布的相图，我们证明了三相点的存在，该点定义了通过泛化进行学习所需的关键数据集规模。这一关键规模受教师模型（即数据）特性的强烈影响，但不受学生RBM特性的影响。尽管如此，审慎选择学生先验分布可通过扩展所谓的信号恢复区域（即机器能有效泛化的区域）来促进训练。