Phase transitions in Restricted Boltzmann Machines with generic priors
This work provides theoretical insights into phase transitions in machine learning models, but it is incremental as it extends prior analyses to more general priors.
The authors studied Generalized Restricted Boltzmann Machines with generic priors, analyzing their replica symmetric phase diagram and showing that retrieval phases are robust across various priors, with the paramagnetic phase boundary linked to optimal training set sizes for generalization in unsupervised learning.
We study Generalised Restricted Boltzmann Machines with generic priors for units and weights, interpolating between Boolean and Gaussian variables. We present a complete analysis of the replica symmetric phase diagram of these systems, which can be regarded as Generalised Hopfield models. We underline the role of the retrieval phase for both inference and learning processes and we show that retrieval is robust for a large class of weight and unit priors, beyond the standard Hopfield scenario. Furthermore we show how the paramagnetic phase boundary is directly related to the optimal size of the training set necessary for good generalisation in a teacher-student scenario of unsupervised learning.