Phase transitions in restricted Boltzmann machines with generic priors

Area of Science:

• Statistical mechanics
• Machine learning theory
• Artificial neural networks

Background:

• Restricted Boltzmann machines (RBMs) are foundational generative models.
• Generalized RBMs with diverse priors offer enhanced flexibility.
• Hopfield networks serve as a benchmark for associative memory models.

Purpose of the Study:

• To analyze the replica symmetric phase diagram of generalized RBMs.
• To investigate the role of the retrieval phase in inference and learning.
• To establish the relationship between phase transitions and generalization in unsupervised learning.

Main Methods:

• Replica symmetric analysis of generalized RBMs.
• Investigation of unit and weight priors (Boolean, Gaussian, and intermediate).
• Teacher-student scenario for evaluating unsupervised learning generalization.

Main Results:

• A complete phase diagram for the replica symmetric phase is presented.
• Retrieval is shown to be robust for a wide range of priors, extending beyond standard Hopfield models.
• The paramagnetic phase boundary is directly linked to the optimal training set size for generalization.

Conclusions:

• Generalized RBMs with diverse priors offer robust retrieval capabilities for inference and learning.
• The study provides theoretical insights into the generalization performance of unsupervised learning models.
• Findings contribute to understanding the interplay between model parameters and learning efficacy.