Barriers and Dynamical Paths in Alternating Gibbs Sampling of Restricted Boltzmann Machines

TL;DR

This paper investigates the efficiency of Alternating Gibbs Sampling in Restricted Boltzmann Machines, revealing its limitations and proposing enhancements using Metropolis-Hastings in the latent space to improve sampling performance.

Contribution

It provides an analytical comparison of AGS and MH sampling in RBMs and introduces a hybrid approach to improve sampling efficiency for weakly dependent features.

Findings

Standard AGS is not more efficient than classical MH sampling.

RBMs can learn meaningful latent representations of data.

Combining Gibbs with MH in latent space improves sampling performance.

Abstract

Restricted Boltzmann Machines (RBM) are bi-layer neural networks used for the unsupervised learning of model distributions from data. The bipartite architecture of RBM naturally defines an elegant sampling procedure, called Alternating Gibbs Sampling (AGS), where the configurations of the latent-variable layer are sampled conditional to the data-variable layer, and vice versa. We study here the performance of AGS on several analytically tractable models borrowed from statistical mechanics. We show that standard AGS is not more efficient than classical Metropolis-Hastings (MH) sampling of the effective energy landscape defined on the data layer. However, RBM can identify meaningful representations of training data in their latent space. Furthermore, using these representations and combining Gibbs sampling with the MH algorithm in the latent space can enhance the sampling performance of the RBM when the hidden units encode weakly dependent features of the data. We illustrate our findings on three datasets: Bars and Stripes and MNIST, well known in machine learning, and the so-called Lattice Proteins, introduced in theoretical biology to study the sequence-to-structure mapping in proteins.