Understanding Minimum Probability Flow for RBMs Under Various Kinds of Dynamics

TL;DR

This paper investigates the use of Minimum Probability Flow (MPF) for training Restricted Boltzmann Machines (RBMs), demonstrating its advantages over contrastive divergence (CD) through theoretical analysis and experimental results.

Contribution

It introduces a generalized form of sampling dynamics in MPF and shows how different choices affect RBM training, outperforming CD in various configurations.

Findings

MPF outperforms CD in training RBMs across multiple configurations.

A generalized sampling dynamics framework for MPF is proposed.

Experimental results validate the effectiveness of MPF over CD.

Abstract

Energy-based models are popular in machine learning due to the elegance of their formulation and their relationship to statistical physics. Among these, the Restricted Boltzmann Machine (RBM), and its staple training algorithm contrastive divergence (CD), have been the prototype for some recent advancements in the unsupervised training of deep neural networks. However, CD has limited theoretical motivation, and can in some cases produce undesirable behavior. Here, we investigate the performance of Minimum Probability Flow (MPF) learning for training RBMs. Unlike CD, with its focus on approximating an intractable partition function via Gibbs sampling, MPF proposes a tractable, consistent, objective function defined in terms of a Taylor expansion of the KL divergence with respect to sampling dynamics. Here we propose a more general form for the sampling dynamics in MPF, and explore the consequences of different choices for these dynamics for training RBMs. Experimental results show MPF outperforming CD for various RBM configurations.