Clarifying MCMC-based training of modern EBMs : Contrastive Divergence versus Maximum Likelihood

TL;DR

This paper clarifies the theoretical foundations of MCMC-based training for Energy-Based Models, contrasting Contrastive Divergence with Maximum Likelihood, and offers new interpretations and experimental insights.

Contribution

It provides a first-principles explanation of MCMC training, critiques existing methods, and introduces a new interpretation of popular algorithms in EBMs.

Findings

Existing algorithms are not true Contrastive Divergence.

New interpretation clarifies theoretical misunderstandings.

Experimental results support the proposed reinterpretation.

Abstract

The Energy-Based Model (EBM) framework is a very general approach to generative modeling that tries to learn and exploit probability distributions only defined though unnormalized scores. It has risen in popularity recently thanks to the impressive results obtained in image generation by parameterizing the distribution with Convolutional Neural Networks (CNN). However, the motivation and theoretical foundations behind modern EBMs are often absent from recent papers and this sometimes results in some confusion. In particular, the theoretical justifications behind the popular MCMC-based learning algorithm Contrastive Divergence (CD) are often glossed over and we find that this leads to theoretical errors in recent influential papers (Du & Mordatch, 2019; Du et al., 2020). After offering a first-principles introduction of MCMC-based training, we argue that the learning algorithm they use can in fact not be described as CD and reinterpret theirs methods in light of a new interpretation. Finally, we discuss the implications of our new interpretation and provide some illustrative experiments.