Efficient Training of Energy-Based Models Using Jarzynski Equality

TL;DR

This paper introduces a novel method for training energy-based models efficiently by leveraging Jarzynski equality and sequential Monte Carlo techniques, outperforming traditional contrastive divergence approaches.

Contribution

It presents a new approach combining Jarzynski equality with modified Langevin dynamics to accurately compute gradients without sampling biases.

Findings

Outperforms contrastive divergence in experiments

Effective on Gaussian mixtures and MNIST datasets

Reduces sampling bias during training

Abstract

Energy-based models (EBMs) are generative models inspired by statistical physics with a wide range of applications in unsupervised learning. Their performance is best measured by the cross-entropy (CE) of the model distribution relative to the data distribution. Using the CE as the objective for training is however challenging because the computation of its gradient with respect to the model parameters requires sampling the model distribution. Here we show how results for nonequilibrium thermodynamics based on Jarzynski equality together with tools from sequential Monte-Carlo sampling can be used to perform this computation efficiently and avoid the uncontrolled approximations made using the standard contrastive divergence algorithm. Specifically, we introduce a modification of the unadjusted Langevin algorithm (ULA) in which each walker acquires a weight that enables the estimation of the gradient of the cross-entropy at any step during GD, thereby bypassing sampling biases induced by slow mixing of ULA. We illustrate these results with numerical experiments on Gaussian mixture distributions as well as the MNIST dataset. We show that the proposed approach outperforms methods based on the contrastive divergence algorithm in all the considered situations.