Efficient Training of Energy-Based Models Using Jarzynski Equality
This work addresses a key bottleneck in unsupervised learning for researchers and practitioners using energy-based models, offering a more efficient training method, though it appears incremental as it builds on existing thermodynamic and sampling techniques.
The paper tackled the challenge of efficiently training energy-based models by computing the gradient of cross-entropy without sampling biases, using Jarzynski equality and sequential Monte-Carlo sampling to modify the unadjusted Langevin algorithm, and demonstrated improved performance over contrastive divergence methods on Gaussian mixture distributions and MNIST.
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.