Generative Models as Out-of-Equilibrium Particle Systems: Training of Energy-Based Models Using Non-equilibrium Thermodynamics

Energy-based models (EBMs) are generative models rooted in principles from statistical physics that find diverse applications in unsupervised learning. The evaluation of their performance often hinges on the cross-entropy (CE), which gauges the model distribution’s fidelity to the underlying data distribution. However, training EBMs using CE as the objective poses challenges due to the need to compute its gradient with respect to the model parameters, a task demanding sampling from the model distribution at each optimization step. By incorporating tools from sequential Monte-Carlo sampling, we achieved efficient computation of the gradient of CE, thereby circumventing the uncontrolled approximations present in standard contrastive divergence algorithms. Numerical experiments conducted on Gaussian mixture distributions, as well as the MNIST and CIFAR-10 datasets, provided empirical support for our theoretical findings. In this proceeding, we present and emphasize our recent results, drawing particular attention on the physical interpretation of the proposed methodology.