Explaining the effects of non-convergent sampling in the training of Energy-Based Models
It explains a key phenomenon for researchers using EBMs, enabling more efficient sampling and groundwork for diffusion models, but is incremental as it builds on prior observations.
The paper quantifies the impact of non-convergent Markov chains in training Energy-Based Models, showing analytically that such training can perfectly reproduce empirical data statistics through a dynamical process rather than equilibrium, and validates this with numerical tests on models like ConvNet EBM and Boltzmann machine.
In this paper, we quantify the impact of using non-convergent Markov chains to train Energy-Based models (EBMs). In particular, we show analytically that EBMs trained with non-persistent short runs to estimate the gradient can perfectly reproduce a set of empirical statistics of the data, not at the level of the equilibrium measure, but through a precise dynamical process. Our results provide a first-principles explanation for the observations of recent works proposing the strategy of using short runs starting from random initial conditions as an efficient way to generate high-quality samples in EBMs, and lay the groundwork for using EBMs as diffusion models. After explaining this effect in generic EBMs, we analyze two solvable models in which the effect of the non-convergent sampling in the trained parameters can be described in detail. Finally, we test these predictions numerically on a ConvNet EBM and a Boltzmann machine.