Explaining the effects of non-convergent sampling in the training of Energy-Based Models - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Conference Papers Year : 2023

Explaining the effects of non-convergent sampling in the training of Energy-Based Models

Abstract

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.

Dates and versions

hal-04344101 , version 1 (14-12-2023)

Licence

Identifiers

Cite

Elisabeth Agoritsas, Giovanni Catania, Aurélien Decelle, Beatriz Seoane. Explaining the effects of non-convergent sampling in the training of Energy-Based Models. ICML 2023 - 40th International Conference on Machine Learning, Jul 2023, Honolulu (Hawaii), United States. ⟨hal-04344101⟩
20 View
0 Download

Altmetric

Share

Gmail Mastodon Facebook X LinkedIn More