Learning Non-Convergent Non-Persistent Short-Run MCMC Toward Energy-Based Model

TL;DR

This paper investigates the use of non-convergent, short-run MCMC in training energy-based models, demonstrating that it can generate realistic images and perform image reconstruction and interpolation, challenging traditional assumptions.

Contribution

It introduces a novel approach of using non-convergent short-run MCMC as a learned generator, showing its effectiveness in image synthesis and reconstruction.

Findings

Learned short-run MCMC can generate realistic images.

It can reconstruct and interpolate observed images.

The approach challenges traditional views on MCMC convergence in EBMs.

Abstract

This paper studies a curious phenomenon in learning energy-based model (EBM) using MCMC. In each learning iteration, we generate synthesized examples by running a non-convergent, non-mixing, and non-persistent short-run MCMC toward the current model, always starting from the same initial distribution such as uniform noise distribution, and always running a fixed number of MCMC steps. After generating synthesized examples, we then update the model parameters according to the maximum likelihood learning gradient, as if the synthesized examples are fair samples from the current model. We treat this non-convergent short-run MCMC as a learned generator model or a flow model. We provide arguments for treating the learned non-convergent short-run MCMC as a valid model. We show that the learned short-run MCMC is capable of generating realistic images. More interestingly, unlike traditional EBM or MCMC, the learned short-run MCMC is capable of reconstructing observed images and interpolating between images, like generator or flow models. The code can be found in the Appendix.