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, with the initial image serving as the latent variables, and discard the learned EBM. 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. Moreover, unlike traditional EBM or MCMC, the learned short-run MCMC is also capable of reconstructing observed images and interpolating different images, like generator model or flow model. The code can be found in the Appendix.
@cite_21: One of the great puzzles that keeps neuroscientists busy is the question of how the brain makes distinctions between separate yet similar events, and encodes memories of these. In a Perspective, [Poucet and Save][1] discuss a new study in rats ([ ][2]) that demonstrates how hippocampal place cells of the rat brain abruptly change their electrical representations of slowly changing environments @PARASPLIT [1]: http: www.sciencemag.org cgi content full 308 5723 799 [2]: http: www.sciencemag.org cgi content short 308 5723 873
Our theoretical understanding of non-convergent MCMC is based on generalized moment matching estimator. It is related to moment matching GAN @cite_21 , however, we do not learn a separate generator model adversarially.