On Learning Non-Convergent Short-Run MCMC Toward Energy-Based Model
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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.
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