Supplementary Materials for Learning Latent Space Energy-Based Prior Model A Theoretical derivations

In this section, we shall derive most of the equations in the main text. A.1 A simple identity Let x p By letting R ( x) = 1, we get (1). We start from some simple results. The simple identity (1) also follows from Kullback-Leibler divergence. Then the learning method with short-run MCMC can be easily understood.