  Maximum likelihood estimation is widely used in training Energy-based models
(EBMs). Training requires samples from an unnormalized distribution, which is
usually intractable, and in practice, these are obtained by MCMC algorithms
such as Langevin dynamics. However, since MCMC in high-dimensional space
converges extremely slowly, the current understanding of maximum likelihood
training, which assumes approximate samples from the model can be drawn, is
problematic. In this paper, we try to understand this training procedure by
replacing Langevin dynamics with deterministic solutions of the associated
gradient descent ODE. Doing so allows us to study the density induced by the
dynamics (if the dynamics are invertible), and connect with GANs by treating
the dynamics as generator models, the initial values as latent variables and
the loss as optimizing a critic defined by the very same energy that determines
the generator through its gradient. Hence the term - self-adversarial loss. We
show that reintroducing the noise in the dynamics does not lead to a
qualitative change in the behavior, and merely reduces the quality of the
generator. We thus show that EBM training is effectively a self-adversarial
procedure rather than maximum likelihood estimation.
