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This paper studies the cooperative training of two generative models forimage modeling and synthesis. Both models are parametrized by convolutionalneural networks (ConvNets). The first model is a deep energy-based model, whoseenergy function is defined by a bottom-up ConvNet, which maps the observedimage to the energy. We call it the descriptor network. The second model is agenerator network, which is a non-linear version of factor analysis. It isdefined by a top-down ConvNet, which maps the latent factors to the observedimage. The maximum likelihood learning algorithms of both models involve MCMCsampling such as Langevin dynamics. We observe that the two learning algorithmscan be seamlessly interwoven into a cooperative learning algorithm that cantrain both models simultaneously. Specifically, within each iteration of thecooperative learning algorithm, the generator model generates initialsynthesized examples to initialize a finite-step MCMC that samples and trainsthe energy-based descriptor model. After that, the generator model learns fromhow the MCMC changes its synthesized examples. That is, the descriptor modelteaches the generator model by MCMC, so that the generator model accumulatesthe MCMC transitions and reproduces them by direct ancestral sampling. We callthis scheme MCMC teaching. We show that the cooperative algorithm can learnhighly realistic generative models.

Cooperative Training of Descriptor and Generator Networks