This paper proposes the divergence triangle as a framework for joint training of a generator model, energy-based model and inference model. The divergence triangle is a compact and symmetric (anti-symmetric) objective function that seamlessly integrates variational learning, adversarial learning, wake-sleep algorithm, and contrastive divergence in a unified probabilistic formulation. This unification makes the processes of sampling, inference, and energy evaluation readily available without the need for costly Markov chain Monte Carlo methods. Our experiments demonstrate that the divergence triangle is capable of learning (1) an energy-based model with well-formed energy landscape, (2) direct sampling in the form of a generator network, and (3) feed-forward inference that faithfully reconstructs observed as well as synthesized data. The maximum likelihood learning of the energy-based model requires expectation with respect to the current model, while the maximum likelihood learning of the generator model requires expectation with respect to the posterior distribution of the latent variables. Both expectations can be approximated by MCMC, such as Gibbs sampling [11], Langevin dynamics, or Hamiltonian Monte Carlo (HMC) [34] . [31, 48] used Langevin dynamics for learning the energy-based models, and [13] used Langevin dynamics for learning the generator model. In both cases,
More recently, a unified divergence triangle framework is proposed for joint training of generator model, energy-based model, and inference model for generative tasks REF .
Divergence Triangle for Joint Training of Generator Model, Energy-Based Model, and Inferential Model
2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)
2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)
Computer Science Mathematics