GumBolt: Extending Gumbel Trick To Boltzmann Priors

Authors:
Amir H Khoshaman D-Wave Systems Inc
Mohammad Amin D-Wave Systems Inc

Introduction:

Boltzmann machines (BMs) are appealing candidates for powerful priors in variational autoencoders (VAEs), as they are capable of capturing nontrivial and multi-modal distributions over discrete variables.Here, the authors propose the GumBolt, a model that extends the Gumbel trick to BM priors in VAEs.

Abstract:

Boltzmann machines (BMs) are appealing candidates for powerful priors in variational autoencoders (VAEs), as they are capable of capturing nontrivial and multi-modal distributions over discrete variables. However, non-differentiability of the discrete units prohibits using the reparameterization trick, essential for low-noise back propagation. The Gumbel trick resolves this problem in a consistent way by relaxing the variables and distributions, but it is incompatible with BM priors. Here, we propose the GumBolt, a model that extends the Gumbel trick to BM priors in VAEs. GumBolt is significantly simpler than the recently proposed methods with BM prior and outperforms them by a considerable margin. It achieves state-of-the-art performance on permutation invariant MNIST and OMNIGLOT datasets in the scope of models with only discrete latent variables. Moreover, the performance can be further improved by allowing multi-sampled (importance-weighted) estimation of log-likelihood in training, which was not possible with previous models.

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