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Training neural network models with discrete (categorical or structured)latent variables can be computationally challenging, due to the need formarginalization over large or combinatorial sets. To circumvent this issue, onetypically resorts to sampling-based approximations of the true marginal,requiring noisy gradient estimators (e.g., score function estimator) orcontinuous relaxations with lower-variance reparameterized gradients (e.g.,Gumbel-Softmax). In this paper, we propose a new training strategy whichreplaces these estimators by an exact yet efficient marginalization. To achievethis, we parameterize discrete distributions over latent assignments usingdifferentiable sparse mappings: sparsemax and its structured counterparts. Ineffect, the support of these distributions is greatly reduced, which enablesefficient marginalization. We report successful results in three tasks coveringa range of latent variable modeling applications: a semisupervised deepgenerative model, a latent communication game, and a generative model with abit-vector latent representation. In all cases, we obtain good performancewhile still achieving the practicality of sampling-based approximations.

Efficient Marginalization of Discrete and Structured Latent Variables via Sparsity