Gradient Estimation with Stochastic Softmax Tricks
This work addresses a bottleneck in training latent variable models for combinatorial spaces, offering a novel framework that improves performance and structure discovery, though it is incremental in building on existing perturbation models.
The paper tackles the challenge of scaling gradient estimators to large combinatorial distributions by introducing stochastic softmax tricks, which generalize the Gumbel-Softmax trick and lead to better-performing latent variable models with improved latent structure discovery.
The Gumbel-Max trick is the basis of many relaxed gradient estimators. These estimators are easy to implement and low variance, but the goal of scaling them comprehensively to large combinatorial distributions is still outstanding. Working within the perturbation model framework, we introduce stochastic softmax tricks, which generalize the Gumbel-Softmax trick to combinatorial spaces. Our framework is a unified perspective on existing relaxed estimators for perturbation models, and it contains many novel relaxations. We design structured relaxations for subset selection, spanning trees, arborescences, and others. When compared to less structured baselines, we find that stochastic softmax tricks can be used to train latent variable models that perform better and discover more latent structure.