Gradient Estimation with Stochastic Softmax Tricks

TL;DR

This paper introduces stochastic softmax tricks, a unified framework that generalizes Gumbel-Softmax for combinatorial spaces, enabling scalable gradient estimation and improved latent variable model training.

Contribution

It presents a novel generalization of the Gumbel-Softmax trick for combinatorial spaces, including new relaxations for various structures within a unified framework.

Findings

Stochastic softmax tricks outperform less structured baselines.

They enable training of better latent variable models.

The framework includes novel relaxations for subset selection and spanning trees.

Abstract

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.