The Gumbel-max trick is a method to draw a sample from a categorical
distribution, given by its unnormalized (log-)probabilities. Over the past
years, the machine learning community has proposed several extensions of this
trick to facilitate, e.g., drawing multiple samples, sampling from structured
domains, or gradient estimation for error backpropagation in neural network
optimization. The goal of this survey article is to present background about
the Gumbel-max trick, and to provide a structured overview of its extensions to
ease algorithm selection. Moreover, it presents a comprehensive outline of
(machine learning) literature in which Gumbel-based algorithms have been
leveraged, reviews commonly-made design choices, and sketches a future
perspective.

本文介绍了使用 Gumbel-max trick 从分类分布中抽样的方法，并概述了该方法的扩展，包括从结构化领域中抽样、多重抽样、通过渐变估计神经网络优化中的误差反向传播等，并提供了以 Gumbel 为基础算法的机器学习文献综述、常见设计选择以及未来展望。

机器学习中离散随机性的 Gumbel-max 技巧及其扩展综述

A Review of the Gumbel-max Trick and its Extensions for Discrete  Stochasticity in Machine Learning

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.

在扰动模型框架下，我们使用随机 softmax 技巧（stochastic softmax tricks）对 Gumbel-Softmax 技巧进行了推广，将其推广到组合空间。与基线相比，我们发现使用随机 softmax 技巧可以训练表现更好、发现更多潜在结构的潜在变量模型。

随机 Softmax 技巧的梯度估计

Gradient Estimation with Stochastic Softmax Tricks

Reparameterization of variational auto-encoders with continuous random
variables is an effective method for reducing the variance of their gradient
estimates. In the discrete case, one can perform reparametrization using the
Gumbel-Max trick, but the resulting objective relies on an $\arg \max$
operation and is non-differentiable. In contrast to previous works which resort
to softmax-based relaxations, we propose to optimize it directly by applying
the direct loss minimization approach. Our proposal extends naturally to
structured discrete latent variable models when evaluating the $\arg \max$
operation is tractable. We demonstrate empirically the effectiveness of the
direct loss minimization technique in variational autoencoders with both
unstructured and structured discrete latent variables.

本研究采用直接损失最小化方法，对可连续随机变量的变分自编码器进行重参数化以降低梯度估计的方差，我们将该方法自然地扩展到结构化离散潜在变量模型，并在无结构和有结构的离散潜在变量的变分自编码器中进行了实证检验。