# Generalized Gumbel-Softmax Gradient Estimator for Generic Discrete Random Variables

arXiv: https://arxiv.org/abs/2003.01847 · HTML: https://mlsanity.com/paper/2003.01847/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Mar 2020.

## Built on by (most cited first, 2 of 2)

- [Simulation-Based Prior Knowledge Elicitation for Parametric Bayesian Models](https://mlsanity.com/paper/2308.11672/) (2023)
- [Designing Dynamic Pricing for Bike-sharing Systems via Differentiable Agent-based Simulation](https://mlsanity.com/paper/2507.23344/) (2025)

## Abstract (arXiv)

Estimating the gradients of stochastic nodes in stochastic computational graphs is one of the crucial research questions in the deep generative modeling community, which enables the gradient descent optimization on neural network parameters. Stochastic gradient estimators of discrete random variables are widely explored, for example, Gumbel-Softmax reparameterization trick for Bernoulli and categorical distributions. Meanwhile, other discrete distribution cases such as the Poisson, geometric, binomial, multinomial, negative binomial, etc. have not been explored. This paper proposes a generalized version of the Gumbel-Softmax estimator, which is able to reparameterize generic discrete distributions, not restricted to the Bernoulli and the categorical. The proposed estimator utilizes the truncation of discrete random variables, the Gumbel-Softmax trick, and a special form of linear transformation. Our experiments consist of (1) synthetic examples and applications on VAE, which show the efficacy of our methods; and (2) topic models, which demonstrate the value of the proposed estimation in practice.