# Lost Relatives of the Gumbel Trick

arXiv: https://arxiv.org/abs/1706.04161 · HTML: https://mlsanity.com/paper/1706.04161/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Jun 2017.

## Built on by (most cited first, 6 of 6)

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- [Solving Satisfiability Modulo Counting for Symbolic and Statistical AI Integration With Provable Guarantees](https://mlsanity.com/paper/2309.08883/) (2023)
- [Classifier Weighted Mixture models](https://mlsanity.com/paper/2501.02989/) (2025)

## Abstract (arXiv)

The Gumbel trick is a method to sample from a discrete probability distribution, or to estimate its normalizing partition function. The method relies on repeatedly applying a random perturbation to the distribution in a particular way, each time solving for the most likely configuration. We derive an entire family of related methods, of which the Gumbel trick is one member, and show that the new methods have superior properties in several settings with minimal additional computational cost. In particular, for the Gumbel trick to yield computational benefits for discrete graphical models, Gumbel perturbations on all configurations are typically replaced with so-called low-rank perturbations. We show how a subfamily of our new methods adapts to this setting, proving new upper and lower bounds on the log partition function and deriving a family of sequential samplers for the Gibbs distribution. Finally, we balance the discussion by showing how the simpler analytical form of the Gumbel trick enables additional theoretical results.