# Properties of the Concrete distribution

arXiv: https://arxiv.org/abs/2211.01306 · HTML: https://mlsanity.com/paper/2211.01306/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 34 references that are in the map.
- First posted on arXiv 2 Nov 2022.

## Builds on (most cited first, 5 of 5)

- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [A Review of the Gumbel-max Trick and its Extensions for Discrete Stochasticity in Machine Learning](https://mlsanity.com/paper/2110.01515/) (2021)
- [An elementary introduction to information geometry](https://mlsanity.com/paper/1808.08271/) (2018)
- [Black-box optimization using geodesics in statistical manifolds](https://mlsanity.com/paper/1309.7168/) (2013)

## Abstract (arXiv)

We examine properties of the Concrete (or Gumbel-softmax) distribution on the simplex. Using the natural vector space structure of the simplex, the Concrete distribution can be regarded as a transformation of the uniform distribution through a reflection and a location-scale transformation. The Fisher information is computed and the corresponding information metric is hyperbolic space. We explicitly give an explicit transformation of the parameters of the distribution to Poincar'e half-space coordinates, which correspond to an orthogonal parameterization, and the Fisher-Rao geodesic distance is computed.