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arXiv · 2211.01306

Properties of the Concrete distribution

David D. K. Chow
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Abstract

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.

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David D. K. Chow. 2022-11-02. Properties of the Concrete distribution. https://arxiv.org/abs/2211.01306

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