Invertible Gaussian Reparameterization: Revisiting the Gumbel-Softmax

Abstract

The Gumbel-Softmax is a continuous distribution over the simplex that is often used as a relaxation of discrete distributions. Because it can be readily interpreted and easily reparameterized, it enjoys widespread use. We propose a conceptually simpler and more flexible alternative family of reparameterizable distributions where Gaussian noise is transformed into a one-hot approximation through an invertible function. This invertible function is composed of a modified softmax and can incorporate diverse transformations that serve different specific purposes. For example, the stick-breaking procedure allows us to extend the reparameterization trick to distributions with countably infinite support, or normalizing flows let us increase the flexibility of the distribution. Our construction enjoys theoretical advantages over the Gumbel-Softmax, such as closed form KL, and significantly outperforms it in a variety of experiments