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 modular and more flexible 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, thus enabling the use of our distribution along nonparametric models, 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.

Weaknesses: * Experiments: While the proposed method outperformed existing approaches in the results presented, the experiments seem rather limited in scope. For example, the VAE experiments included in the main text were done using linear encoder/decoder, which is very rarely used in practice. This is particularly concerning because for the nonlinear experiment included in the appendix, GS outperformed IGR on FMNIST (see Table 1). Although this was the only dataset on which IGR didn't outperform GS, it does raise the question of how IGR would scales to more difficult tasks (e.g. In this light, it would really strengthen this paper if the authors could demonstrate that IGR outperforms GS on more challenging tasks as well as compared to other methods such as VIMCO [1] and VQ-VAE [2].

This paper presents a simple alternative to the Gumbel-Softmax based on Gaussians and invertible transformations to the hypersimplex. As one reviewer noted, "the proposed approach is simple, has nice properties, and extensible". Many reviewers criticized the lack of experiments on non-linear models in the main text. Some reviewers felt that the clarity of the draft could be improved, in particular the motivation. This was a borderline paper, however I would like to recommend acceptance.

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 modular and more flexible 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, thus enabling the use of our distribution along nonparametric models, or normalizing flows let us increase the flexibility of the distribution.