Invertible Gaussian Reparameterization: Revisiting the Gumbel-Softmax
This work addresses a bottleneck in probabilistic modeling for researchers and practitioners by offering a more flexible and efficient alternative to existing methods, though it is incremental in building on the Gumbel-Softmax framework.
The paper tackles the problem of reparameterizing discrete distributions by proposing a modular family of distributions using invertible Gaussian transformations, which outperforms the Gumbel-Softmax in experiments with theoretical advantages like closed-form KL divergence.
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. Our code is available at https://github.com/cunningham-lab/igr.