Categorical Reparameterization with Gumbel-Softmax

TLDR

Categorical variables naturally represent discrete structure, yet stochastic neural networks rarely use them because samples are non‑differentiable. The study introduces an efficient gradient estimator that replaces non‑differentiable categorical samples with differentiable Gumbel‑Softmax samples. It employs a Gumbel‑Softmax distribution that can be smoothly annealed into a categorical distribution. The Gumbel‑Softmax estimator outperforms state‑of‑the‑art gradient estimators on structured output prediction, unsupervised generative modeling with categorical latents, and yields large speedups in semi‑supervised classification.

Abstract

Categorical variables are a natural choice for representing discrete structure in the world. However, stochastic neural networks rarely use categorical latent variables due to the inability to backpropagate through samples. In this work, we present an efficient gradient estimator that replaces the non-differentiable sample from a categorical distribution with a differentiable sample from a novel Gumbel-Softmax distribution. This distribution has the essential property that it can be smoothly annealed into a categorical distribution. We show that our Gumbel-Softmax estimator outperforms state-of-the-art gradient estimators on structured output prediction and unsupervised generative modeling tasks with categorical latent variables, and enables large speedups on semi-supervised classification.