The Gumbel-softmax distribution, or Concrete distribution, is often used to
relax the discrete characteristics of a categorical distribution and enable
back-propagation through differentiable reparameterization. Although it
reliably yields low variance gradients, it still relies on a stochastic
sampling process for optimization. In this work, we present a relaxed
categorical analytic bound (ReCAB), a novel divergence-like metric which
corresponds to the upper bound of the Kullback-Leibler divergence (KLD) of a
relaxed categorical distribution. The proposed metric is easy to implement
because it has a closed form solution, and empirical results show that it is
close to the actual KLD. Along with this new metric, we propose a relaxed
categorical analytic bound variational autoencoder (ReCAB-VAE) that
successfully models both continuous and relaxed discrete latent
representations. We implement an emotional text-to-speech synthesis system
based on the proposed framework, and show that the proposed system flexibly and
stably controls emotion expressions with better speech quality compared to
baselines that use stochastic estimation or categorical distribution
approximation.

本文提出了一种放松的分类分析上界（ReCAB）及其在生成模型中的应用，相对于基于随机抽样的方法，该方法具有封闭的公式解，同时提出了基于该方法的情感语音合成系统，相较于基线系统，该系统具有更好的语音质量和稳定性。