# ReCAB-VAE: Gumbel-Softmax Variational Inference Based on Analytic Divergence

arXiv: https://arxiv.org/abs/2205.04104 · HTML: https://mlsanity.com/paper/2205.04104/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 25 references that are in the map.
- First posted on arXiv 9 May 2022.

## Builds on (most cited first, 19 of 19)

- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [StarGAN: Unified Generative Adversarial Networks for Multi-Domain Image-to-Image Translation](https://mlsanity.com/paper/1711.09020/) (2017)
- [Conditional Image Generation with PixelCNN Decoders](https://mlsanity.com/paper/1606.05328/) (2016)
- [Natural TTS Synthesis by Conditioning WaveNet on Mel Spectrogram Predictions](https://mlsanity.com/paper/1712.05884/) (2017)
- [Semi-Supervised Learning with Deep Generative Models](https://mlsanity.com/paper/1406.5298/) (2014)
- [Neural Relational Inference for Interacting Systems](https://mlsanity.com/paper/1802.04687/) (2018)
- [WaveGlow: A Flow-based Generative Network for Speech Synthesis](https://mlsanity.com/paper/1811.00002/) (2018)
- [Style Tokens: Unsupervised Style Modeling, Control and Transfer in End-to-End Speech Synthesis](https://mlsanity.com/paper/1803.09017/) (2018)
- [Towards End-to-End Prosody Transfer for Expressive Speech Synthesis with Tacotron](https://mlsanity.com/paper/1803.09047/) (2018)
- [Learning Disentangled Joint Continuous and Discrete Representations](https://mlsanity.com/paper/1804.00104/) (2018)
- [Improved Variational Autoencoders for Text Modeling using Dilated Convolutions](https://mlsanity.com/paper/1702.08139/) (2017)
- [Learning Disentangled Representations with Semi-Supervised Deep Generative Models](https://mlsanity.com/paper/1706.00400/) (2017)
- [Gaussian Process Prior Variational Autoencoders](https://mlsanity.com/paper/1810.11738/) (2018)
- [Learning latent representations for style control and transfer in end-to-end speech synthesis](https://mlsanity.com/paper/1812.04342/) (2018)
- [Fully-hierarchical fine-grained prosody modeling for interpretable speech synthesis](https://mlsanity.com/paper/2002.03785/) (2020)
- [Emotional End-to-End Neural Speech Synthesizer](https://mlsanity.com/paper/1711.05447/) (2017)
- [Semi-Supervised Generative Modeling for Controllable Speech Synthesis](https://mlsanity.com/paper/1910.01709/) (2019)

## Built on by (most cited first, 1 of 1)

- [The Gaussian-Multinoulli Restricted Boltzmann Machine: A Potts Model Extension of the GRBM](https://mlsanity.com/paper/2505.11635/) (2025)

## Abstract (arXiv)

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.