# Resetting a fixed broken ELBO

arXiv: https://arxiv.org/abs/2312.06828 · HTML: https://mlsanity.com/paper/2312.06828/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 13 references that are in the map.
- First posted on arXiv 11 Dec 2023.

## Builds on (most cited first, 2 of 2)

- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Factor Analysis, Probabilistic Principal Component Analysis, Variational Inference, and Variational Autoencoder: Tutorial and Survey](https://mlsanity.com/paper/2101.00734/) (2021)

## Abstract (arXiv)

Variational autoencoders (VAEs) are one class of generative probabilistic latent-variable models designed for inference based on known data. They balance reconstruction and regularizer terms. A variational approximation produces an evidence lower bound (ELBO). Multiplying the regularizer term by beta provides a beta-VAE/ELBO, improving disentanglement of the latent space. However, any beta value different than unity violates the laws of conditional probability. To provide a similarly-parameterized VAE, we develop a Renyi (versus Shannon) entropy VAE, and a variational approximation RELBO that introduces a similar parameter. The Renyi VAE has an additional Renyi regularizer-like term with a conditional distribution that is not learned. The term is evaluated essentially analytically using a Singular Value Decomposition method.