# Dynamic Narrowing of VAE Bottlenecks Using GECO and L0 Regularization

arXiv: https://arxiv.org/abs/2003.10901 · HTML: https://mlsanity.com/paper/2003.10901/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Mar 2020.

## Built on by (most cited first, 3 of 3)

- [ARD-VAE: A Statistical Formulation to Find the Relevant Latent Dimensions of Variational Autoencoders](https://mlsanity.com/paper/2501.10901/) (2025)
- [Adversarial Disentanglement by Backpropagation with Physics-Informed Variational Autoencoder](https://mlsanity.com/paper/2506.13658/) (2025)
- [RENs: Relevance Encoding Networks](https://mlsanity.com/paper/2205.13061/) (2022)

## Abstract (arXiv)

When designing variational autoencoders (VAEs) or other types of latent space models, the dimensionality of the latent space is typically defined upfront. In this process, it is possible that the number of dimensions is under- or overprovisioned for the application at hand. In case the dimensionality is not predefined, this parameter is usually determined using time- and resource-consuming cross-validation. For these reasons we have developed a technique to shrink the latent space dimensionality of VAEs automatically and on-the-fly during training using Generalized ELBO with Constrained Optimization (GECO) and the L0-Augment-REINFORCE-Merge (L0-ARM) gradient estimator. The GECO optimizer ensures that we are not violating a predefined upper bound on the reconstruction error. This paper presents the algorithmic details of our method along with experimental results on five different datasets. We find that our training procedure is stable and that the latent space can be pruned effectively without violating the GECO constraints.