# Ordering Dimensions with Nested Dropout Normalizing Flows

arXiv: https://arxiv.org/abs/2006.08777 · HTML: https://mlsanity.com/paper/2006.08777/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jun 2020.

## Built on by (most cited first, 7 of 7)

- [A Review of Change of Variable Formulas for Generative Modeling](https://mlsanity.com/paper/2308.02652/) (2023)
- [Variational Nested Dropout](https://mlsanity.com/paper/2101.11353/) (2021)
- [Information-Ordered Bottlenecks for Adaptive Semantic Compression](https://mlsanity.com/paper/2305.11213/) (2023)
- [Tunable Latent Generative Priors for Compressed Sensing and Inverse Problems](https://mlsanity.com/paper/2603.07357/) (2026)
- [FloDR: An invertible dimensionality reduction method based on a normalising flow](https://mlsanity.com/paper/2607.26278/) (2026)
- [From Core to Detail: Unsupervised Disentanglement with Entropy-Ordered Flows](https://mlsanity.com/paper/2602.06940/) (2026)
- [NFMap: Topographic 2D Manifold Learning with Invertible Normalizing Flows](https://mlsanity.com/paper/2610.16750/) (2026)

## Abstract (arXiv)

The latent space of normalizing flows must be of the same dimensionality as their output space. This constraint presents a problem if we want to learn low-dimensional, semantically meaningful representations. Recent work has provided compact representations by fitting flows constrained to manifolds, but hasn't defined a density off that manifold. In this work we consider flows with full support in data space, but with ordered latent variables. Like in PCA, the leading latent dimensions define a sequence of manifolds that lie close to the data. We note a trade-off between the flow likelihood and the quality of the ordering, depending on the parameterization of the flow.