# Autoencoding topology

arXiv: https://arxiv.org/abs/1803.00156 · HTML: https://mlsanity.com/paper/1803.00156/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Mar 2018.

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

- [Topological Obstructions to Autoencoding](https://mlsanity.com/paper/2102.08380/) (2021)
- [Manifold Learning by Mixture Models of VAEs for Inverse Problems](https://mlsanity.com/paper/2303.15244/) (2023)
- [Atlas Generative Models and Geodesic Interpolation](https://mlsanity.com/paper/2102.00264/) (2021)
- [Topologically-Informed Atlas Learning](https://mlsanity.com/paper/2110.00429/) (2021)
- [Atlas Based Representation and Metric Learning on Manifolds](https://mlsanity.com/paper/2106.07062/) (2021)
- [State Representation Learning Using an Unbalanced Atlas](https://mlsanity.com/paper/2305.10267/) (2023)
- [Dimensionality reduction and width of deep neural networks based on topological degree theory](https://mlsanity.com/paper/2511.06821/) (2025)

## Abstract (arXiv)

The problem of learning a manifold structure on a dataset is framed in terms of a generative model, to which we use ideas behind autoencoders (namely adversarial/Wasserstein autoencoders) to fit deep neural networks. From a machine learning perspective, the resulting structure, an atlas of a manifold, may be viewed as a combination of dimensionality reduction and "fuzzy" clustering.