# Topologically-Informed Atlas Learning

arXiv: https://arxiv.org/abs/2110.00429 · HTML: https://mlsanity.com/paper/2110.00429/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 41 references that are in the map.
- First posted on arXiv 1 Oct 2021.

## Builds on (most cited first, 4 of 4)

- [A Modern Take on the Bias-Variance Tradeoff in Neural Networks](https://mlsanity.com/paper/1810.08591/) (2018)
- [Parts-Based Articulated Object Localization in Clutter Using Belief Propagation](https://mlsanity.com/paper/2008.02881/) (2020)
- [On the manipulation of articulated objects in human-robot cooperation scenarios](https://mlsanity.com/paper/1801.01757/) (2018)
- [Autoencoding topology](https://mlsanity.com/paper/1803.00156/) (2018)

## Built on by (most cited first, 4 of 4)

- [Manifold Learning by Mixture Models of VAEs for Inverse Problems](https://mlsanity.com/paper/2303.15244/) (2023)
- [CHyLL: Learning Continuous Neural Representations of Hybrid Systems](https://mlsanity.com/paper/2512.10117/) (2025)
- [Atlas flow : compatible local structures on the manifold](https://mlsanity.com/paper/2210.14149/) (2022)
- [SPLATART: Articulated Gaussian Splatting with Estimated Object Structure](https://mlsanity.com/paper/2506.12184/) (2025)

## Abstract (arXiv)

We present a new technique that enables manifold learning to accurately embed data manifolds that contain holes, without discarding any topological information. Manifold learning aims to embed high dimensional data into a lower dimensional Euclidean space by learning a coordinate chart, but it requires that the entire manifold can be embedded in a single chart. This is impossible for manifolds with holes. In such cases, it is necessary to learn an atlas: a collection of charts that collectively cover the entire manifold. We begin with many small charts, and combine them in a bottom-up approach, where charts are only combined if doing so will not introduce problematic topological features. When it is no longer possible to combine any charts, each chart is individually embedded with standard manifold learning techniques, completing the construction of the atlas. We show the efficacy of our method by constructing atlases for challenging synthetic manifolds; learning human motion embeddings from motion capture data; and learning kinematic models of articulated objects.