# Autoencoding Dynamics: Topological Limitations and Capabilities

arXiv: https://arxiv.org/abs/2511.04807 · HTML: https://mlsanity.com/paper/2511.04807/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 18 references that are in the map.
- First posted on arXiv 6 Nov 2025.

## Builds on (most cited first, 5 of 5)

- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Topological Obstructions to Autoencoding](https://mlsanity.com/paper/2102.08380/) (2021)
- [Why should autoencoders work?](https://mlsanity.com/paper/2310.02250/) (2023)
- [Global linearization of asymptotically stable systems without hyperbolicity](https://mlsanity.com/paper/2502.07708/) (2025)

## Built on by (most cited first, 1 of 1)

- [Deep learning from a control vantage point](https://mlsanity.com/paper/2610.14385/) (2026)

## Abstract (arXiv)

Given a "data manifold" Msubset ℝn and "latent space" ℝℓ, an autoencoder is a pair of continuous maps consisting of an "encoder" Ecolon ℝn→ ℝℓ and "decoder" Dcolon ℝℓ→ ℝn such that the "round trip" map Dcirc E is as close as possible to the identity map mboxidM on M. We present various topological limitations and capabilites inherent to the search for an autoencoder, and describe capabilities for autoencoding dynamical systems having M as an invariant manifold.