Autoencoding Dynamics: Topological Limitations and Capabilities
Not on the map. Why?
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.
Key facts. Cited by 1 paper 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
5 of 18 references.
References · 5
- 2013Auto-Encoding Variational Bayescited by 4,053
- 2017Deep learning for universal linear embeddings of nonlinear dynamicscited by 494
- 2021Topological Obstructions to Autoencodingcited by 20
- 2023Why should autoencoders work?cited by 3
- 2025Global linearization of asymptotically stable systems without hyperbolicitycited by 1
Built on by
Citing papers per year: 2026: 1.
1 paper.
- 2026Deep learning from a control vantage pointcited by 0
- 2026Deep learning from a control vantage point9 Oct 2026