arXiv:2511.04807v2 Announce Type: replace
Abstract: Given a “data manifold” $Msubset mathbb{R}^n$ and “latent space” $mathbb{R}^ell$, an autoencoder is a pair of continuous maps consisting of an “encoder” $Ecolon mathbb{R}^nto mathbb{R}^ell$ and “decoder” $Dcolon mathbb{R}^ellto mathbb{R}^n$ such that the “round trip” map $Dcirc E$ is as close as possible to the identity map $mbox{id}_M$ 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.