{"ID":2845527,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.04807","arxiv_id":"2511.04807","title":"Autoencoding Dynamics: Topological Limitations and Capabilities","abstract":"Given a \"data manifold\" $M\\subset \\mathbb{R}^n$ and \"latent space\" $\\mathbb{R}^\\ell$, an autoencoder is a pair of continuous maps consisting of an \"encoder\" $E\\colon \\mathbb{R}^n\\to \\mathbb{R}^\\ell$ and \"decoder\" $D\\colon \\mathbb{R}^\\ell\\to \\mathbb{R}^n$ such that the \"round trip\" map $D\\circ E$ 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.","short_abstract":"Given a \"data manifold\" $M\\subset \\mathbb{R}^n$ and \"latent space\" $\\mathbb{R}^\\ell$, an autoencoder is a pair of continuous maps consisting of an \"encoder\" $E\\colon \\mathbb{R}^n\\to \\mathbb{R}^\\ell$ and \"decoder\" $D\\colon \\mathbb{R}^\\ell\\to \\mathbb{R}^n$ such that the \"round trip\" map $D\\circ E$ is as close as possible...","url_abs":"https://arxiv.org/abs/2511.04807","url_pdf":"https://arxiv.org/pdf/2511.04807v2","authors":"[\"Matthew D. Kvalheim\",\"Eduardo D. Sontag\"]","published":"2025-11-06T20:53:37Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"math.DS\"]","methods":"[]","has_code":false}