{"paper":{"title":"Contractivity of neural ODEs: an eigenvalue optimization problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.OC"],"primary_cat":"math.NA","authors_text":"Anton Savostianov, Arturo De Marinis, Francesco Tudisco, Nicola Guglielmi","submitted_at":"2024-02-20T15:35:40Z","abstract_excerpt":"We propose a novel methodology to solve a key eigenvalue optimization problem which arises in the contractivity analysis of neural ODEs. When looking at contractivity properties of a one layer weight-tied neural ODE $\\dot{u}(t)=\\sigma(Au(t)+b)$ (with $u,b \\in {\\mathbb R}^n$, $A$ is a given $n \\times n$ matrix, $\\sigma : {\\mathbb R} \\to {\\mathbb R}$ denotes an activation function and for a vector $z \\in {\\mathbb R}^n$, $\\sigma(z) \\in {\\mathbb R}^n$ has to be interpreted entry-wise), we are led to study the logarithmic norm of a set of products of type $D A$, where $D$ is a diagonal matrix such "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.13092","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2402.13092/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}