{"paper":{"title":"Deep Operator Network Approximation Rates for Lipschitz Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","cs.NA"],"primary_cat":"math.NA","authors_text":"Andreas Stein, Christoph Schwab, Jakob Zech","submitted_at":"2023-07-19T08:46:47Z","abstract_excerpt":"We establish universality and expression rate bounds for a class of neural Deep Operator Networks (DON) emulating Lipschitz (or H\\\"older) continuous maps $\\mathcal G:\\mathcal X\\to\\mathcal Y$ between (subsets of) separable Hilbert spaces $\\mathcal X$, $\\mathcal Y$. The DON architecture considered uses linear encoders $\\mathcal E$ and decoders $\\mathcal D$ via (biorthogonal) Riesz bases of $\\mathcal X$, $\\mathcal Y$, and an approximator network of an infinite-dimensional, parametric coordinate map that is Lipschitz continuous on the sequence space $\\ell^2(\\mathbb N)$. Unlike previous works ([Her"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.09835","kind":"arxiv","version":1},"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/2307.09835/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"}