{"paper":{"title":"Tractability of approximation by general shallow networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"cs.LG","authors_text":"Hrushikesh Mhaskar, Tong Mao","submitted_at":"2023-08-07T00:14:46Z","abstract_excerpt":"In this paper, we present a sharper version of the results in the paper Dimension independent bounds for general shallow networks; Neural Networks, \\textbf{123} (2020), 142-152. Let $\\mathbb{X}$ and $\\mathbb{Y}$ be compact metric spaces. We consider approximation of functions of the form $ x\\mapsto\\int_{\\mathbb{Y}} G( x, y)d\\tau( y)$, $ x\\in\\mathbb{X}$, by $G$-networks of the form $ x\\mapsto \\sum_{k=1}^n a_kG( x, y_k)$, $ y_1,\\cdots, y_n\\in\\mathbb{Y}$, $a_1,\\cdots, a_n\\in\\mathbb{R}$. Defining the dimensions of $\\mathbb{X}$ and $\\mathbb{Y}$ in terms of covering numbers, we obtain dimension inde"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.03230","kind":"arxiv","version":2},"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/2308.03230/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"}