{"paper":{"title":"Density of Neural Network Classes on Compact Subsets of Topological Vector Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Arash Ghorbanalizadeh, Mohammad Javad Baghbanbashi","submitted_at":"2026-05-21T13:39:44Z","abstract_excerpt":"We prove density results for neural-network classes on compact sets \\(K\\subset X\\), where \\(X\\) is a topological vector space whose continuous dual \\(X^*\\) separates points. Let \\(\\Psi:\\mathbb R\\to\\mathbb R\\) be a continuous squashing function. We show that the class \\[ \\Sigma_X(\\Psi) = \\left\\{ \\sum_{j=1}^{N}\\omega_j\\Psi(f_j(x)+b_j): N\\in\\mathbb N,\\ \\omega_j,b_j\\in\\mathbb R,\\ f_j\\in X^* \\right\\} \\] is dense in \\(C(K)\\) with respect to the uniform norm. As a consequence, if \\(\\mu\\) is a Radon probability measure supported on \\(K\\), then \\(\\Sigma_X(\\Psi)\\) is dense in \\(L^p(K,\\mu)\\) for every \\("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.22482","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/2605.22482/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"}