{"paper":{"title":"On Generalized Barron Spaces for Shallow Neural Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Leqi Zhang, Shuai Lu","submitted_at":"2026-08-07T06:04:08Z","abstract_excerpt":"Classical Barron spaces are function spaces specifically designed for shallow neural networks mostly with ReLU, $\\mathrm{ReLU}^k$ (RePU) or Lipschitz continuous activation functions. In the present work, we introduce a generalized Barron space \\( B_{\\sigma}^{\\varphi} \\) for shallow neural networks with a generic activation function possessing certain smoothness properties. The subscript \\( \\sigma \\) denotes the activation function, while the superscript \\( \\varphi \\) controls the smoothness of the generalized Barron spaces, defined via a \\( \\varphi \\)-weighted integral norm imposed on neural n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.06843","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/2608.06843/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"}