{"paper":{"title":"On the Sample Complexity of Two-Layer Networks: Lipschitz vs. Element-Wise Lipschitz Activation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Amit Daniely, Elad Granot","submitted_at":"2022-11-17T16:27:15Z","abstract_excerpt":"We investigate the sample complexity of bounded two-layer neural networks using different activation functions.\n  In particular, we consider the class\n  $$ \\mathcal{H} = \\left\\{\\textbf{x}\\mapsto \\langle \\textbf{v}, \\sigma \\circ W\\textbf{b} + \\textbf{b} \\rangle : \\textbf{b}\\in\\mathbb{R}^d, W \\in \\mathbb{R}^{\\mathcal{T}\\times d}, \\textbf{v} \\in \\mathbb{R}^{\\mathcal{T}}\\right\\} $$\n  where the spectral norm of $W$ and $\\textbf{v}$ is bounded by $O(1)$, the Frobenius norm of $W$ is bounded from its initialization by $R > 0$, and $\\sigma$ is a Lipschitz activation function.\n  We prove that if $\\sigm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.09634","kind":"arxiv","version":4},"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/2211.09634/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"}