{"paper":{"title":"Provably learning a multi-head attention layer","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","stat.ML"],"primary_cat":"cs.LG","authors_text":"Sitan Chen, Yuanzhi Li","submitted_at":"2024-02-06T15:39:09Z","abstract_excerpt":"The multi-head attention layer is one of the key components of the transformer architecture that sets it apart from traditional feed-forward models. Given a sequence length $k$, attention matrices $\\mathbf{\\Theta}_1,\\ldots,\\mathbf{\\Theta}_m\\in\\mathbb{R}^{d\\times d}$, and projection matrices $\\mathbf{W}_1,\\ldots,\\mathbf{W}_m\\in\\mathbb{R}^{d\\times d}$, the corresponding multi-head attention layer $F: \\mathbb{R}^{k\\times d}\\to \\mathbb{R}^{k\\times d}$ transforms length-$k$ sequences of $d$-dimensional tokens $\\mathbf{X}\\in\\mathbb{R}^{k\\times d}$ via $F(\\mathbf{X}) \\triangleq \\sum^m_{i=1} \\mathrm{s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.04084","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/2402.04084/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"}