{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:VMOIB4ZAXQJLG7FMOXYGTAC4TC","short_pith_number":"pith:VMOIB4ZA","schema_version":"1.0","canonical_sha256":"ab1c80f320bc12b37cac75f069805c98b5f5edf87992818970c4f358b8b95197","source":{"kind":"arxiv","id":"2310.12680","version":2},"attestation_state":"computed","paper":{"title":"On the Optimization and Generalization of Multi-head Attention","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.OC","stat.ML"],"primary_cat":"cs.LG","authors_text":"Christos Thrampoulidis, Hossein Taheri, Puneesh Deora, Rouzbeh Ghaderi","submitted_at":"2023-10-19T12:18:24Z","abstract_excerpt":"The training and generalization dynamics of the Transformer's core mechanism, namely the Attention mechanism, remain under-explored. Besides, existing analyses primarily focus on single-head attention. Inspired by the demonstrated benefits of overparameterization when training fully-connected networks, we investigate the potential optimization and generalization advantages of using multiple attention heads. Towards this goal, we derive convergence and generalization guarantees for gradient-descent training of a single-layer multi-head self-attention model, under a suitable realizability condit"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2310.12680","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2023-10-19T12:18:24Z","cross_cats_sorted":["math.OC","stat.ML"],"title_canon_sha256":"9a71bbfa85f4a47fa7f9b4e8fb7c22cc34dfbc16aa6d2ba83e64dcbbf9206ada","abstract_canon_sha256":"0dd01b9afa80be24dbe80274135d3a394fe72a0fbcdba796048d5cdf35204686"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:19:24.678837Z","signature_b64":"l2HIGicvyrXIgM3Zi3LyVyzQ3tvdYc2grp7tG07jPB/zz4uY8hr9l4xdOEAGkyY0ovVgbEMgBCz27ZwGFRaqBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ab1c80f320bc12b37cac75f069805c98b5f5edf87992818970c4f358b8b95197","last_reissued_at":"2026-07-05T09:19:24.678218Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:19:24.678218Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Optimization and Generalization of Multi-head Attention","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.OC","stat.ML"],"primary_cat":"cs.LG","authors_text":"Christos Thrampoulidis, Hossein Taheri, Puneesh Deora, Rouzbeh Ghaderi","submitted_at":"2023-10-19T12:18:24Z","abstract_excerpt":"The training and generalization dynamics of the Transformer's core mechanism, namely the Attention mechanism, remain under-explored. Besides, existing analyses primarily focus on single-head attention. Inspired by the demonstrated benefits of overparameterization when training fully-connected networks, we investigate the potential optimization and generalization advantages of using multiple attention heads. Towards this goal, we derive convergence and generalization guarantees for gradient-descent training of a single-layer multi-head self-attention model, under a suitable realizability condit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.12680","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/2310.12680/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2310.12680","created_at":"2026-07-05T09:19:24.678310+00:00"},{"alias_kind":"arxiv_version","alias_value":"2310.12680v2","created_at":"2026-07-05T09:19:24.678310+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.12680","created_at":"2026-07-05T09:19:24.678310+00:00"},{"alias_kind":"pith_short_12","alias_value":"VMOIB4ZAXQJL","created_at":"2026-07-05T09:19:24.678310+00:00"},{"alias_kind":"pith_short_16","alias_value":"VMOIB4ZAXQJLG7FM","created_at":"2026-07-05T09:19:24.678310+00:00"},{"alias_kind":"pith_short_8","alias_value":"VMOIB4ZA","created_at":"2026-07-05T09:19:24.678310+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.26749","citing_title":"Structure Before Collapse: Transient semantic geometry in next-token prediction","ref_index":201,"is_internal_anchor":false},{"citing_arxiv_id":"2306.14048","citing_title":"H$_2$O: Heavy-Hitter Oracle for Efficient Generative Inference of Large Language Models","ref_index":114,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/VMOIB4ZAXQJLG7FMOXYGTAC4TC","json":"https://pith.science/pith/VMOIB4ZAXQJLG7FMOXYGTAC4TC.json","graph_json":"https://pith.science/api/pith-number/VMOIB4ZAXQJLG7FMOXYGTAC4TC/graph.json","events_json":"https://pith.science/api/pith-number/VMOIB4ZAXQJLG7FMOXYGTAC4TC/events.json","paper":"https://pith.science/paper/VMOIB4ZA"},"agent_actions":{"view_html":"https://pith.science/pith/VMOIB4ZAXQJLG7FMOXYGTAC4TC","download_json":"https://pith.science/pith/VMOIB4ZAXQJLG7FMOXYGTAC4TC.json","view_paper":"https://pith.science/paper/VMOIB4ZA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2310.12680&json=true","fetch_graph":"https://pith.science/api/pith-number/VMOIB4ZAXQJLG7FMOXYGTAC4TC/graph.json","fetch_events":"https://pith.science/api/pith-number/VMOIB4ZAXQJLG7FMOXYGTAC4TC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VMOIB4ZAXQJLG7FMOXYGTAC4TC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VMOIB4ZAXQJLG7FMOXYGTAC4TC/action/storage_attestation","attest_author":"https://pith.science/pith/VMOIB4ZAXQJLG7FMOXYGTAC4TC/action/author_attestation","sign_citation":"https://pith.science/pith/VMOIB4ZAXQJLG7FMOXYGTAC4TC/action/citation_signature","submit_replication":"https://pith.science/pith/VMOIB4ZAXQJLG7FMOXYGTAC4TC/action/replication_record"}},"created_at":"2026-07-05T09:19:24.678310+00:00","updated_at":"2026-07-05T09:19:24.678310+00:00"}