{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:VMOIB4ZAXQJLG7FMOXYGTAC4TC","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"0dd01b9afa80be24dbe80274135d3a394fe72a0fbcdba796048d5cdf35204686","cross_cats_sorted":["math.OC","stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2023-10-19T12:18:24Z","title_canon_sha256":"9a71bbfa85f4a47fa7f9b4e8fb7c22cc34dfbc16aa6d2ba83e64dcbbf9206ada"},"schema_version":"1.0","source":{"id":"2310.12680","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2310.12680","created_at":"2026-07-05T09:19:24Z"},{"alias_kind":"arxiv_version","alias_value":"2310.12680v2","created_at":"2026-07-05T09:19:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.12680","created_at":"2026-07-05T09:19:24Z"},{"alias_kind":"pith_short_12","alias_value":"VMOIB4ZAXQJL","created_at":"2026-07-05T09:19:24Z"},{"alias_kind":"pith_short_16","alias_value":"VMOIB4ZAXQJLG7FM","created_at":"2026-07-05T09:19:24Z"},{"alias_kind":"pith_short_8","alias_value":"VMOIB4ZA","created_at":"2026-07-05T09:19:24Z"}],"graph_snapshots":[{"event_id":"sha256:c56cd6a5185c2ebe254c0e952246f4d5c03aa2f0962d764c0007b0dc014ced02","target":"graph","created_at":"2026-07-05T09:19:24Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2310.12680/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Christos Thrampoulidis, Hossein Taheri, Puneesh Deora, Rouzbeh Ghaderi","cross_cats":["math.OC","stat.ML"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2023-10-19T12:18:24Z","title":"On the Optimization and Generalization of Multi-head Attention"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.12680","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:1de557564adf40c20b393623888498aa8709e52c03caabc03e7633822b34aabb","target":"record","created_at":"2026-07-05T09:19:24Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"0dd01b9afa80be24dbe80274135d3a394fe72a0fbcdba796048d5cdf35204686","cross_cats_sorted":["math.OC","stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2023-10-19T12:18:24Z","title_canon_sha256":"9a71bbfa85f4a47fa7f9b4e8fb7c22cc34dfbc16aa6d2ba83e64dcbbf9206ada"},"schema_version":"1.0","source":{"id":"2310.12680","kind":"arxiv","version":2}},"canonical_sha256":"ab1c80f320bc12b37cac75f069805c98b5f5edf87992818970c4f358b8b95197","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ab1c80f320bc12b37cac75f069805c98b5f5edf87992818970c4f358b8b95197","first_computed_at":"2026-07-05T09:19:24.678218Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:19:24.678218Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"l2HIGicvyrXIgM3Zi3LyVyzQ3tvdYc2grp7tG07jPB/zz4uY8hr9l4xdOEAGkyY0ovVgbEMgBCz27ZwGFRaqBA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:19:24.678837Z","signed_message":"canonical_sha256_bytes"},"source_id":"2310.12680","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1de557564adf40c20b393623888498aa8709e52c03caabc03e7633822b34aabb","sha256:c56cd6a5185c2ebe254c0e952246f4d5c03aa2f0962d764c0007b0dc014ced02"],"state_sha256":"38ffe66cf7fac4235bc0b31955d36b23fac0dcb5e647afc01641388b39df10d3"}