{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:YHAWLF2ZTN34WMMTJGW6PVFDGG","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":"5c2df1aa0087f2839f9788b11192c07fe60d8a7975295c07ab4e7253a0e4d7bc","cross_cats_sorted":["cs.CL"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-02-07T16:50:27Z","title_canon_sha256":"89d44b34cf849f1b7bd86e07e5a217b5a380db64a9fdd2deee9239097df1b027"},"schema_version":"1.0","source":{"id":"2502.05076","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.05076","created_at":"2026-07-05T10:11:02Z"},{"alias_kind":"arxiv_version","alias_value":"2502.05076v1","created_at":"2026-07-05T10:11:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.05076","created_at":"2026-07-05T10:11:02Z"},{"alias_kind":"pith_short_12","alias_value":"YHAWLF2ZTN34","created_at":"2026-07-05T10:11:02Z"},{"alias_kind":"pith_short_16","alias_value":"YHAWLF2ZTN34WMMT","created_at":"2026-07-05T10:11:02Z"},{"alias_kind":"pith_short_8","alias_value":"YHAWLF2Z","created_at":"2026-07-05T10:11:02Z"}],"graph_snapshots":[{"event_id":"sha256:1f1a40a35fcb9dbd11812df33aff49641acf3e13f7a8b5963efeb7e7eb48fb15","target":"graph","created_at":"2026-07-05T10:11:02Z","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/2502.05076/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we investigate the ability of single-layer attention-only transformers (i.e. attention layers) to memorize facts contained in databases from a linear-algebraic perspective. We associate with each database a 3-tensor, propose the rank of this tensor as a measure of the size of the database, and provide bounds on the rank in terms of properties of the database. We also define a 3-tensor corresponding to an attention layer, and empirically demonstrate the relationship between its rank and database rank on a dataset of toy models and random databases. By highlighting the roles playe","authors_text":"Liang Ze Wong","cross_cats":["cs.CL"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-02-07T16:50:27Z","title":"Paying Attention to Facts: Quantifying the Knowledge Capacity of Attention Layers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.05076","kind":"arxiv","version":1},"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":"sha256:515cda30dd0389e763ff058bc932544a3bca1a0e135cfe4c5d2bad9e0ac53af8","target":"record","created_at":"2026-07-05T10:11:02Z","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":"5c2df1aa0087f2839f9788b11192c07fe60d8a7975295c07ab4e7253a0e4d7bc","cross_cats_sorted":["cs.CL"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-02-07T16:50:27Z","title_canon_sha256":"89d44b34cf849f1b7bd86e07e5a217b5a380db64a9fdd2deee9239097df1b027"},"schema_version":"1.0","source":{"id":"2502.05076","kind":"arxiv","version":1}},"canonical_sha256":"c1c16597599b77cb319349ade7d4a331b44d2ef516a68c1a3e13e25057813016","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c1c16597599b77cb319349ade7d4a331b44d2ef516a68c1a3e13e25057813016","first_computed_at":"2026-07-05T10:11:02.818543Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:11:02.818543Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2jw75xjRgCehZ03yorp4WbsM5RhERxPF50sjeO5JFQWcouyxvNCP7hoM4dVJO1Cl61/NcAc4F1zOu/9DMqnwCw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:11:02.819086Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.05076","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:515cda30dd0389e763ff058bc932544a3bca1a0e135cfe4c5d2bad9e0ac53af8","sha256:1f1a40a35fcb9dbd11812df33aff49641acf3e13f7a8b5963efeb7e7eb48fb15"],"state_sha256":"c308c6ec0c012b4e52f90b2e83c030deb69d4a5aad8e1e3f60d2b379034d5065"}