{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:XKPPQXOOIBVDCHYRBYD6S5QDIO","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":"a9b0262b41a4c99b228a8f17fbfe63dc76be9bef79548f1b6fb19684221809c5","cross_cats_sorted":["cs.AI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-07-26T08:41:58Z","title_canon_sha256":"c5591ee6924be1dac361835d305bf4bea751ba666e43dd498b73a300ae7c7251"},"schema_version":"1.0","source":{"id":"2407.18601","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.18601","created_at":"2026-07-05T11:50:27Z"},{"alias_kind":"arxiv_version","alias_value":"2407.18601v3","created_at":"2026-07-05T11:50:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.18601","created_at":"2026-07-05T11:50:27Z"},{"alias_kind":"pith_short_12","alias_value":"XKPPQXOOIBVD","created_at":"2026-07-05T11:50:27Z"},{"alias_kind":"pith_short_16","alias_value":"XKPPQXOOIBVDCHYR","created_at":"2026-07-05T11:50:27Z"},{"alias_kind":"pith_short_8","alias_value":"XKPPQXOO","created_at":"2026-07-05T11:50:27Z"}],"graph_snapshots":[{"event_id":"sha256:0804eeaf15472d2b4b9cd8390675992d3bba0d0e7008aa39031ca9b8cc0a8a68","target":"graph","created_at":"2026-07-05T11:50:27Z","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/2407.18601/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Attention regulates information transfer between tokens. For this, query and key vectors are compared, typically in terms of a scalar product, $\\mathbf{Q}^T\\mathbf{K}$, together with a subsequent softmax normalization. In geometric terms, the standard dot-product attention (DPA) leads to large/small attention weights for parallel/antiparallel queries and keys. Here we study expressive attention (EA), which is based on $(\\mathbf{Q}^T\\mathbf{K})^2$, the squared dot product. In this case, attention is enhanced when query and key are either parallel or antiparallel, and suppressed for orthogonal c","authors_text":"Claudius Gros","cross_cats":["cs.AI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-07-26T08:41:58Z","title":"Reorganizing attention-space geometry with expressive attention"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.18601","kind":"arxiv","version":3},"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":"sha256:2c3d44d584e366db8ad57cef525ec57cb1d0193a908839ff12dca652f4de0aa6","target":"record","created_at":"2026-07-05T11:50:27Z","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":"a9b0262b41a4c99b228a8f17fbfe63dc76be9bef79548f1b6fb19684221809c5","cross_cats_sorted":["cs.AI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-07-26T08:41:58Z","title_canon_sha256":"c5591ee6924be1dac361835d305bf4bea751ba666e43dd498b73a300ae7c7251"},"schema_version":"1.0","source":{"id":"2407.18601","kind":"arxiv","version":3}},"canonical_sha256":"ba9ef85dce406a311f110e07e9760343bff7a7c00ab7e8c0052946d20cc0f952","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ba9ef85dce406a311f110e07e9760343bff7a7c00ab7e8c0052946d20cc0f952","first_computed_at":"2026-07-05T11:50:27.594897Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:50:27.594897Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vRTIVb2ZzJw43+VEGk7pHKyAL+Etw8bXNLOf91h57mZ5OYmDJY4rFHz/Ff8P2gr2MXnJb3/VT+5OcBmxAmgsCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:50:27.595369Z","signed_message":"canonical_sha256_bytes"},"source_id":"2407.18601","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2c3d44d584e366db8ad57cef525ec57cb1d0193a908839ff12dca652f4de0aa6","sha256:0804eeaf15472d2b4b9cd8390675992d3bba0d0e7008aa39031ca9b8cc0a8a68"],"state_sha256":"491061837b944d31cd5ee68d0fb067513c6c4f550e4d59dd09a1dee0a394ebe5"}