{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:6CERFW2NHLMUCXZDACYRYIT2OO","short_pith_number":"pith:6CERFW2N","schema_version":"1.0","canonical_sha256":"f08912db4d3ad9415f2300b11c227a73b423e8a3c1d445405a35e6b6411e98d2","source":{"kind":"arxiv","id":"2607.07047","version":1},"attestation_state":"computed","paper":{"title":"Riemannian Geometry for Pre-trained Language Model Embeddings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.CL","authors_text":"Alexandre Quemy, Bart{\\l}omiej Sobieski, Gr\\'egoire Cattan, Przemys{\\l}aw Klocek, Szczepan Konior","submitted_at":"2026-07-08T06:23:46Z","abstract_excerpt":"Understanding the geometric structure of pre-trained language model embeddings matters for interpretability and safety. We ask whether sentence-level classification signal lives in the Riemannian geometry of contextual token embeddings, and probe it by extracting per-token pullback metrics from a learned encoder's analytical Jacobian and aggregating them with the Fr\\'echet mean on the symmetric positive definite (SPD) manifold; we call this procedure Riemannian Mean Pooling (RMP). Across three datasets with non-trivial linguistic structure (CoLA, CREAK, RTE), RMP outperforms Euclidean mean poo"},"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":"2607.07047","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CL","submitted_at":"2026-07-08T06:23:46Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"60c24c87fa0929529916ca69ee02fd237d25ccb2143b12a95e53405c098498e0","abstract_canon_sha256":"48844f37b8dc1f754544121364fa7239492838757613cd0d8e26d2736270c626"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-09T01:20:13.188603Z","signature_b64":"rep9XC//AjqDAq9w9TmsUKySbgvUW/VqPcPjOqgzxxwC761ePr9Aa+V6RDGCGqkflXJbfpy4n7Qz70ds0O+1DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f08912db4d3ad9415f2300b11c227a73b423e8a3c1d445405a35e6b6411e98d2","last_reissued_at":"2026-07-09T01:20:13.188251Z","signature_status":"signed_v1","first_computed_at":"2026-07-09T01:20:13.188251Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Riemannian Geometry for Pre-trained Language Model Embeddings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.CL","authors_text":"Alexandre Quemy, Bart{\\l}omiej Sobieski, Gr\\'egoire Cattan, Przemys{\\l}aw Klocek, Szczepan Konior","submitted_at":"2026-07-08T06:23:46Z","abstract_excerpt":"Understanding the geometric structure of pre-trained language model embeddings matters for interpretability and safety. We ask whether sentence-level classification signal lives in the Riemannian geometry of contextual token embeddings, and probe it by extracting per-token pullback metrics from a learned encoder's analytical Jacobian and aggregating them with the Fr\\'echet mean on the symmetric positive definite (SPD) manifold; we call this procedure Riemannian Mean Pooling (RMP). Across three datasets with non-trivial linguistic structure (CoLA, CREAK, RTE), RMP outperforms Euclidean mean poo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.07047","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/2607.07047/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":"2607.07047","created_at":"2026-07-09T01:20:13.188306+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.07047v1","created_at":"2026-07-09T01:20:13.188306+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.07047","created_at":"2026-07-09T01:20:13.188306+00:00"},{"alias_kind":"pith_short_12","alias_value":"6CERFW2NHLMU","created_at":"2026-07-09T01:20:13.188306+00:00"},{"alias_kind":"pith_short_16","alias_value":"6CERFW2NHLMUCXZD","created_at":"2026-07-09T01:20:13.188306+00:00"},{"alias_kind":"pith_short_8","alias_value":"6CERFW2N","created_at":"2026-07-09T01:20:13.188306+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6CERFW2NHLMUCXZDACYRYIT2OO","json":"https://pith.science/pith/6CERFW2NHLMUCXZDACYRYIT2OO.json","graph_json":"https://pith.science/api/pith-number/6CERFW2NHLMUCXZDACYRYIT2OO/graph.json","events_json":"https://pith.science/api/pith-number/6CERFW2NHLMUCXZDACYRYIT2OO/events.json","paper":"https://pith.science/paper/6CERFW2N"},"agent_actions":{"view_html":"https://pith.science/pith/6CERFW2NHLMUCXZDACYRYIT2OO","download_json":"https://pith.science/pith/6CERFW2NHLMUCXZDACYRYIT2OO.json","view_paper":"https://pith.science/paper/6CERFW2N","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.07047&json=true","fetch_graph":"https://pith.science/api/pith-number/6CERFW2NHLMUCXZDACYRYIT2OO/graph.json","fetch_events":"https://pith.science/api/pith-number/6CERFW2NHLMUCXZDACYRYIT2OO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6CERFW2NHLMUCXZDACYRYIT2OO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6CERFW2NHLMUCXZDACYRYIT2OO/action/storage_attestation","attest_author":"https://pith.science/pith/6CERFW2NHLMUCXZDACYRYIT2OO/action/author_attestation","sign_citation":"https://pith.science/pith/6CERFW2NHLMUCXZDACYRYIT2OO/action/citation_signature","submit_replication":"https://pith.science/pith/6CERFW2NHLMUCXZDACYRYIT2OO/action/replication_record"}},"created_at":"2026-07-09T01:20:13.188306+00:00","updated_at":"2026-07-09T01:20:13.188306+00:00"}