{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:UL6AZTX25LGGIHBA7XOC4P4WLC","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":"27e8352ea521a7c6827148525e36afbdfbf9b3b8f83abba3667e894665b07b97","cross_cats_sorted":["cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2021-07-16T13:22:29Z","title_canon_sha256":"a4cda4797ba553fb6251ef0d685cb2b8781ed6fc6d912bdba0661860ca103d02"},"schema_version":"1.0","source":{"id":"2107.07889","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2107.07889","created_at":"2026-07-05T02:58:30Z"},{"alias_kind":"arxiv_version","alias_value":"2107.07889v1","created_at":"2026-07-05T02:58:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2107.07889","created_at":"2026-07-05T02:58:30Z"},{"alias_kind":"pith_short_12","alias_value":"UL6AZTX25LGG","created_at":"2026-07-05T02:58:30Z"},{"alias_kind":"pith_short_16","alias_value":"UL6AZTX25LGGIHBA","created_at":"2026-07-05T02:58:30Z"},{"alias_kind":"pith_short_8","alias_value":"UL6AZTX2","created_at":"2026-07-05T02:58:30Z"}],"graph_snapshots":[{"event_id":"sha256:1169bd5e1821d45344746f2d89df11186c72ebd291a2b640daadda22a2d7aea9","target":"graph","created_at":"2026-07-05T02:58:30Z","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/2107.07889/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In applications such as natural language processing or computer vision, one is given a large $n \\times d$ matrix $A = (a_{i,j})$ and would like to compute a matrix decomposition, e.g., a low rank approximation, of a function $f(A) = (f(a_{i,j}))$ applied entrywise to $A$. A very important special case is the likelihood function $f\\left( A \\right ) = \\log{\\left( \\left| a_{ij}\\right| +1\\right)}$. A natural way to do this would be to simply apply $f$ to each entry of $A$, and then compute the matrix decomposition, but this requires storing all of $A$ as well as multiple passes over its entries. R","authors_text":"David P. Woodruff, Jiaxin Wang, Yifei Jiang, Yi Li, Yiming Sun","cross_cats":["cs.LG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2021-07-16T13:22:29Z","title":"Single Pass Entrywise-Transformed Low Rank Approximation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.07889","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:f73870e3b08a2a9579259291d4ad8244ae415fc7f6e7bde672e6dc8ff0e0b976","target":"record","created_at":"2026-07-05T02:58:30Z","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":"27e8352ea521a7c6827148525e36afbdfbf9b3b8f83abba3667e894665b07b97","cross_cats_sorted":["cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2021-07-16T13:22:29Z","title_canon_sha256":"a4cda4797ba553fb6251ef0d685cb2b8781ed6fc6d912bdba0661860ca103d02"},"schema_version":"1.0","source":{"id":"2107.07889","kind":"arxiv","version":1}},"canonical_sha256":"a2fc0ccefaeacc641c20fddc2e3f96588982fc6177d8d21f79cc5f1521e7b2eb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a2fc0ccefaeacc641c20fddc2e3f96588982fc6177d8d21f79cc5f1521e7b2eb","first_computed_at":"2026-07-05T02:58:30.239029Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:58:30.239029Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Za8T4U2xh8tzSsVMzZx9HsgGvIhP1P9TmA4gonJLDsxWi24RpIgquNGXsQh2qWn9ODsaB2XsOttHrzPqJd2ADQ==","signature_status":"signed_v1","signed_at":"2026-07-05T02:58:30.239409Z","signed_message":"canonical_sha256_bytes"},"source_id":"2107.07889","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f73870e3b08a2a9579259291d4ad8244ae415fc7f6e7bde672e6dc8ff0e0b976","sha256:1169bd5e1821d45344746f2d89df11186c72ebd291a2b640daadda22a2d7aea9"],"state_sha256":"eef1958370eff2f2f71ff1afa8391017297ad60f06e7e63aea7a5b9cd44f99aa"}