{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:OZNAUTRTDIR6VB7AMHDXFIIYF2","short_pith_number":"pith:OZNAUTRT","schema_version":"1.0","canonical_sha256":"765a0a4e331a23ea87e061c772a1182e9f4c87b0045c593988110fc6e74fca62","source":{"kind":"arxiv","id":"2311.01960","version":1},"attestation_state":"computed","paper":{"title":"Hardness of Low Rank Approximation of Entrywise Transformed Matrix Products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"cs.DS","authors_text":"David Woodruff, Qiuyi (Richard) Zhang, Tamas Sarlos, Xingyou Song","submitted_at":"2023-11-03T14:56:24Z","abstract_excerpt":"Inspired by fast algorithms in natural language processing, we study low rank approximation in the entrywise transformed setting where we want to find a good rank $k$ approximation to $f(U \\cdot V)$, where $U, V^\\top \\in \\mathbb{R}^{n \\times r}$ are given, $r = O(\\log(n))$, and $f(x)$ is a general scalar function. Previous work in sublinear low rank approximation has shown that if both (1) $U = V^\\top$ and (2) $f(x)$ is a PSD kernel function, then there is an $O(nk^{\\omega-1})$ time constant relative error approximation algorithm, where $\\omega \\approx 2.376$ is the exponent of matrix multipli"},"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":"2311.01960","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2023-11-03T14:56:24Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"ef90f0734291f90752fdf2da65eeb612fcf82f39d460c144f2aa15239dbac607","abstract_canon_sha256":"210fe6184ada9ae59f27f7a30d584b23f371322f59a0e409e9b471f9ccd764a4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:08:47.951601Z","signature_b64":"UB7sAeqogyhVtxBr0aYPTkvjHhHM88JMfypnv2v00SqmcdjwKzJJvdetPFq5TUyAGGoRIYs1DBxdLFwr84OwAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"765a0a4e331a23ea87e061c772a1182e9f4c87b0045c593988110fc6e74fca62","last_reissued_at":"2026-07-05T07:08:47.951077Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:08:47.951077Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hardness of Low Rank Approximation of Entrywise Transformed Matrix Products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"cs.DS","authors_text":"David Woodruff, Qiuyi (Richard) Zhang, Tamas Sarlos, Xingyou Song","submitted_at":"2023-11-03T14:56:24Z","abstract_excerpt":"Inspired by fast algorithms in natural language processing, we study low rank approximation in the entrywise transformed setting where we want to find a good rank $k$ approximation to $f(U \\cdot V)$, where $U, V^\\top \\in \\mathbb{R}^{n \\times r}$ are given, $r = O(\\log(n))$, and $f(x)$ is a general scalar function. Previous work in sublinear low rank approximation has shown that if both (1) $U = V^\\top$ and (2) $f(x)$ is a PSD kernel function, then there is an $O(nk^{\\omega-1})$ time constant relative error approximation algorithm, where $\\omega \\approx 2.376$ is the exponent of matrix multipli"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.01960","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/2311.01960/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":"2311.01960","created_at":"2026-07-05T07:08:47.951145+00:00"},{"alias_kind":"arxiv_version","alias_value":"2311.01960v1","created_at":"2026-07-05T07:08:47.951145+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.01960","created_at":"2026-07-05T07:08:47.951145+00:00"},{"alias_kind":"pith_short_12","alias_value":"OZNAUTRTDIR6","created_at":"2026-07-05T07:08:47.951145+00:00"},{"alias_kind":"pith_short_16","alias_value":"OZNAUTRTDIR6VB7A","created_at":"2026-07-05T07:08:47.951145+00:00"},{"alias_kind":"pith_short_8","alias_value":"OZNAUTRT","created_at":"2026-07-05T07:08:47.951145+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/OZNAUTRTDIR6VB7AMHDXFIIYF2","json":"https://pith.science/pith/OZNAUTRTDIR6VB7AMHDXFIIYF2.json","graph_json":"https://pith.science/api/pith-number/OZNAUTRTDIR6VB7AMHDXFIIYF2/graph.json","events_json":"https://pith.science/api/pith-number/OZNAUTRTDIR6VB7AMHDXFIIYF2/events.json","paper":"https://pith.science/paper/OZNAUTRT"},"agent_actions":{"view_html":"https://pith.science/pith/OZNAUTRTDIR6VB7AMHDXFIIYF2","download_json":"https://pith.science/pith/OZNAUTRTDIR6VB7AMHDXFIIYF2.json","view_paper":"https://pith.science/paper/OZNAUTRT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2311.01960&json=true","fetch_graph":"https://pith.science/api/pith-number/OZNAUTRTDIR6VB7AMHDXFIIYF2/graph.json","fetch_events":"https://pith.science/api/pith-number/OZNAUTRTDIR6VB7AMHDXFIIYF2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OZNAUTRTDIR6VB7AMHDXFIIYF2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OZNAUTRTDIR6VB7AMHDXFIIYF2/action/storage_attestation","attest_author":"https://pith.science/pith/OZNAUTRTDIR6VB7AMHDXFIIYF2/action/author_attestation","sign_citation":"https://pith.science/pith/OZNAUTRTDIR6VB7AMHDXFIIYF2/action/citation_signature","submit_replication":"https://pith.science/pith/OZNAUTRTDIR6VB7AMHDXFIIYF2/action/replication_record"}},"created_at":"2026-07-05T07:08:47.951145+00:00","updated_at":"2026-07-05T07:08:47.951145+00:00"}