{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:HOAGXX62KCP372UX5BCG6HCF4K","short_pith_number":"pith:HOAGXX62","schema_version":"1.0","canonical_sha256":"3b806bdfda509fbfea97e8446f1c45e2bfcb94e598c617328bc61c77e72cf394","source":{"kind":"arxiv","id":"2302.11068","version":3},"attestation_state":"computed","paper":{"title":"Low Rank Matrix Completion via Robust Alternating Minimization in Nearly Linear Time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","math.OC","stat.ML"],"primary_cat":"cs.LG","authors_text":"Junze Yin, Lichen Zhang, Yuzhou Gu, Zhao Song","submitted_at":"2023-02-21T23:49:36Z","abstract_excerpt":"Given a matrix $M\\in \\mathbb{R}^{m\\times n}$, the low rank matrix completion problem asks us to find a rank-$k$ approximation of $M$ as $UV^\\top$ for $U\\in \\mathbb{R}^{m\\times k}$ and $V\\in \\mathbb{R}^{n\\times k}$ by only observing a few entries specified by a set of entries $\\Omega\\subseteq [m]\\times [n]$. In particular, we examine an approach that is widely used in practice -- the alternating minimization framework. Jain, Netrapalli, and Sanghavi [JNS13] showed that if $M$ has incoherent rows and columns, then alternating minimization provably recovers the matrix $M$ by observing a nearly li"},"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":"2302.11068","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-02-21T23:49:36Z","cross_cats_sorted":["cs.DS","math.OC","stat.ML"],"title_canon_sha256":"1070719c8c702ed8c6e89fb293d2a502b078292cf58d64d53b0c4a10d54b4f5f","abstract_canon_sha256":"bdb4521be43260ba07d76880f5eeae3de21b19965ebef91d4cbbce75630d7ede"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:03:05.604670Z","signature_b64":"uP++GN3/uWbpIZVwYXwPNHBqc0BuVPy/KvetVSmF1ju1whFrX6cD3AQyAMJbR/ItjFL8hcJMK2NrNX0rKNp2Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3b806bdfda509fbfea97e8446f1c45e2bfcb94e598c617328bc61c77e72cf394","last_reissued_at":"2026-07-05T08:03:05.604209Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:03:05.604209Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Low Rank Matrix Completion via Robust Alternating Minimization in Nearly Linear Time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","math.OC","stat.ML"],"primary_cat":"cs.LG","authors_text":"Junze Yin, Lichen Zhang, Yuzhou Gu, Zhao Song","submitted_at":"2023-02-21T23:49:36Z","abstract_excerpt":"Given a matrix $M\\in \\mathbb{R}^{m\\times n}$, the low rank matrix completion problem asks us to find a rank-$k$ approximation of $M$ as $UV^\\top$ for $U\\in \\mathbb{R}^{m\\times k}$ and $V\\in \\mathbb{R}^{n\\times k}$ by only observing a few entries specified by a set of entries $\\Omega\\subseteq [m]\\times [n]$. In particular, we examine an approach that is widely used in practice -- the alternating minimization framework. Jain, Netrapalli, and Sanghavi [JNS13] showed that if $M$ has incoherent rows and columns, then alternating minimization provably recovers the matrix $M$ by observing a nearly li"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.11068","kind":"arxiv","version":3},"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/2302.11068/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":"2302.11068","created_at":"2026-07-05T08:03:05.604265+00:00"},{"alias_kind":"arxiv_version","alias_value":"2302.11068v3","created_at":"2026-07-05T08:03:05.604265+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.11068","created_at":"2026-07-05T08:03:05.604265+00:00"},{"alias_kind":"pith_short_12","alias_value":"HOAGXX62KCP3","created_at":"2026-07-05T08:03:05.604265+00:00"},{"alias_kind":"pith_short_16","alias_value":"HOAGXX62KCP372UX","created_at":"2026-07-05T08:03:05.604265+00:00"},{"alias_kind":"pith_short_8","alias_value":"HOAGXX62","created_at":"2026-07-05T08:03:05.604265+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/HOAGXX62KCP372UX5BCG6HCF4K","json":"https://pith.science/pith/HOAGXX62KCP372UX5BCG6HCF4K.json","graph_json":"https://pith.science/api/pith-number/HOAGXX62KCP372UX5BCG6HCF4K/graph.json","events_json":"https://pith.science/api/pith-number/HOAGXX62KCP372UX5BCG6HCF4K/events.json","paper":"https://pith.science/paper/HOAGXX62"},"agent_actions":{"view_html":"https://pith.science/pith/HOAGXX62KCP372UX5BCG6HCF4K","download_json":"https://pith.science/pith/HOAGXX62KCP372UX5BCG6HCF4K.json","view_paper":"https://pith.science/paper/HOAGXX62","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2302.11068&json=true","fetch_graph":"https://pith.science/api/pith-number/HOAGXX62KCP372UX5BCG6HCF4K/graph.json","fetch_events":"https://pith.science/api/pith-number/HOAGXX62KCP372UX5BCG6HCF4K/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HOAGXX62KCP372UX5BCG6HCF4K/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HOAGXX62KCP372UX5BCG6HCF4K/action/storage_attestation","attest_author":"https://pith.science/pith/HOAGXX62KCP372UX5BCG6HCF4K/action/author_attestation","sign_citation":"https://pith.science/pith/HOAGXX62KCP372UX5BCG6HCF4K/action/citation_signature","submit_replication":"https://pith.science/pith/HOAGXX62KCP372UX5BCG6HCF4K/action/replication_record"}},"created_at":"2026-07-05T08:03:05.604265+00:00","updated_at":"2026-07-05T08:03:05.604265+00:00"}