{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:LK6YIMV5ZL6RFEFJFOOVCQVFGP","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":"43e712cfcf2bd9b48ea274f109e7022a6e8fa5521e140a122a4f55b452703497","cross_cats_sorted":["cs.LG","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-08-24T02:56:17Z","title_canon_sha256":"0803bac7ebf676a572fbf20392dbcd5fc12c7837f9b1823a55152ff9edd23f5c"},"schema_version":"1.0","source":{"id":"1908.09078","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.09078","created_at":"2026-07-04T23:59:36Z"},{"alias_kind":"arxiv_version","alias_value":"1908.09078v1","created_at":"2026-07-04T23:59:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.09078","created_at":"2026-07-04T23:59:36Z"},{"alias_kind":"pith_short_12","alias_value":"LK6YIMV5ZL6R","created_at":"2026-07-04T23:59:36Z"},{"alias_kind":"pith_short_16","alias_value":"LK6YIMV5ZL6RFEFJ","created_at":"2026-07-04T23:59:36Z"},{"alias_kind":"pith_short_8","alias_value":"LK6YIMV5","created_at":"2026-07-04T23:59:36Z"}],"graph_snapshots":[{"event_id":"sha256:32b68fabe2f0f26c5bffdb6a2bfec5c1b43ece13843ee6b670fee9e3e1751c88","target":"graph","created_at":"2026-07-04T23:59:36Z","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/1908.09078/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper is concerned with the factorization form of the rank regularized loss minimization problem. To cater for the scenario in which only a coarse estimation is available for the rank of the true matrix, an $\\ell_{2,0}$-norm regularized term is added to the factored loss function to reduce the rank adaptively; and account for the ambiguities in the factorization, a balanced term is then introduced. For the least squares loss, under a restricted condition number assumption on the sampling operator, we establish the KL property of exponent $1/2$ of the nonsmooth factored composite function ","authors_text":"Shaohua Pan, Shujun Bi, Ting Tao","cross_cats":["cs.LG","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-08-24T02:56:17Z","title":"KL property of exponent $1/2$ of $\\ell_{2,0}$-norm and DC regularized factorizations for low-rank matrix recovery"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.09078","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:a4f7fe04d8b85caf2b19d397ae7f87b09d27f950b0092e703d541c7ae26256a2","target":"record","created_at":"2026-07-04T23:59:36Z","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":"43e712cfcf2bd9b48ea274f109e7022a6e8fa5521e140a122a4f55b452703497","cross_cats_sorted":["cs.LG","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-08-24T02:56:17Z","title_canon_sha256":"0803bac7ebf676a572fbf20392dbcd5fc12c7837f9b1823a55152ff9edd23f5c"},"schema_version":"1.0","source":{"id":"1908.09078","kind":"arxiv","version":1}},"canonical_sha256":"5abd8432bdcafd1290a92b9d5142a533c78292dabde85fdde7a3b7607a5ea285","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5abd8432bdcafd1290a92b9d5142a533c78292dabde85fdde7a3b7607a5ea285","first_computed_at":"2026-07-04T23:59:36.576810Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:59:36.576810Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8Kdumaod7adTirY2Cr/Dy7A+bUZ1SGfGfg224H1vyoN0mjhIU9KIBs6Ix8rDwieWeIxDU8VYkXhWywFwJ9TUAA==","signature_status":"signed_v1","signed_at":"2026-07-04T23:59:36.577203Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.09078","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a4f7fe04d8b85caf2b19d397ae7f87b09d27f950b0092e703d541c7ae26256a2","sha256:32b68fabe2f0f26c5bffdb6a2bfec5c1b43ece13843ee6b670fee9e3e1751c88"],"state_sha256":"a4126a25778dd23073b8db787b8ad0f5bc38638c07b69881d30b916d3ecb06e7"}