{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:NISBNLXZ426VETGFHSDZO5KVPB","short_pith_number":"pith:NISBNLXZ","canonical_record":{"source":{"id":"1708.00146","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-08-01T03:21:55Z","cross_cats_sorted":["cs.AI","stat.ML"],"title_canon_sha256":"9e449f94622a1f929a7b6779c83f7b2f0fd144e28953070bb1689842fc17fac6","abstract_canon_sha256":"1f16de8411a5d6fe9d4b3eae694963497d5dbeef904abd9c07fa897c741ac69e"},"schema_version":"1.0"},"canonical_sha256":"6a2416aef9e6bd524cc53c879775557840fabc6d673d81c2d88ecfbd1a47075e","source":{"kind":"arxiv","id":"1708.00146","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.00146","created_at":"2026-05-18T00:10:04Z"},{"alias_kind":"arxiv_version","alias_value":"1708.00146v3","created_at":"2026-05-18T00:10:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.00146","created_at":"2026-05-18T00:10:04Z"},{"alias_kind":"pith_short_12","alias_value":"NISBNLXZ426V","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"NISBNLXZ426VETGF","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"NISBNLXZ","created_at":"2026-05-18T12:31:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:NISBNLXZ426VETGFHSDZO5KVPB","target":"record","payload":{"canonical_record":{"source":{"id":"1708.00146","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-08-01T03:21:55Z","cross_cats_sorted":["cs.AI","stat.ML"],"title_canon_sha256":"9e449f94622a1f929a7b6779c83f7b2f0fd144e28953070bb1689842fc17fac6","abstract_canon_sha256":"1f16de8411a5d6fe9d4b3eae694963497d5dbeef904abd9c07fa897c741ac69e"},"schema_version":"1.0"},"canonical_sha256":"6a2416aef9e6bd524cc53c879775557840fabc6d673d81c2d88ecfbd1a47075e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:04.087833Z","signature_b64":"u/rZxbwHBeXh+N9eVhM8seObWEK2W8OMPb/Nr2z4jyz5TnYZw44JK6JL5MGXsYJQMT1cx5CB4+fhZeoxcczcAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6a2416aef9e6bd524cc53c879775557840fabc6d673d81c2d88ecfbd1a47075e","last_reissued_at":"2026-05-18T00:10:04.087117Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:04.087117Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.00146","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:10:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B4cuV7dShXU7QtcdZmLnUxfVma4b0iA1XH63aeHL09KGO6XbjrrgHX4QmlETSGfsOAg09p8J+HxkKfZ0oBRKDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T18:45:52.407629Z"},"content_sha256":"5e1dce938b72de0d059596acedb8f98bdd828172816008ec815f32c6991f74ba","schema_version":"1.0","event_id":"sha256:5e1dce938b72de0d059596acedb8f98bdd828172816008ec815f32c6991f74ba"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:NISBNLXZ426VETGFHSDZO5KVPB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Large-Scale Low-Rank Matrix Learning with Nonconvex Regularizers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","stat.ML"],"primary_cat":"cs.LG","authors_text":"James T.Kwok, Quanming Yao, Taifeng Wang, Tie-Yan Liu","submitted_at":"2017-08-01T03:21:55Z","abstract_excerpt":"Low-rank modeling has many important applications in computer vision and machine learning. While the matrix rank is often approximated by the convex nuclear norm, the use of nonconvex low-rank regularizers has demonstrated better empirical performance. However, the resulting optimization problem is much more challenging. Recent state-of-the-art requires an expensive full SVD in each iteration. In this paper, we show that for many commonly-used nonconvex low-rank regularizers, a cutoff can be derived to automatically threshold the singular values obtained from the proximal operator. This allows"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.00146","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":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:10:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sSqekkcFXvJxDuhmiv7kEwlM9CTI5VLTIU9pXmp1DY5sqFP5SiicWwbBKVk5qBc8k2seFwyKtn8FyDGij6psDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T18:45:52.408127Z"},"content_sha256":"15f2e44fab1c40a6e59d7392319421a7130661a6f4a2fc5614405b4e94dd306e","schema_version":"1.0","event_id":"sha256:15f2e44fab1c40a6e59d7392319421a7130661a6f4a2fc5614405b4e94dd306e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NISBNLXZ426VETGFHSDZO5KVPB/bundle.json","state_url":"https://pith.science/pith/NISBNLXZ426VETGFHSDZO5KVPB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NISBNLXZ426VETGFHSDZO5KVPB/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-21T18:45:52Z","links":{"resolver":"https://pith.science/pith/NISBNLXZ426VETGFHSDZO5KVPB","bundle":"https://pith.science/pith/NISBNLXZ426VETGFHSDZO5KVPB/bundle.json","state":"https://pith.science/pith/NISBNLXZ426VETGFHSDZO5KVPB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NISBNLXZ426VETGFHSDZO5KVPB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:NISBNLXZ426VETGFHSDZO5KVPB","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":"1f16de8411a5d6fe9d4b3eae694963497d5dbeef904abd9c07fa897c741ac69e","cross_cats_sorted":["cs.AI","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-08-01T03:21:55Z","title_canon_sha256":"9e449f94622a1f929a7b6779c83f7b2f0fd144e28953070bb1689842fc17fac6"},"schema_version":"1.0","source":{"id":"1708.00146","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.00146","created_at":"2026-05-18T00:10:04Z"},{"alias_kind":"arxiv_version","alias_value":"1708.00146v3","created_at":"2026-05-18T00:10:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.00146","created_at":"2026-05-18T00:10:04Z"},{"alias_kind":"pith_short_12","alias_value":"NISBNLXZ426V","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"NISBNLXZ426VETGF","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"NISBNLXZ","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:15f2e44fab1c40a6e59d7392319421a7130661a6f4a2fc5614405b4e94dd306e","target":"graph","created_at":"2026-05-18T00:10:04Z","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"},"paper":{"abstract_excerpt":"Low-rank modeling has many important applications in computer vision and machine learning. While the matrix rank is often approximated by the convex nuclear norm, the use of nonconvex low-rank regularizers has demonstrated better empirical performance. However, the resulting optimization problem is much more challenging. Recent state-of-the-art requires an expensive full SVD in each iteration. In this paper, we show that for many commonly-used nonconvex low-rank regularizers, a cutoff can be derived to automatically threshold the singular values obtained from the proximal operator. This allows","authors_text":"James T.Kwok, Quanming Yao, Taifeng Wang, Tie-Yan Liu","cross_cats":["cs.AI","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-08-01T03:21:55Z","title":"Large-Scale Low-Rank Matrix Learning with Nonconvex Regularizers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.00146","kind":"arxiv","version":3},"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":"sha256:5e1dce938b72de0d059596acedb8f98bdd828172816008ec815f32c6991f74ba","target":"record","created_at":"2026-05-18T00:10:04Z","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":"1f16de8411a5d6fe9d4b3eae694963497d5dbeef904abd9c07fa897c741ac69e","cross_cats_sorted":["cs.AI","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-08-01T03:21:55Z","title_canon_sha256":"9e449f94622a1f929a7b6779c83f7b2f0fd144e28953070bb1689842fc17fac6"},"schema_version":"1.0","source":{"id":"1708.00146","kind":"arxiv","version":3}},"canonical_sha256":"6a2416aef9e6bd524cc53c879775557840fabc6d673d81c2d88ecfbd1a47075e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6a2416aef9e6bd524cc53c879775557840fabc6d673d81c2d88ecfbd1a47075e","first_computed_at":"2026-05-18T00:10:04.087117Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:04.087117Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u/rZxbwHBeXh+N9eVhM8seObWEK2W8OMPb/Nr2z4jyz5TnYZw44JK6JL5MGXsYJQMT1cx5CB4+fhZeoxcczcAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:04.087833Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.00146","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5e1dce938b72de0d059596acedb8f98bdd828172816008ec815f32c6991f74ba","sha256:15f2e44fab1c40a6e59d7392319421a7130661a6f4a2fc5614405b4e94dd306e"],"state_sha256":"c308ea2b603ea058c98113c32a978390c8a2f52abacf72d38fa519cc6ded45aa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dTpWR3YICAAw+7aBG4BQM0sNQOAmZ/uPoiAINzAbjbnXzkwmj95aQSbJoc6e4BQ/z2TFShqo70Khm+aeZCVbCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-21T18:45:52.412838Z","bundle_sha256":"6aab406ee6d18ec42556d283b3228008a2caa71fd7e08fc3731a8c1150e1a781"}}