{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:QBEPCHA5LZI2FGNH73AQ7V5TYY","short_pith_number":"pith:QBEPCHA5","canonical_record":{"source":{"id":"2302.10963","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-02-21T19:47:31Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"4c3e66789b9fcb71e04fc0c7db03bf4daec2d8fba60fcf4e2b78da13d112e972","abstract_canon_sha256":"197a1b0f8c855d2e2590a4e3efc3ec4339a9b1cfc98053bdfc276e98b4f85e10"},"schema_version":"1.0"},"canonical_sha256":"8048f11c1d5e51a299a7fec10fd7b3c6121eee0f4f10ae0a8cb41d9803771150","source":{"kind":"arxiv","id":"2302.10963","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2302.10963","created_at":"2026-07-05T10:44:12Z"},{"alias_kind":"arxiv_version","alias_value":"2302.10963v3","created_at":"2026-07-05T10:44:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.10963","created_at":"2026-07-05T10:44:12Z"},{"alias_kind":"pith_short_12","alias_value":"QBEPCHA5LZI2","created_at":"2026-07-05T10:44:12Z"},{"alias_kind":"pith_short_16","alias_value":"QBEPCHA5LZI2FGNH","created_at":"2026-07-05T10:44:12Z"},{"alias_kind":"pith_short_8","alias_value":"QBEPCHA5","created_at":"2026-07-05T10:44:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:QBEPCHA5LZI2FGNH73AQ7V5TYY","target":"record","payload":{"canonical_record":{"source":{"id":"2302.10963","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-02-21T19:47:31Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"4c3e66789b9fcb71e04fc0c7db03bf4daec2d8fba60fcf4e2b78da13d112e972","abstract_canon_sha256":"197a1b0f8c855d2e2590a4e3efc3ec4339a9b1cfc98053bdfc276e98b4f85e10"},"schema_version":"1.0"},"canonical_sha256":"8048f11c1d5e51a299a7fec10fd7b3c6121eee0f4f10ae0a8cb41d9803771150","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:44:12.169559Z","signature_b64":"/peIceU4yD9mYrkbgMQJ1/VNAASDLeG8trhGSDX+aQDkmy7k4MaAM0Yt14jKX+0XF9SanN0pWkTHYUbyIK1wBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8048f11c1d5e51a299a7fec10fd7b3c6121eee0f4f10ae0a8cb41d9803771150","last_reissued_at":"2026-07-05T10:44:12.169165Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:44:12.169165Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2302.10963","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":"2026-07-05T10:44:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hCBt7IDyA90UuRUf5uiB7zv96UztkF1m2sz/IxLyL4lofhsCHqqUSsrzKr6vQ/AKaJCZ3RenKHjtaSDMtYTOCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T20:39:05.223844Z"},"content_sha256":"c39c98dab613c2132404457ec579692d06cb16bf3b895cbe3bcbc2c4889f7dd3","schema_version":"1.0","event_id":"sha256:c39c98dab613c2132404457ec579692d06cb16bf3b895cbe3bcbc2c4889f7dd3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:QBEPCHA5LZI2FGNH73AQ7V5TYY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Can Learning Be Explained By Local Optimality In Robust Low-rank Matrix Recovery?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.LG","authors_text":"Jianhao Ma, Salar Fattahi","submitted_at":"2023-02-21T19:47:31Z","abstract_excerpt":"We explore the local landscape of low-rank matrix recovery, focusing on reconstructing a $d_1\\times d_2$ matrix $X^\\star$ with rank $r$ from $m$ linear measurements, some potentially noisy. When the noise is distributed according to an outlier model, minimizing a nonsmooth $\\ell_1$-loss with a simple sub-gradient method can often perfectly recover the ground truth matrix $X^\\star$. Given this, a natural question is what optimization property (if any) enables such learning behavior. The most plausible answer is that the ground truth $X^\\star$ manifests as a local optimum of the loss function. I"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.10963","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/2302.10963/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:44:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ht9o2H0yKiYdawYCi3gNkMBWLp/c8pKzgoYUjB1dUxV9WYEKfCBso8JoCq516+IAv2/cPS8AjjX02gY3hiHlAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T20:39:05.224803Z"},"content_sha256":"c6c34669505ff28c8ef13318901deaa032d4f57c7b271a2639097d4ccd117182","schema_version":"1.0","event_id":"sha256:c6c34669505ff28c8ef13318901deaa032d4f57c7b271a2639097d4ccd117182"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QBEPCHA5LZI2FGNH73AQ7V5TYY/bundle.json","state_url":"https://pith.science/pith/QBEPCHA5LZI2FGNH73AQ7V5TYY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QBEPCHA5LZI2FGNH73AQ7V5TYY/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":"2026-08-09T20:39:05Z","links":{"resolver":"https://pith.science/pith/QBEPCHA5LZI2FGNH73AQ7V5TYY","bundle":"https://pith.science/pith/QBEPCHA5LZI2FGNH73AQ7V5TYY/bundle.json","state":"https://pith.science/pith/QBEPCHA5LZI2FGNH73AQ7V5TYY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QBEPCHA5LZI2FGNH73AQ7V5TYY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:QBEPCHA5LZI2FGNH73AQ7V5TYY","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":"197a1b0f8c855d2e2590a4e3efc3ec4339a9b1cfc98053bdfc276e98b4f85e10","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-02-21T19:47:31Z","title_canon_sha256":"4c3e66789b9fcb71e04fc0c7db03bf4daec2d8fba60fcf4e2b78da13d112e972"},"schema_version":"1.0","source":{"id":"2302.10963","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2302.10963","created_at":"2026-07-05T10:44:12Z"},{"alias_kind":"arxiv_version","alias_value":"2302.10963v3","created_at":"2026-07-05T10:44:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.10963","created_at":"2026-07-05T10:44:12Z"},{"alias_kind":"pith_short_12","alias_value":"QBEPCHA5LZI2","created_at":"2026-07-05T10:44:12Z"},{"alias_kind":"pith_short_16","alias_value":"QBEPCHA5LZI2FGNH","created_at":"2026-07-05T10:44:12Z"},{"alias_kind":"pith_short_8","alias_value":"QBEPCHA5","created_at":"2026-07-05T10:44:12Z"}],"graph_snapshots":[{"event_id":"sha256:c6c34669505ff28c8ef13318901deaa032d4f57c7b271a2639097d4ccd117182","target":"graph","created_at":"2026-07-05T10:44:12Z","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/2302.10963/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We explore the local landscape of low-rank matrix recovery, focusing on reconstructing a $d_1\\times d_2$ matrix $X^\\star$ with rank $r$ from $m$ linear measurements, some potentially noisy. When the noise is distributed according to an outlier model, minimizing a nonsmooth $\\ell_1$-loss with a simple sub-gradient method can often perfectly recover the ground truth matrix $X^\\star$. Given this, a natural question is what optimization property (if any) enables such learning behavior. The most plausible answer is that the ground truth $X^\\star$ manifests as a local optimum of the loss function. I","authors_text":"Jianhao Ma, Salar Fattahi","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-02-21T19:47:31Z","title":"Can Learning Be Explained By Local Optimality In Robust Low-rank Matrix Recovery?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.10963","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:c39c98dab613c2132404457ec579692d06cb16bf3b895cbe3bcbc2c4889f7dd3","target":"record","created_at":"2026-07-05T10:44:12Z","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":"197a1b0f8c855d2e2590a4e3efc3ec4339a9b1cfc98053bdfc276e98b4f85e10","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-02-21T19:47:31Z","title_canon_sha256":"4c3e66789b9fcb71e04fc0c7db03bf4daec2d8fba60fcf4e2b78da13d112e972"},"schema_version":"1.0","source":{"id":"2302.10963","kind":"arxiv","version":3}},"canonical_sha256":"8048f11c1d5e51a299a7fec10fd7b3c6121eee0f4f10ae0a8cb41d9803771150","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8048f11c1d5e51a299a7fec10fd7b3c6121eee0f4f10ae0a8cb41d9803771150","first_computed_at":"2026-07-05T10:44:12.169165Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:44:12.169165Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/peIceU4yD9mYrkbgMQJ1/VNAASDLeG8trhGSDX+aQDkmy7k4MaAM0Yt14jKX+0XF9SanN0pWkTHYUbyIK1wBA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:44:12.169559Z","signed_message":"canonical_sha256_bytes"},"source_id":"2302.10963","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c39c98dab613c2132404457ec579692d06cb16bf3b895cbe3bcbc2c4889f7dd3","sha256:c6c34669505ff28c8ef13318901deaa032d4f57c7b271a2639097d4ccd117182"],"state_sha256":"fdb76acc81b261afd72af407b28b44bc98d06d0522f1ec4f173881a978453ddc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BUzJBsczJRxrJ2fTUBKGyspndUUieMvnybr9FRdFj+rJTcuUshcqMRAN7N9RvtXamPrMlB6KJpnP0sOeW6ncCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T20:39:05.230646Z","bundle_sha256":"22177e06744388fb68f174ecfdfcccd6f6e52ddc045bce3f95ebdcb9b017eeaf"}}