{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:TVHFKFWZOCFXDLWA4T3CDM23NK","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":"ee0dbcdf4caa09680f77321e9e2454c14f7f35cb56f3a8467d219771ae749c93","cross_cats_sorted":["math.OC","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-03-06T00:07:53Z","title_canon_sha256":"cc7b90cfd668e7d59065347b585d7da2c432212e46bd3650e229dfbe2483f671"},"schema_version":"1.0","source":{"id":"2203.02839","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2203.02839","created_at":"2026-07-05T06:42:39Z"},{"alias_kind":"arxiv_version","alias_value":"2203.02839v2","created_at":"2026-07-05T06:42:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.02839","created_at":"2026-07-05T06:42:39Z"},{"alias_kind":"pith_short_12","alias_value":"TVHFKFWZOCFX","created_at":"2026-07-05T06:42:39Z"},{"alias_kind":"pith_short_16","alias_value":"TVHFKFWZOCFXDLWA","created_at":"2026-07-05T06:42:39Z"},{"alias_kind":"pith_short_8","alias_value":"TVHFKFWZ","created_at":"2026-07-05T06:42:39Z"}],"graph_snapshots":[{"event_id":"sha256:6593dfc78c7c182b2d6662156ecfd509d9c9115fe64f768840c09533ecf84de7","target":"graph","created_at":"2026-07-05T06:42:39Z","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/2203.02839/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the asymmetric matrix factorization problem under a natural nonconvex formulation with arbitrary overparametrization. The model-free setting is considered, with minimal assumption on the rank or singular values of the observed matrix, where the global optima provably overfit. We show that vanilla gradient descent with small random initialization sequentially recovers the principal components of the observed matrix. Consequently, when equipped with proper early stopping, gradient descent produces the best low-rank approximation of the observed matrix without explicit regularization. We","authors_text":"Lijun Ding, Liwei Jiang, Yudong Chen","cross_cats":["math.OC","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-03-06T00:07:53Z","title":"Algorithmic Regularization in Model-free Overparametrized Asymmetric Matrix Factorization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.02839","kind":"arxiv","version":2},"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":"sha256:72bb01bff8fc81ca2cd1698b76ef3af1e87bc4a646f96d13891af7b657eccf34","target":"record","created_at":"2026-07-05T06:42:39Z","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":"ee0dbcdf4caa09680f77321e9e2454c14f7f35cb56f3a8467d219771ae749c93","cross_cats_sorted":["math.OC","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-03-06T00:07:53Z","title_canon_sha256":"cc7b90cfd668e7d59065347b585d7da2c432212e46bd3650e229dfbe2483f671"},"schema_version":"1.0","source":{"id":"2203.02839","kind":"arxiv","version":2}},"canonical_sha256":"9d4e5516d9708b71aec0e4f621b35b6ab9469d14b5dde59eb590c8705e9acace","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9d4e5516d9708b71aec0e4f621b35b6ab9469d14b5dde59eb590c8705e9acace","first_computed_at":"2026-07-05T06:42:39.195083Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:42:39.195083Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dQiuVgA8rVdxSiAuiPliZz8OZYzy5rX35JJRLVPA1XBQSfzBnBlE4FB7VU2FBQCjkxeawfL3eDjvPzUXGIZqCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T06:42:39.195494Z","signed_message":"canonical_sha256_bytes"},"source_id":"2203.02839","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:72bb01bff8fc81ca2cd1698b76ef3af1e87bc4a646f96d13891af7b657eccf34","sha256:6593dfc78c7c182b2d6662156ecfd509d9c9115fe64f768840c09533ecf84de7"],"state_sha256":"e1b1b95d6dbf1af43dc2663f8cb4916dcb5c69c741442fa80ccf3bbd60a88cb8"}