{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:NKOBSWLPTFWFDCZSJMGVCJYJUB","short_pith_number":"pith:NKOBSWLP","canonical_record":{"source":{"id":"2503.06982","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-03-10T06:57:10Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"d5112c6ded60ef0661b2a8cbf503c0424a6cc439692ed62f9f1ed2e9f106d82a","abstract_canon_sha256":"7d9d169da7f258511b9e22ee4dd894c2792ff4d9586b99ad7103fcaca653ee2b"},"schema_version":"1.0"},"canonical_sha256":"6a9c19596f996c518b324b0d512709a063fe7dbcb4f41dc55d428d30cd218077","source":{"kind":"arxiv","id":"2503.06982","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.06982","created_at":"2026-07-05T10:27:47Z"},{"alias_kind":"arxiv_version","alias_value":"2503.06982v1","created_at":"2026-07-05T10:27:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.06982","created_at":"2026-07-05T10:27:47Z"},{"alias_kind":"pith_short_12","alias_value":"NKOBSWLPTFWF","created_at":"2026-07-05T10:27:47Z"},{"alias_kind":"pith_short_16","alias_value":"NKOBSWLPTFWFDCZS","created_at":"2026-07-05T10:27:47Z"},{"alias_kind":"pith_short_8","alias_value":"NKOBSWLP","created_at":"2026-07-05T10:27:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:NKOBSWLPTFWFDCZSJMGVCJYJUB","target":"record","payload":{"canonical_record":{"source":{"id":"2503.06982","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-03-10T06:57:10Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"d5112c6ded60ef0661b2a8cbf503c0424a6cc439692ed62f9f1ed2e9f106d82a","abstract_canon_sha256":"7d9d169da7f258511b9e22ee4dd894c2792ff4d9586b99ad7103fcaca653ee2b"},"schema_version":"1.0"},"canonical_sha256":"6a9c19596f996c518b324b0d512709a063fe7dbcb4f41dc55d428d30cd218077","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:27:47.101506Z","signature_b64":"JT6nmH7W0nm76tmK5C5x5VkLfQOr9WA725WZad9lzlqcHfKXhTFOiIMTkTT7MPUE92RhdgEGvoBOBDu+SbZXCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6a9c19596f996c518b324b0d512709a063fe7dbcb4f41dc55d428d30cd218077","last_reissued_at":"2026-07-05T10:27:47.100969Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:27:47.100969Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2503.06982","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:27:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aXs9HXLPvC5S2m6hO3sZPnArsa+x5fS9o97jkZEnPgavEwJjHXV9ZNiMnFZPtAFWnF8hwjIMlqelF/rWIXnkAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T08:15:04.289191Z"},"content_sha256":"3c88b4cd3f81c4d1d906e7d4c498efccf9ccc3ca1b7621399310061643225247","schema_version":"1.0","event_id":"sha256:3c88b4cd3f81c4d1d906e7d4c498efccf9ccc3ca1b7621399310061643225247"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:NKOBSWLPTFWFDCZSJMGVCJYJUB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Understanding the Learning Dynamics of LoRA: A Gradient Flow Perspective on Low-Rank Adaptation in Matrix Factorization","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Enrique Mallada, Hancheng Min, Jinqi Luo, Lachlan Ewen MacDonald, Rene Vidal, Salma Tarmoun, Ziqing Xu","submitted_at":"2025-03-10T06:57:10Z","abstract_excerpt":"Despite the empirical success of Low-Rank Adaptation (LoRA) in fine-tuning pre-trained models, there is little theoretical understanding of how first-order methods with carefully crafted initialization adapt models to new tasks. In this work, we take the first step towards bridging this gap by theoretically analyzing the learning dynamics of LoRA for matrix factorization (MF) under gradient flow (GF), emphasizing the crucial role of initialization. For small initialization, we theoretically show that GF converges to a neighborhood of the optimal solution, with smaller initialization leading to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.06982","kind":"arxiv","version":1},"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/2503.06982/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":"2026-07-05T10:27:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HZKM3ygsmpxlF506lx0G1zRVQlGxQLakoaBXSt5EjzTjfFv5FiPFb2pC2HtaCymAd4pdzhMl+kt5l45gJIZqCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T08:15:04.289594Z"},"content_sha256":"1b097af345d75f295003ae9dc2f65c205429b676b4d5534613f8d16b018c39ed","schema_version":"1.0","event_id":"sha256:1b097af345d75f295003ae9dc2f65c205429b676b4d5534613f8d16b018c39ed"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NKOBSWLPTFWFDCZSJMGVCJYJUB/bundle.json","state_url":"https://pith.science/pith/NKOBSWLPTFWFDCZSJMGVCJYJUB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NKOBSWLPTFWFDCZSJMGVCJYJUB/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":"2026-07-06T08:15:04Z","links":{"resolver":"https://pith.science/pith/NKOBSWLPTFWFDCZSJMGVCJYJUB","bundle":"https://pith.science/pith/NKOBSWLPTFWFDCZSJMGVCJYJUB/bundle.json","state":"https://pith.science/pith/NKOBSWLPTFWFDCZSJMGVCJYJUB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NKOBSWLPTFWFDCZSJMGVCJYJUB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:NKOBSWLPTFWFDCZSJMGVCJYJUB","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":"7d9d169da7f258511b9e22ee4dd894c2792ff4d9586b99ad7103fcaca653ee2b","cross_cats_sorted":["cs.AI"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-03-10T06:57:10Z","title_canon_sha256":"d5112c6ded60ef0661b2a8cbf503c0424a6cc439692ed62f9f1ed2e9f106d82a"},"schema_version":"1.0","source":{"id":"2503.06982","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.06982","created_at":"2026-07-05T10:27:47Z"},{"alias_kind":"arxiv_version","alias_value":"2503.06982v1","created_at":"2026-07-05T10:27:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.06982","created_at":"2026-07-05T10:27:47Z"},{"alias_kind":"pith_short_12","alias_value":"NKOBSWLPTFWF","created_at":"2026-07-05T10:27:47Z"},{"alias_kind":"pith_short_16","alias_value":"NKOBSWLPTFWFDCZS","created_at":"2026-07-05T10:27:47Z"},{"alias_kind":"pith_short_8","alias_value":"NKOBSWLP","created_at":"2026-07-05T10:27:47Z"}],"graph_snapshots":[{"event_id":"sha256:1b097af345d75f295003ae9dc2f65c205429b676b4d5534613f8d16b018c39ed","target":"graph","created_at":"2026-07-05T10:27:47Z","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/2503.06982/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Despite the empirical success of Low-Rank Adaptation (LoRA) in fine-tuning pre-trained models, there is little theoretical understanding of how first-order methods with carefully crafted initialization adapt models to new tasks. In this work, we take the first step towards bridging this gap by theoretically analyzing the learning dynamics of LoRA for matrix factorization (MF) under gradient flow (GF), emphasizing the crucial role of initialization. For small initialization, we theoretically show that GF converges to a neighborhood of the optimal solution, with smaller initialization leading to","authors_text":"Enrique Mallada, Hancheng Min, Jinqi Luo, Lachlan Ewen MacDonald, Rene Vidal, Salma Tarmoun, Ziqing Xu","cross_cats":["cs.AI"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-03-10T06:57:10Z","title":"Understanding the Learning Dynamics of LoRA: A Gradient Flow Perspective on Low-Rank Adaptation in Matrix Factorization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.06982","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":"sha256:3c88b4cd3f81c4d1d906e7d4c498efccf9ccc3ca1b7621399310061643225247","target":"record","created_at":"2026-07-05T10:27:47Z","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":"7d9d169da7f258511b9e22ee4dd894c2792ff4d9586b99ad7103fcaca653ee2b","cross_cats_sorted":["cs.AI"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-03-10T06:57:10Z","title_canon_sha256":"d5112c6ded60ef0661b2a8cbf503c0424a6cc439692ed62f9f1ed2e9f106d82a"},"schema_version":"1.0","source":{"id":"2503.06982","kind":"arxiv","version":1}},"canonical_sha256":"6a9c19596f996c518b324b0d512709a063fe7dbcb4f41dc55d428d30cd218077","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6a9c19596f996c518b324b0d512709a063fe7dbcb4f41dc55d428d30cd218077","first_computed_at":"2026-07-05T10:27:47.100969Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:27:47.100969Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JT6nmH7W0nm76tmK5C5x5VkLfQOr9WA725WZad9lzlqcHfKXhTFOiIMTkTT7MPUE92RhdgEGvoBOBDu+SbZXCg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:27:47.101506Z","signed_message":"canonical_sha256_bytes"},"source_id":"2503.06982","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3c88b4cd3f81c4d1d906e7d4c498efccf9ccc3ca1b7621399310061643225247","sha256:1b097af345d75f295003ae9dc2f65c205429b676b4d5534613f8d16b018c39ed"],"state_sha256":"c0b395713245201d0eb3e764bd0a8b91da74f148116e6e216b0294fd7dd873a5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sNpiJvwVRsi9AOx6xctZai/lBcfsDXcrEBCwva0Ih36ZL7CsjAdGZ7xCYjHvV2KORMlTYOmkkIn7zFP/VTYsDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T08:15:04.291573Z","bundle_sha256":"c87fa35f3490c48ba023ee5b4b85a633612065105fe3b65c7a020d8dcf18eed4"}}