{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:5HBYSCC7PFSGXVFNRWXCIASQED","short_pith_number":"pith:5HBYSCC7","schema_version":"1.0","canonical_sha256":"e9c389085f79646bd4ad8dae24025020f2ba399064ab9e7b2cd06bf8fb2022b0","source":{"kind":"arxiv","id":"2402.11867","version":3},"attestation_state":"computed","paper":{"title":"LoRA Training in the NTK Regime has No Spurious Local Minima","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.LG","authors_text":"Ernest K. Ryu, Jason D. Lee, Uijeong Jang","submitted_at":"2024-02-19T06:22:09Z","abstract_excerpt":"Low-rank adaptation (LoRA) has become the standard approach for parameter-efficient fine-tuning of large language models (LLM), but our theoretical understanding of LoRA has been limited. In this work, we theoretically analyze LoRA fine-tuning in the neural tangent kernel (NTK) regime with $N$ data points, showing: (i) full fine-tuning (without LoRA) admits a low-rank solution of rank $r\\lesssim \\sqrt{N}$; (ii) using LoRA with rank $r\\gtrsim \\sqrt{N}$ eliminates spurious local minima, allowing gradient descent to find the low-rank solutions; (iii) the low-rank solution found using LoRA general"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2402.11867","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-02-19T06:22:09Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"d464c3d1440f89805d3304f9f049966be1df713d06b49e9b7540df6751df6c10","abstract_canon_sha256":"d06f3b65474f518b2eee68560b095760650a2378294b06b34457cc9728f9d578"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:24:02.213126Z","signature_b64":"vDbuSkmcb1OuUvCp93ij99tvFjPgYk7nhrV2SMBnmrO+CyHG+fqgC5pCXDpB3vG3Sq6OyJ+h2PpR7Gs31ShUDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e9c389085f79646bd4ad8dae24025020f2ba399064ab9e7b2cd06bf8fb2022b0","last_reissued_at":"2026-07-05T08:24:02.212618Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:24:02.212618Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"LoRA Training in the NTK Regime has No Spurious Local Minima","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.LG","authors_text":"Ernest K. Ryu, Jason D. Lee, Uijeong Jang","submitted_at":"2024-02-19T06:22:09Z","abstract_excerpt":"Low-rank adaptation (LoRA) has become the standard approach for parameter-efficient fine-tuning of large language models (LLM), but our theoretical understanding of LoRA has been limited. In this work, we theoretically analyze LoRA fine-tuning in the neural tangent kernel (NTK) regime with $N$ data points, showing: (i) full fine-tuning (without LoRA) admits a low-rank solution of rank $r\\lesssim \\sqrt{N}$; (ii) using LoRA with rank $r\\gtrsim \\sqrt{N}$ eliminates spurious local minima, allowing gradient descent to find the low-rank solutions; (iii) the low-rank solution found using LoRA general"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.11867","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/2402.11867/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2402.11867","created_at":"2026-07-05T08:24:02.212684+00:00"},{"alias_kind":"arxiv_version","alias_value":"2402.11867v3","created_at":"2026-07-05T08:24:02.212684+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.11867","created_at":"2026-07-05T08:24:02.212684+00:00"},{"alias_kind":"pith_short_12","alias_value":"5HBYSCC7PFSG","created_at":"2026-07-05T08:24:02.212684+00:00"},{"alias_kind":"pith_short_16","alias_value":"5HBYSCC7PFSGXVFN","created_at":"2026-07-05T08:24:02.212684+00:00"},{"alias_kind":"pith_short_8","alias_value":"5HBYSCC7","created_at":"2026-07-05T08:24:02.212684+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.05899","citing_title":"High-Dimensional Theory of LoRA Fine-Tuning in a Solvable Attention Model","ref_index":15,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/5HBYSCC7PFSGXVFNRWXCIASQED","json":"https://pith.science/pith/5HBYSCC7PFSGXVFNRWXCIASQED.json","graph_json":"https://pith.science/api/pith-number/5HBYSCC7PFSGXVFNRWXCIASQED/graph.json","events_json":"https://pith.science/api/pith-number/5HBYSCC7PFSGXVFNRWXCIASQED/events.json","paper":"https://pith.science/paper/5HBYSCC7"},"agent_actions":{"view_html":"https://pith.science/pith/5HBYSCC7PFSGXVFNRWXCIASQED","download_json":"https://pith.science/pith/5HBYSCC7PFSGXVFNRWXCIASQED.json","view_paper":"https://pith.science/paper/5HBYSCC7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2402.11867&json=true","fetch_graph":"https://pith.science/api/pith-number/5HBYSCC7PFSGXVFNRWXCIASQED/graph.json","fetch_events":"https://pith.science/api/pith-number/5HBYSCC7PFSGXVFNRWXCIASQED/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5HBYSCC7PFSGXVFNRWXCIASQED/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5HBYSCC7PFSGXVFNRWXCIASQED/action/storage_attestation","attest_author":"https://pith.science/pith/5HBYSCC7PFSGXVFNRWXCIASQED/action/author_attestation","sign_citation":"https://pith.science/pith/5HBYSCC7PFSGXVFNRWXCIASQED/action/citation_signature","submit_replication":"https://pith.science/pith/5HBYSCC7PFSGXVFNRWXCIASQED/action/replication_record"}},"created_at":"2026-07-05T08:24:02.212684+00:00","updated_at":"2026-07-05T08:24:02.212684+00:00"}