{"paper":{"title":"On the Convergence of Stochastic Low-Rank Adaptation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.LG","authors_text":"Chengchang Liu, John C.S. Lui, Ru Wang","submitted_at":"2026-07-24T04:41:26Z","abstract_excerpt":"Low-rank adaptation (LoRA) optimizes $J(B,A)=\\mathcal L(W_\\mathrm{base}+sBA)$ over two adapters $B \\in \\mathbb{R}^{m \\times r}$ and $A \\in \\mathbb{R}^{r \\times n}$ that form a low-rank update to a frozen pretrained weight matrix $W_\\mathrm{base} \\in \\mathbb{R}^{m \\times n}$. The prior analysis shows LoRA-GD takes $\\exp\\{\\mathcal{O}(\\epsilon^{-2})\\}$ oracle calls to find an $\\epsilon$-stationary point such that $\\|\\nabla J(B,A)\\|\\leq \\epsilon$ in the deterministic setting. We sharpen the analysis and show that $\\mathcal{O}(\\epsilon^{-4})$ full-gradient evaluations suffice for the same first-ord"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.21975","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/2607.21975/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"}