{"paper":{"title":"A Rank Stabilization Scaling Factor for Fine-Tuning with LoRA","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"LoRA adapters should be scaled by dividing by the square root of the rank rather than the full rank to stabilize learning.","cross_cats":["cs.LG"],"primary_cat":"cs.CL","authors_text":"Damjan Kalajdzievski","submitted_at":"2023-11-28T03:23:20Z","abstract_excerpt":"As large language models (LLMs) have become increasingly compute and memory intensive, parameter-efficient fine-tuning (PEFT) methods are now a common strategy to fine-tune LLMs. A popular PEFT method is Low-Rank Adapters (LoRA), which adds trainable low-rank \"adapters\" to selected layers. Each adapter consists of a low-rank matrix product, multiplicatively scaled by a rank-dependent factor. This scaling factor, which divides adapters by a factor of the rank, results in slowed learning and stunted performance for LoRA with higher-rank adapters. Consequently, the use of LoRA in practice has gen"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"we study the impact of the scaling factor on the learning process and prove that LoRA adapters should be divided by a factor of the square root of the rank","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The proof that 1/sqrt(rank) is optimal rests on unstated assumptions about initialization variance, gradient flow, and the precise form of the LoRA update rule during fine-tuning; these assumptions are not detailed in the provided abstract.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"LoRA adapters should be scaled by 1/sqrt(rank) rather than 1/rank to stabilize learning and enable effective use of higher ranks during fine-tuning of large language models.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"LoRA adapters should be scaled by dividing by the square root of the rank rather than the full rank to stabilize learning.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"228ad1f7685270356943d91311780a58336dccb02bf917c3b10a87eac8f2f96d"},"source":{"id":"2312.03732","kind":"arxiv","version":1},"verdict":{"id":"c9b1eb0e-c4c8-43ef-a1df-9e713c8a8353","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T22:02:04.412118Z","strongest_claim":"we study the impact of the scaling factor on the learning process and prove that LoRA adapters should be divided by a factor of the square root of the rank","one_line_summary":"LoRA adapters should be scaled by 1/sqrt(rank) rather than 1/rank to stabilize learning and enable effective use of higher ranks during fine-tuning of large language models.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The proof that 1/sqrt(rank) is optimal rests on unstated assumptions about initialization variance, gradient flow, and the precise form of the LoRA update rule during fine-tuning; these assumptions are not detailed in the provided abstract.","pith_extraction_headline":"LoRA adapters should be scaled by dividing by the square root of the rank rather than the full rank to stabilize learning."},"references":{"count":91,"sample":[{"doi":"","year":2023,"title":"2023 , publisher =","work_id":"4e8b0b95-ae6c-4edf-8218-6b1fbbfd9734","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.5281/zenodo.5371628","year":null,"title":"Aaron Gokaslan, Vanya Cohen, Ellie Pavlick, and Stefanie Tellex","work_id":"27d00efc-1c8b-4af4-bd30-5dfa575d0989","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2018,"title":"Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge , author=. 2018 , eprint=","work_id":"9880c11f-6c71-4e36-9736-affdf3d20344","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2019,"title":"HellaSwag: Can a Machine Really Finish Your Sentence? , author=. 2019 , eprint=","work_id":"b5234106-7b98-47af-87c3-45d428066901","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2021,"title":"Measuring Massive Multitask Language Understanding , author=. 2021 , eprint=","work_id":"01eb26fa-b178-499b-bc7b-b2ff5dd67b24","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":91,"snapshot_sha256":"fea4b5c0f7a8f09e836708a7210ddf6567efda57631d4dc9edc69c6adae48df3","internal_anchors":6},"formal_canon":{"evidence_count":2,"snapshot_sha256":"1fded5ab56adef58140b9f279197ddf9fd002341cffcd2bd1c2d972b2a474ac4"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}