# LoFT: Low-Rank Adaptation That Behaves Like Full Fine-Tuning

arXiv: https://arxiv.org/abs/2505.21289 · HTML: https://mlsanity.com/paper/2505.21289/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 49 references that are in the map.
- First posted on arXiv 27 May 2025.

## Builds on (most cited first, 30 of 40)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [Prefix-Tuning: Optimizing Continuous Prompts for Generation](https://mlsanity.com/paper/2101.00190/) (2021)
- [The Power of Scale for Parameter-Efficient Prompt Tuning](https://mlsanity.com/paper/2104.08691/) (2021)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [Visual Prompt Tuning](https://mlsanity.com/paper/2203.12119/) (2022)
- [Is Your Code Generated by ChatGPT Really Correct? Rigorous Evaluation of Large Language Models for Code Generation](https://mlsanity.com/paper/2305.01210/) (2023)
- [Moment Matching for Multi-Source Domain Adaptation](https://mlsanity.com/paper/1812.01754/) (2018)
- [Towards a Unified View of Parameter-Efficient Transfer Learning](https://mlsanity.com/paper/2110.04366/) (2021)
- [AdapterFusion: Non-Destructive Task Composition for Transfer Learning](https://mlsanity.com/paper/2005.00247/) (2020)
- [DoRA: Weight-Decomposed Low-Rank Adaptation](https://mlsanity.com/paper/2402.09353/) (2024)
- [Skin Lesion Analysis Toward Melanoma Detection 2018: A Challenge Hosted by the International Skin Imaging Collaboration (ISIC)](https://mlsanity.com/paper/1902.03368/) (2019)
- [Vision Transformer Adapter for Dense Predictions](https://mlsanity.com/paper/2205.08534/) (2022)
- [LoRA+: Efficient Low Rank Adaptation of Large Models](https://mlsanity.com/paper/2402.12354/) (2024)
- [Visual Transformers: Token-based Image Representation and Processing for Computer Vision](https://mlsanity.com/paper/2006.03677/) (2020)
- [LoRA Learns Less and Forgets Less](https://mlsanity.com/paper/2405.09673/) (2024)
- [LLM-Adapters: An Adapter Family for Parameter-Efficient Fine-Tuning of Large Language Models](https://mlsanity.com/paper/2304.01933/) (2023)
- [VeRA: Vector-based Random Matrix Adaptation](https://mlsanity.com/paper/2310.11454/) (2023)
- [PiSSA: Principal Singular Values and Singular Vectors Adaptation of Large Language Models](https://mlsanity.com/paper/2404.02948/) (2024)
- [OpenCodeInterpreter: Integrating Code Generation with Execution and Refinement](https://mlsanity.com/paper/2402.14658/) (2024)
- [A Rank Stabilization Scaling Factor for Fine-Tuning with LoRA](https://mlsanity.com/paper/2312.03732/) (2023)
- [Orca-Math: Unlocking the potential of SLMs in Grade School Math](https://mlsanity.com/paper/2402.14830/) (2024)
- [Towards Resolving the Implicit Bias of Gradient Descent for Matrix Factorization: Greedy Low-Rank Learning](https://mlsanity.com/paper/2012.09839/) (2020)
- [Platypus: Quick, Cheap, and Powerful Refinement of LLMs](https://mlsanity.com/paper/2308.07317/) (2023)
- [LoRA-GA: Low-Rank Adaptation with Gradient Approximation](https://mlsanity.com/paper/2407.05000/) (2024)
- [Heterogeneous LoRA for Federated Fine-tuning of On-Device Foundation Models](https://mlsanity.com/paper/2401.06432/) (2024)

## Built on by (most cited first, 14 of 14)

- [Learning Rate Matters: Vanilla LoRA May Suffice for LLM Fine-tuning](https://mlsanity.com/paper/2602.04998/) (2026)
- [Can Muon Fine-tune Adam-Pretrained Models?](https://mlsanity.com/paper/2605.10468/) (2026)
- [DecoHD: Decomposed Hyperdimensional Classification under Extreme Memory Budgets](https://mlsanity.com/paper/2511.03911/) (2025)
- [FlexRank: Nested Low-Rank Knowledge Decomposition for Adaptive Model Deployment](https://mlsanity.com/paper/2602.02680/) (2026)
- [Taming Momentum: Rethinking Optimizer States Through Low-Rank Approximation](https://mlsanity.com/paper/2602.24283/) (2026)
- [Faster Than SVD, Smarter Than SGD: The OPLoRA Alternating Update](https://mlsanity.com/paper/2509.19977/) (2025)
- [SDS-LoRA: Overcoming Anisotropic Gradient Scaling in Low-Rank Adaptation](https://mlsanity.com/paper/2606.16454/) (2026)
- [Beyond SGD, Without SVD: Proximal Subspace Iteration LoRA with Diagonal Fractional K-FAC](https://mlsanity.com/paper/2602.16456/) (2026)
- [A Multi-View Media Profiling Suite: Resources, Evaluation, and Analysis](https://mlsanity.com/paper/2605.01336/) (2026)
- [LOFT: Low-Rank Orthogonal Fine-Tuning via Task-Aware Support Selection](https://mlsanity.com/paper/2605.11872/) (2026)
- [PreLort: Prefix-Nested LoRA for Federated Fine-Tuning under Rank Heterogeneity](https://mlsanity.com/paper/2606.15963/) (2026)
- [LoRA-TSD: Tangent-Space Spectral Descent for LoRA via Muon-Style Updates](https://mlsanity.com/paper/2609.02734/) (2026)
- [Position Anchor Tuning: Towards Efficient Adaptation of Pre-Trained Point Cloud Transformers](https://mlsanity.com/paper/2609.18056/) (2026)
- [DT-LoRA: Reaching Beyond the Tangent Space of Low-Rank Adaptation](https://mlsanity.com/paper/2610.17730/) (2026)

## Abstract (arXiv)

Large pre-trained models are commonly adapted to downstream tasks using parameter-efficient fine-tuning methods such as Low-Rank Adaptation (LoRA), which injects small trainable low-rank matrices instead of updating all weights. While LoRA dramatically reduces trainable parameters with little overhead, it can still underperform full fine-tuning in accuracy and often converges more slowly. We introduce LoFT, a novel low-rank adaptation method that behaves like full fine-tuning by aligning the optimizer's internal dynamics with those of updating all model weights. LoFT not only learns weight updates in a low-rank subspace (like LoRA) but also properly projects the optimizer's first and second moments (Adam's momentum and variance) into the same subspace, mirroring full-model updates. By aligning the low-rank update itself with the full update, LoFT eliminates the need for tuning extra hyperparameters, e.g., the LoRA scaling factor α. Empirically, this approach substantially narrows the performance gap between adapter-based tuning and full fine-tuning and consistently outperforms standard LoRA-style methods, all without increasing inference cost.