# LoRA vs Full Fine-tuning: An Illusion of Equivalence

arXiv: https://arxiv.org/abs/2410.21228 · HTML: https://mlsanity.com/paper/2410.21228/

## Key facts

- Cited by 109 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 50 references that are in the map.
- First posted on arXiv 28 Oct 2024.

## Builds on (most cited first, 30 of 32)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [A Broad-Coverage Challenge Corpus for Sentence Understanding through Inference](https://mlsanity.com/paper/1704.05426/) (2017)
- [FEVER: a large-scale dataset for Fact Extraction and VERification](https://mlsanity.com/paper/1803.05355/) (2018)
- [Aligning Books and Movies: Towards Story-like Visual Explanations by Watching Movies and Reading Books](https://mlsanity.com/paper/1506.06724/) (2015)
- [DoRA: Weight-Decomposed Low-Rank Adaptation](https://mlsanity.com/paper/2402.09353/) (2024)
- [MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models](https://mlsanity.com/paper/2309.12284/) (2023)
- [Intrinsic Dimensionality Explains the Effectiveness of Language Model Fine-Tuning](https://mlsanity.com/paper/2012.13255/) (2020)
- [LoRA+: Efficient Low Rank Adaptation of Large Models](https://mlsanity.com/paper/2402.12354/) (2024)
- [Measuring the Intrinsic Dimension of Objective Landscapes](https://mlsanity.com/paper/1804.08838/) (2018)
- [LoRA Learns Less and Forgets Less](https://mlsanity.com/paper/2405.09673/) (2024)
- [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)
- [Magicoder: Empowering Code Generation with OSS-Instruct](https://mlsanity.com/paper/2312.02120/) (2023)
- [A Rank Stabilization Scaling Factor for Fine-Tuning with LoRA](https://mlsanity.com/paper/2312.03732/) (2023)
- [Camels in a Changing Climate: Enhancing LM Adaptation with Tulu 2](https://mlsanity.com/paper/2311.10702/) (2023)
- [A Simple Method for Commonsense Reasoning](https://mlsanity.com/paper/1806.02847/) (2018)
- [The Truth is in There: Improving Reasoning in Language Models with Layer-Selective Rank Reduction](https://mlsanity.com/paper/2312.13558/) (2023)
- [Flora: Low-Rank Adapters Are Secretly Gradient Compressors](https://mlsanity.com/paper/2402.03293/) (2024)
- [Asymmetry in Low-Rank Adapters of Foundation Models](https://mlsanity.com/paper/2402.16842/) (2024)
- [Chain of LoRA: Efficient Fine-tuning of Language Models via Residual Learning](https://mlsanity.com/paper/2401.04151/) (2024)
- [A Closer Look at the Limitations of Instruction Tuning](https://mlsanity.com/paper/2402.05119/) (2024)

## Built on by (most cited first, 30 of 109)

- [Transformer Copilot: Learning from The Mistake Log in LLM Fine-tuning](https://mlsanity.com/paper/2505.16270/) (2025)
- [RL Is Neither a Panacea Nor a Mirage: Understanding Supervised vs. Reinforcement Learning Fine-Tuning for LLMs](https://mlsanity.com/paper/2508.16546/) (2025)
- [Keeping Yourself is Important in Downstream Tuning Multimodal Large Language Model](https://mlsanity.com/paper/2503.04543/) (2025)
- [Learning to Reason in 13 Parameters](https://mlsanity.com/paper/2602.04118/) (2026)
- [ALL-FEM: Agentic Large Language models Fine-tuned for Finite Element Methods](https://mlsanity.com/paper/2603.21011/) (2026)
- [Attention, Please! Revisiting Attentive Probing Through the Lens of Efficiency](https://mlsanity.com/paper/2506.10178/) (2025)
- [SOFT: Selective Data Obfuscation for Protecting LLM Fine-tuning against Membership Inference Attacks](https://mlsanity.com/paper/2506.10424/) (2025)
- [Riemannian Optimization for LoRA on the Stiefel Manifold](https://mlsanity.com/paper/2508.17901/) (2025)
- [On the Convergence Rate of LoRA Gradient Descent](https://mlsanity.com/paper/2512.18248/) (2025)
- [Learning Rate Scaling across LoRA Ranks and Transfer to Full Finetuning](https://mlsanity.com/paper/2602.06204/) (2026)
- [Position: Modular Memory is the Key to Continual Learning Agents](https://mlsanity.com/paper/2603.01761/) (2026)
- [Can Muon Fine-tune Adam-Pretrained Models?](https://mlsanity.com/paper/2605.10468/) (2026)
- [PiCa: Parameter-Efficient Fine-Tuning with Column Space Projection](https://mlsanity.com/paper/2505.20211/) (2025)
- [PLoRA: Efficient Concurrent LoRA Training for Large Language Models](https://mlsanity.com/paper/2508.02932/) (2025)
- [Subliminal Learning is a LoRA Artifact](https://mlsanity.com/paper/2606.00831/) (2026)
- [One Student, Many Teachers: Multi-Task On-Policy Distillation via Soft-Prompt Privileged Context](https://mlsanity.com/paper/2607.18293/) (2026)
- [Adaptive Parameter-Efficient Federated Fine-Tuning on Heterogeneous Devices](https://mlsanity.com/paper/2412.20004/) (2024)
- [GRASP: Replace Redundant Layers with Adaptive Singular Parameters for Efficient Model Compression](https://mlsanity.com/paper/2501.00339/) (2024)
- [Accidental Vulnerability: Factors in Fine-Tuning that Shift Model Safeguards](https://mlsanity.com/paper/2505.16789/) (2025)
- [Planted in Pretraining, Swayed by Finetuning: A Case Study on the Origins of Cognitive Biases in LLMs](https://mlsanity.com/paper/2507.07186/) (2025)
- [How Much is Too Much? Exploring LoRA Rank Trade-offs for Retaining Knowledge and Domain Robustness](https://mlsanity.com/paper/2512.15634/) (2025)
- [Optimizer-Model Consistency: Full Finetuning with the Same Optimizer as Pretraining Forgets Less](https://mlsanity.com/paper/2605.06654/) (2026)
- [A Comparative Analysis of LLM Adaptation: SFT, LoRA, and ICL in Data-Scarce Scenarios](https://mlsanity.com/paper/2511.00130/) (2025)
- [Omni-Attribute: Open-vocabulary Attribute Encoder for Visual Concept Personalization](https://mlsanity.com/paper/2512.10955/) (2025)
- [Why LoRA Fails to Forget: Regularized Low-Rank Adaptation Against Backdoors in Language Models](https://mlsanity.com/paper/2601.06305/) (2026)
- [Beware of the Batch Size: Hyperparameter Bias in Evaluating LoRA](https://mlsanity.com/paper/2602.09492/) (2026)
- [CLOVER: Cross-Layer Orthogonal Vectors Pruning and Fine-Tuning](https://mlsanity.com/paper/2411.17426/) (2024)
- [How Relevance Emerges: Interpreting LoRA Fine-Tuning in Reranking LLMs](https://mlsanity.com/paper/2504.08780/) (2025)
- [Merging Smarter, Generalizing Better: Enhancing Model Merging on OOD Data](https://mlsanity.com/paper/2506.09093/) (2025)
- [CLIP-SVD: Efficient and Interpretable Vision-Language Adaptation via Singular Values](https://mlsanity.com/paper/2509.03740/) (2025)

## Abstract (arXiv)

Fine-tuning is a crucial paradigm for adapting pre-trained large language models to downstream tasks. Recently, methods like Low-Rank Adaptation (LoRA) have been shown to effectively fine-tune LLMs with an extreme reduction in trainable parameters. But, are their learned solutions really equivalent? We study how LoRA and full-finetuning change pre-trained models by analyzing the model's weight matrices through the lens of their spectral properties. We find that LoRA and full fine-tuning yield weight matrices whose singular value decompositions exhibit very different structure: weight matrices trained with LoRA have new, high-ranking singular vectors, which we call intruder dimensions, while those trained with full fine-tuning do not. Further, we extend the finding that LoRA forgets less than full fine-tuning and find its forgetting is vastly localized to the intruder dimension -- by causally intervening on the intruder dimensions by changing their associated singular values post-fine-tuning, we show that they cause forgetting. Moreover, scaling them down significantly improves modeling of the pre-training distribution with a minimal drop in downstream task performance. Given this, we should expect accumulating intruder dimensions to be harmful and lead to more forgetting. This will be amplified during continual learning because of sequentially fine-tuning, and we show that LoRA models do accumulate intruder dimensions here tend to perform worse in this setting, emphasizing the practicality of our findings.