# Asymmetry in Low-Rank Adapters of Foundation Models

arXiv: https://arxiv.org/abs/2402.16842 · HTML: https://mlsanity.com/paper/2402.16842/

## Key facts

- Cited by 86 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 40 references that are in the map.
- First posted on arXiv 26 Feb 2024.

## Builds on (most cited first, 28 of 28)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [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)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [BART: Denoising Sequence-to-Sequence Pre-training for Natural Language Generation, Translation, and Comprehension](https://mlsanity.com/paper/1910.13461/) (2019)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [HuggingFace's Transformers: State-of-the-art Natural Language Processing](https://mlsanity.com/paper/1910.03771/) (2019)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [Don't Give Me the Details, Just the Summary! Topic-Aware Convolutional Neural Networks for Extreme Summarization](https://mlsanity.com/paper/1808.08745/) (2018)
- [In Search of Lost Domain Generalization](https://mlsanity.com/paper/2007.01434/) (2020)
- [Few-Shot Parameter-Efficient Fine-Tuning is Better and Cheaper than In-Context Learning](https://mlsanity.com/paper/2205.05638/) (2022)
- [A Survey of Quantization Methods for Efficient Neural Network Inference](https://mlsanity.com/paper/2103.13630/) (2021)
- [Fine-Tuning can Distort Pretrained Features and Underperform Out-of-Distribution](https://mlsanity.com/paper/2202.10054/) (2022)
- [Intrinsic Dimensionality Explains the Effectiveness of Language Model Fine-Tuning](https://mlsanity.com/paper/2012.13255/) (2020)
- [How Far Can Camels Go? Exploring the State of Instruction Tuning on Open Resources](https://mlsanity.com/paper/2306.04751/) (2023)
- [AdaLoRA: Adaptive Budget Allocation for Parameter-Efficient Fine-Tuning](https://mlsanity.com/paper/2303.10512/) (2023)
- [SVDiff: Compact Parameter Space for Diffusion Fine-Tuning](https://mlsanity.com/paper/2303.11305/) (2023)
- [Information-theoretic analysis of generalization capability of learning algorithms](https://mlsanity.com/paper/1705.07809/) (2017)
- [What's Hidden in a Randomly Weighted Neural Network?](https://mlsanity.com/paper/1911.13299/) (2019)
- [Scaling Down to Scale Up: A Guide to Parameter-Efficient Fine-Tuning](https://mlsanity.com/paper/2303.15647/) (2023)
- [Parameter-Efficient Orthogonal Finetuning via Butterfly Factorization](https://mlsanity.com/paper/2311.06243/) (2023)
- [The Expressive Power of Low-Rank Adaptation](https://mlsanity.com/paper/2310.17513/) (2023)
- [LQ-LoRA: Low-rank Plus Quantized Matrix Decomposition for Efficient Language Model Finetuning](https://mlsanity.com/paper/2311.12023/) (2023)
- [A Thorough Examination of the CNN/Daily Mail Reading Comprehension Task](https://mlsanity.com/paper/1606.02858/) (2016)
- [ComPEFT: Compression for Communicating Parameter Efficient Updates via Sparsification and Quantization](https://mlsanity.com/paper/2311.13171/) (2023)
- [PRILoRA: Pruned and Rank-Increasing Low-Rank Adaptation](https://mlsanity.com/paper/2401.11316/) (2024)

## Built on by (most cited first, 30 of 86)

- [Improving LoRA in Privacy-preserving Federated Learning](https://mlsanity.com/paper/2403.12313/) (2024)
- [LoRA vs Full Fine-tuning: An Illusion of Equivalence](https://mlsanity.com/paper/2410.21228/) (2024)
- [Selective Aggregation for Low-Rank Adaptation in Federated Learning](https://mlsanity.com/paper/2410.01463/) (2024)
- [A Survey on LoRA of Large Language Models](https://mlsanity.com/paper/2407.11046/) (2024)
- [The Impact of Initialization on LoRA Finetuning Dynamics](https://mlsanity.com/paper/2406.08447/) (2024)
- [MakeAnything: Harnessing Diffusion Transformers for Multi-Domain Procedural Sequence Generation](https://mlsanity.com/paper/2502.01572/) (2025)
- [Low-Rank Adaptation for Foundation Models: A Comprehensive Review](https://mlsanity.com/paper/2501.00365/) (2024)
- [Scaling Laws for Forgetting during Finetuning with Pretraining Data Injection](https://mlsanity.com/paper/2502.06042/) (2025)
- [FlyLoRA: Boosting Task Decoupling and Parameter Efficiency via Implicit Rank-Wise Mixture-of-Experts](https://mlsanity.com/paper/2510.08396/) (2025)
- [MoRA: High-Rank Updating for Parameter-Efficient Fine-Tuning](https://mlsanity.com/paper/2405.12130/) (2024)
- [CL-LoRA: Continual Low-Rank Adaptation for Rehearsal-Free Class-Incremental Learning](https://mlsanity.com/paper/2505.24816/) (2025)
- [RobustMerge: Parameter-Efficient Model Merging for MLLMs with Direction Robustness](https://mlsanity.com/paper/2502.17159/) (2025)
- [Compress then Serve: Serving Thousands of LoRA Adapters with Little Overhead](https://mlsanity.com/paper/2407.00066/) (2024)
- [PoLAR: Polar-Decomposed Low-Rank Adapter Representation](https://mlsanity.com/paper/2506.03133/) (2025)
- [LoRI: Reducing Cross-Task Interference in Multi-Task Low-Rank Adaptation](https://mlsanity.com/paper/2504.07448/) (2025)
- [Robust Federated Finetuning of LLMs via Alternating Optimization of LoRA](https://mlsanity.com/paper/2502.01755/) (2025)
- [On the Crucial Role of Initialization for Matrix Factorization](https://mlsanity.com/paper/2410.18965/) (2024)
- [Decentralized Low-Rank Fine-Tuning of Large Language Models](https://mlsanity.com/paper/2501.15361/) (2025)
- [LoFT: Low-Rank Adaptation That Behaves Like Full Fine-Tuning](https://mlsanity.com/paper/2505.21289/) (2025)
- [Randomized Asymmetric Chain of LoRA: The First Meaningful Theoretical Framework for Low-Rank Adaptation](https://mlsanity.com/paper/2410.08305/) (2024)
- [Quantum-PEFT: Ultra parameter-efficient fine-tuning](https://mlsanity.com/paper/2503.05431/) (2025)
- [Sharp Generalization Bounds for Foundation Models with Asymmetric Randomized Low-Rank Adapters](https://mlsanity.com/paper/2506.14530/) (2025)
- [Merge before Forget: A Single LoRA Continual Learning via Continual Merging](https://mlsanity.com/paper/2512.23017/) (2025)
- [SuperLoRA: Parameter-Efficient Unified Adaptation of Multi-Layer Attention Modules](https://mlsanity.com/paper/2403.11887/) (2024)
- [S2FT: Efficient, Scalable and Generalizable LLM Fine-tuning by Structured Sparsity](https://mlsanity.com/paper/2412.06289/) (2024)
- [DeLoRA: Decoupling Angles and Strength in Low-rank Adaptation](https://mlsanity.com/paper/2503.18225/) (2025)
- [Riemannian Optimization for LoRA on the Stiefel Manifold](https://mlsanity.com/paper/2508.17901/) (2025)
- [Theoretical Insights into Fine-Tuning Attention Mechanism: Generalization and Optimization](https://mlsanity.com/paper/2410.02247/) (2024)
- [DL-QAT: Weight-Decomposed Low-Rank Quantization-Aware Training for Large Language Models](https://mlsanity.com/paper/2504.09223/) (2025)
- [MALoRA: Mixture of Asymmetric Low-Rank Adaptation for Enhanced Multi-Task Learning](https://mlsanity.com/paper/2410.22782/) (2024)

## Abstract (arXiv)

Parameter-efficient fine-tuning optimizes large, pre-trained foundation models by updating a subset of parameters; in this class, Low-Rank Adaptation (LoRA) is particularly effective. Inspired by an effort to investigate the different roles of LoRA matrices during fine-tuning, this paper characterizes and leverages unexpected asymmetry in the importance of low-rank adapter matrices. Specifically, when updating the parameter matrices of a neural network by adding a product BA, we observe that the B and A matrices have distinct functions: A extracts features from the input, while B uses these features to create the desired output. Based on this observation, we demonstrate that fine-tuning B is inherently more effective than fine-tuning A, and that a random untrained A should perform nearly as well as a fine-tuned one. Using an information-theoretic lens, we also bound the generalization of low-rank adapters, showing that the parameter savings of exclusively training B improves the bound. We support our conclusions with experiments on RoBERTa, BART-Large, LLaMA-2, and ViTs.