# RoSA: Accurate Parameter-Efficient Fine-Tuning via Robust Adaptation

arXiv: https://arxiv.org/abs/2401.04679 · HTML: https://mlsanity.com/paper/2401.04679/

## Key facts

- Cited by 48 papers in the map (data through 14 Oct 2026).
- Builds on 52 of its 77 references that are in the map.
- First posted on arXiv 9 Jan 2024.

## Builds on (most cited first, 30 of 52)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [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)
- [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)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [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)
- [Finetuned Language Models Are Zero-Shot Learners](https://mlsanity.com/paper/2109.01652/) (2021)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [OPT: Open Pre-trained Transformer Language Models](https://mlsanity.com/paper/2205.01068/) (2022)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [Self-Instruct: Aligning Language Models with Self-Generated Instructions](https://mlsanity.com/paper/2212.10560/) (2022)
- [Multitask Prompted Training Enables Zero-Shot Task Generalization](https://mlsanity.com/paper/2110.08207/) (2021)
- [Spider: A Large-Scale Human-Labeled Dataset for Complex and Cross-Domain Semantic Parsing and Text-to-SQL Task](https://mlsanity.com/paper/1809.08887/) (2018)
- [SparseGPT: Massive Language Models Can Be Accurately Pruned in One-Shot](https://mlsanity.com/paper/2301.00774/) (2023)
- [A General Language Assistant as a Laboratory for Alignment](https://mlsanity.com/paper/2112.00861/) (2021)
- [LLM.int8(): 8-bit Matrix Multiplication for Transformers at Scale](https://mlsanity.com/paper/2208.07339/) (2022)
- [Few-Shot Parameter-Efficient Fine-Tuning is Better and Cheaper than In-Context Learning](https://mlsanity.com/paper/2205.05638/) (2022)
- [Towards a Unified View of Parameter-Efficient Transfer Learning](https://mlsanity.com/paper/2110.04366/) (2021)
- [Super-NaturalInstructions: Generalization via Declarative Instructions on 1600+ NLP Tasks](https://mlsanity.com/paper/2204.07705/) (2022)
- [GPT Understands, Too](https://mlsanity.com/paper/2103.10385/) (2021)
- [P-Tuning v2: Prompt Tuning Can Be Comparable to Fine-tuning Universally Across Scales and Tasks](https://mlsanity.com/paper/2110.07602/) (2021)
- [Seq2SQL: Generating Structured Queries from Natural Language using Reinforcement Learning](https://mlsanity.com/paper/1709.00103/) (2017)
- [Sparsity in Deep Learning: Pruning and growth for efficient inference and training in neural networks](https://mlsanity.com/paper/2102.00554/) (2021)
- [Rigging the Lottery: Making All Tickets Winners](https://mlsanity.com/paper/1911.11134/) (2019)
- [The State of Sparsity in Deep Neural Networks](https://mlsanity.com/paper/1902.09574/) (2019)
- [MetaICL: Learning to Learn In Context](https://mlsanity.com/paper/2110.15943/) (2021)

## Built on by (most cited first, 30 of 48)

- [LoRA Learns Less and Forgets Less](https://mlsanity.com/paper/2405.09673/) (2024)
- [Get More with LESS: Synthesizing Recurrence with KV Cache Compression for Efficient LLM Inference](https://mlsanity.com/paper/2402.09398/) (2024)
- [LDAdam: Adaptive Optimization from Low-Dimensional Gradient Statistics](https://mlsanity.com/paper/2410.16103/) (2024)
- [Lottery Ticket Adaptation: Mitigating Destructive Interference in LLMs](https://mlsanity.com/paper/2406.16797/) (2024)
- [SLoPe: Double-Pruned Sparse Plus Lazy Low-Rank Adapter Pretraining of LLMs](https://mlsanity.com/paper/2405.16325/) (2024)
- [Parameter Efficient Fine-tuning via Explained Variance Adaptation](https://mlsanity.com/paper/2410.07170/) (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)
- [Random Masking Finds Winning Tickets for Parameter Efficient Fine-tuning](https://mlsanity.com/paper/2405.02596/) (2024)
- [Sparse High Rank Adapters](https://mlsanity.com/paper/2406.13175/) (2024)
- [On the Crucial Role of Initialization for Matrix Factorization](https://mlsanity.com/paper/2410.18965/) (2024)
- [HALO: Hadamard-Assisted Lower-Precision Optimization for LLMs](https://mlsanity.com/paper/2501.02625/) (2025)
- [SLiM: One-shot Quantization and Sparsity with Low-rank Approximation for LLM Weight Compression](https://mlsanity.com/paper/2410.09615/) (2024)
- [Understanding Forgetting in LLM Supervised Fine-Tuning and Preference Learning -- A Convex Optimization Perspective](https://mlsanity.com/paper/2410.15483/) (2024)
- [Parameter-Efficient Continual Fine-Tuning: A Survey](https://mlsanity.com/paper/2504.13822/) (2025)
- [Learning Rate Matters: Vanilla LoRA May Suffice for LLM Fine-tuning](https://mlsanity.com/paper/2602.04998/) (2026)
- [GIFT-SW: Gaussian noise Injected Fine-Tuning of Salient Weights for LLMs](https://mlsanity.com/paper/2408.15300/) (2024)
- [The Iterative Optimal Brain Surgeon: Faster Sparse Recovery by Leveraging Second-Order Information](https://mlsanity.com/paper/2408.17163/) (2024)
- [GaLore+: Boosting Low-Rank Adaptation for LLMs with Cross-Head Projection](https://mlsanity.com/paper/2412.19820/) (2024)
- [Exploring Sparsity for Parameter Efficient Fine Tuning Using Wavelets for Vision](https://mlsanity.com/paper/2505.12532/) (2025)
- [Two Sparse Matrices are Better than One: Sparsifying Neural Networks with Double Sparse Factorization](https://mlsanity.com/paper/2409.18850/) (2024)
- [Panza: Design and Analysis of a Fully-Local Personalized Text Writing Assistant](https://mlsanity.com/paper/2407.10994/) (2024)
- [Rapid Switching and Multi-Adapter Fusion via Sparse High Rank Adapters](https://mlsanity.com/paper/2407.16712/) (2024)
- [Parameter-Efficient Fine-Tuning via Circular Convolution](https://mlsanity.com/paper/2407.19342/) (2024)
- [FANAL -- Financial Activity News Alerting Language Modeling Framework](https://mlsanity.com/paper/2412.03527/) (2024)
- [Transformed Low-rank Adaptation via Tensor Decomposition and Its Applications to Text-to-image Models](https://mlsanity.com/paper/2501.08727/) (2025)
- [Low-Rank Adaptation Redux for Large Models](https://mlsanity.com/paper/2604.21905/) (2026)
- [A Bayesian Interpretation of Adaptive Low-Rank Adaptation](https://mlsanity.com/paper/2409.10673/) (2024)
- [RECAST: Reparameterized, Compact weight Adaptation for Sequential Tasks](https://mlsanity.com/paper/2411.16870/) (2024)
- [Revisiting LoRA through the Lens of Parameter Redundancy: Spectral Encoding Helps](https://mlsanity.com/paper/2506.16787/) (2025)

## Abstract (arXiv)

We investigate parameter-efficient fine-tuning (PEFT) methods that can provide good accuracy under limited computational and memory budgets in the context of large language models (LLMs). We present a new PEFT method called Robust Adaptation (RoSA) inspired by robust principal component analysis that jointly trains textitlow-rank and textithighly-sparse components on top of a set of fixed pretrained weights to efficiently approximate the performance of a full-fine-tuning (FFT) solution. Across a series of challenging generative tasks such as grade-school math and SQL query generation, which require fine-tuning for good performance, we show that RoSA outperforms LoRA, pure sparse fine-tuning, and alternative hybrid methods at the same parameter budget, and can even recover the performance of FFT on some tasks. We provide system support for RoSA to complement the training algorithm, specifically in the form of sparse GPU kernels which enable memory- and computationally-efficient training, and show that it is also compatible with low-precision base weights, resulting in the first joint representation combining quantization, low-rank and sparse approximations. Our code is available at https://github.com/IST-DASLab/RoSA.