# LQ-LoRA: Low-rank Plus Quantized Matrix Decomposition for Efficient Language Model Finetuning

arXiv: https://arxiv.org/abs/2311.12023 · HTML: https://mlsanity.com/paper/2311.12023/

## Key facts

- Cited by 92 papers in the map (data through 14 Oct 2026).
- Builds on 49 of its 74 references that are in the map.
- First posted on arXiv 20 Nov 2023.

## Builds on (most cited first, 30 of 49)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [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)
- [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)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (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)
- [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)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [Self-Instruct: Aligning Language Models with Self-Generated Instructions](https://mlsanity.com/paper/2212.10560/) (2022)
- [Sparks of Artificial General Intelligence: Early experiments with GPT-4](https://mlsanity.com/paper/2303.12712/) (2023)
- [BLOOM: A 176B-Parameter Open-Access Multilingual Language Model](https://mlsanity.com/paper/2211.05100/) (2022)
- [SmoothQuant: Accurate and Efficient Post-Training Quantization for Large Language Models](https://mlsanity.com/paper/2211.10438/) (2022)
- [BitFit: Simple Parameter-efficient Fine-tuning for Transformer-based Masked Language-models](https://mlsanity.com/paper/2106.10199/) (2021)
- [LLM.int8(): 8-bit Matrix Multiplication for Transformers at Scale](https://mlsanity.com/paper/2208.07339/) (2022)
- [ZeroQuant: Efficient and Affordable Post-Training Quantization for Large-Scale Transformers](https://mlsanity.com/paper/2206.01861/) (2022)
- [OmniQuant: Omnidirectionally Calibrated Quantization for Large Language Models](https://mlsanity.com/paper/2308.13137/) (2023)
- [SpQR: A Sparse-Quantized Representation for Near-Lossless LLM Weight Compression](https://mlsanity.com/paper/2306.03078/) (2023)
- [Parameter-Efficient Transfer Learning with Diff Pruning](https://mlsanity.com/paper/2012.07463/) (2020)
- [ZeRO-Offload: Democratizing Billion-Scale Model Training](https://mlsanity.com/paper/2101.06840/) (2021)
- [Optimal Brain Compression: A Framework for Accurate Post-Training Quantization and Pruning](https://mlsanity.com/paper/2208.11580/) (2022)
- [SqueezeLLM: Dense-and-Sparse Quantization](https://mlsanity.com/paper/2306.07629/) (2023)
- [Parameter-efficient Multi-task Fine-tuning for Transformers via Shared Hypernetworks](https://mlsanity.com/paper/2106.04489/) (2021)

## Built on by (most cited first, 30 of 92)

- [Parameter-Efficient Fine-Tuning for Large Models: A Comprehensive Survey](https://mlsanity.com/paper/2403.14608/) (2024)
- [SVDQuant: Absorbing Outliers by Low-Rank Components for 4-Bit Diffusion Models](https://mlsanity.com/paper/2411.05007/) (2024)
- [LLM Inference Unveiled: Survey and Roofline Model Insights](https://mlsanity.com/paper/2402.16363/) (2024)
- [EfficientQAT: Efficient Quantization-Aware Training for Large Language Models](https://mlsanity.com/paper/2407.11062/) (2024)
- [Asymmetry in Low-Rank Adapters of Foundation Models](https://mlsanity.com/paper/2402.16842/) (2024)
- [SliM-LLM: Salience-Driven Mixed-Precision Quantization for Large Language Models](https://mlsanity.com/paper/2405.14917/) (2024)
- [PV-Tuning: Beyond Straight-Through Estimation for Extreme LLM Compression](https://mlsanity.com/paper/2405.14852/) (2024)
- [Compressing Large Language Models using Low Rank and Low Precision Decomposition](https://mlsanity.com/paper/2405.18886/) (2024)
- [Parameter-Efficient Fine-Tuning in Large Models: A Survey of Methodologies](https://mlsanity.com/paper/2410.19878/) (2024)
- [Low-Rank Quantization-Aware Training for LLMs](https://mlsanity.com/paper/2406.06385/) (2024)
- [Talking Heads: Understanding Inter-layer Communication in Transformer Language Models](https://mlsanity.com/paper/2406.09519/) (2024)
- [Mixture Compressor for Mixture-of-Experts LLMs Gains More](https://mlsanity.com/paper/2410.06270/) (2024)
- [Low-Rank Adaptation for Foundation Models: A Comprehensive Review](https://mlsanity.com/paper/2501.00365/) (2024)
- [Computational Limits of Low-Rank Adaptation (LoRA) Fine-Tuning for Transformer Models](https://mlsanity.com/paper/2406.03136/) (2024)
- [Lottery Ticket Adaptation: Mitigating Destructive Interference in LLMs](https://mlsanity.com/paper/2406.16797/) (2024)
- [A Survey of Low-bit Large Language Models: Basics, Systems, and Algorithms](https://mlsanity.com/paper/2409.16694/) (2024)
- [Fast Matrix Multiplications for Lookup Table-Quantized LLMs](https://mlsanity.com/paper/2407.10960/) (2024)
- [Zeroth-Order Fine-Tuning of LLMs with Extreme Sparsity](https://mlsanity.com/paper/2406.02913/) (2024)
- [ApiQ: Finetuning of 2-Bit Quantized Large Language Model](https://mlsanity.com/paper/2402.05147/) (2024)
- [A Survey: Collaborative Hardware and Software Design in the Era of Large Language Models](https://mlsanity.com/paper/2410.07265/) (2024)
- [Quantization Meets dLLMs: A Systematic Study of Post-training Quantization for Diffusion LLMs](https://mlsanity.com/paper/2508.14896/) (2025)
- [QERA: an Analytical Framework for Quantization Error Reconstruction](https://mlsanity.com/paper/2410.06040/) (2024)
- [SLoPe: Double-Pruned Sparse Plus Lazy Low-Rank Adapter Pretraining of LLMs](https://mlsanity.com/paper/2405.16325/) (2024)
- [LoRI: Reducing Cross-Task Interference in Multi-Task Low-Rank Adaptation](https://mlsanity.com/paper/2504.07448/) (2025)
- [QeRL: Beyond Efficiency -- Quantization-enhanced Reinforcement Learning for LLMs](https://mlsanity.com/paper/2510.11696/) (2025)
- [ZeroQuant(4+2): Redefining LLMs Quantization with a New FP6-Centric Strategy for Diverse Generative Tasks](https://mlsanity.com/paper/2312.08583/) (2023)
- [Agentic Retrieval-Augmented Generation for Time Series Analysis](https://mlsanity.com/paper/2408.14484/) (2024)
- [LoQT: Low-Rank Adapters for Quantized Pretraining](https://mlsanity.com/paper/2405.16528/) (2024)
- [SLiM: One-shot Quantization and Sparsity with Low-rank Approximation for LLM Weight Compression](https://mlsanity.com/paper/2410.09615/) (2024)
- [UORA: Uniform Orthogonal Reinitialization Adaptation in Parameter-Efficient Fine-Tuning of Large Models](https://mlsanity.com/paper/2505.20154/) (2025)

## Abstract (arXiv)

We propose a simple approach for memory-efficient adaptation of pretrained language models. Our approach uses an iterative algorithm to decompose each pretrained matrix into a high-precision low-rank component and a memory-efficient quantized component. During finetuning, the quantized component remains fixed and only the low-rank component is updated. We present an integer linear programming formulation of the quantization component which enables dynamic configuration of quantization parameters (e.g., bit-width, block size) for each matrix given an overall target memory budget. We further explore a data-aware version of the algorithm which uses an approximation of the Fisher information matrix to weight the reconstruction objective during matrix decomposition. Experiments on finetuning RoBERTa and LLaMA-2 (7B and 70B) demonstrate that our low-rank plus quantized matrix decomposition approach (LQ-LoRA) outperforms strong QLoRA and GPTQ-LoRA baselines and enables aggressive quantization to sub-3 bits with only minor performance degradations. When finetuned on a language modeling calibration dataset, LQ-LoRA can also be used for model compression; in this setting our 2.75-bit LLaMA-2-70B model (which has 2.85 bits on average when including the low-rank components and requires 27GB of GPU memory) performs respectably compared to the 16-bit baseline.