# Low-Rank Quantization-Aware Training for LLMs

arXiv: https://arxiv.org/abs/2406.06385 · HTML: https://mlsanity.com/paper/2406.06385/

## Key facts

- Cited by 43 papers in the map (data through 14 Oct 2026).
- Builds on 59 of its 72 references that are in the map.
- First posted on arXiv 10 Jun 2024.

## Builds on (most cited first, 30 of 59)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [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)
- [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)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [Quantization and Training of Neural Networks for Efficient Integer-Arithmetic-Only Inference](https://mlsanity.com/paper/1712.05877/) (2017)
- [SmoothQuant: Accurate and Efficient Post-Training Quantization for Large Language Models](https://mlsanity.com/paper/2211.10438/) (2022)
- [AWQ: Activation-aware Weight Quantization for LLM Compression and Acceleration](https://mlsanity.com/paper/2306.00978/) (2023)
- [Training Deep Nets with Sublinear Memory Cost](https://mlsanity.com/paper/1604.06174/) (2016)
- [Learned Step Size Quantization](https://mlsanity.com/paper/1902.08153/) (2019)
- [Up or Down? Adaptive Rounding for Post-Training Quantization](https://mlsanity.com/paper/2004.10568/) (2020)
- [DoReFa-Net: Training Low Bitwidth Convolutional Neural Networks with Low Bitwidth Gradients](https://mlsanity.com/paper/1606.06160/) (2016)
- [Datasets: A Community Library for Natural Language Processing](https://mlsanity.com/paper/2109.02846/) (2021)
- [ZeroQuant: Efficient and Affordable Post-Training Quantization for Large-Scale Transformers](https://mlsanity.com/paper/2206.01861/) (2022)
- [Quantizing deep convolutional networks for efficient inference: A whitepaper](https://mlsanity.com/paper/1806.08342/) (2018)
- [BRECQ: Pushing the Limit of Post-Training Quantization by Block Reconstruction](https://mlsanity.com/paper/2102.05426/) (2021)
- [A White Paper on Neural Network Quantization](https://mlsanity.com/paper/2106.08295/) (2021)
- [Quantized Neural Networks: Training Neural Networks with Low Precision Weights and Activations](https://mlsanity.com/paper/1609.07061/) (2016)
- [OmniQuant: Omnidirectionally Calibrated Quantization for Large Language Models](https://mlsanity.com/paper/2308.13137/) (2023)
- [QuIP: 2-Bit Quantization of Large Language Models With Guarantees](https://mlsanity.com/paper/2307.13304/) (2023)
- [Deep Learning with Limited Numerical Precision](https://mlsanity.com/paper/1502.02551/) (2015)

## Built on by (most cited first, 30 of 43)

- [A Survey of Low-bit Large Language Models: Basics, Systems, and Algorithms](https://mlsanity.com/paper/2409.16694/) (2024)
- [ABQ-LLM: Arbitrary-Bit Quantized Inference Acceleration for Large Language Models](https://mlsanity.com/paper/2408.08554/) (2024)
- [AutoNeural: Co-Designing Vision-Language Models for NPU Inference](https://mlsanity.com/paper/2512.02924/) (2025)
- [FPTQuant: Function-Preserving Transforms for LLM Quantization](https://mlsanity.com/paper/2506.04985/) (2025)
- [What Makes Low-Bit Quantization-Aware Training Work for Reasoning LLMs? A Systematic Study](https://mlsanity.com/paper/2601.14888/) (2026)
- [LiquidGEMM: Hardware-Efficient W4A8 GEMM Kernel for High-Performance LLM Serving](https://mlsanity.com/paper/2509.01229/) (2025)
- [EoRA: Fine-tuning-free Compensation for Compressed LLM with Eigenspace Low-Rank Approximation](https://mlsanity.com/paper/2410.21271/) (2024)
- [GQSA: Group Quantization and Sparsity for Accelerating Large Language Model Inference](https://mlsanity.com/paper/2412.17560/) (2024)
- [RoSTE: An Efficient Quantization-Aware Supervised Fine-Tuning Approach for Large Language Models](https://mlsanity.com/paper/2502.09003/) (2025)
- [LoTA-QAF: Lossless Ternary Adaptation for Quantization-Aware Fine-Tuning](https://mlsanity.com/paper/2505.18724/) (2025)
- [iFairy: the First 2-bit Complex LLM with All Parameters in ±1, ± i](https://mlsanity.com/paper/2508.05571/) (2025)
- [Interpreting the Effects of Quantization on LLMs](https://mlsanity.com/paper/2508.16785/) (2025)
- [Mixed-Precision Quantization for Language Models: Techniques and Prospects](https://mlsanity.com/paper/2510.16805/) (2025)
- [MASQuant: Modality-Aware Smoothing Quantization for Multimodal Large Language Models](https://mlsanity.com/paper/2603.04800/) (2026)
- [FreeAct: Freeing Activations for LLM Quantization](https://mlsanity.com/paper/2603.01776/) (2026)
- [FineGates: LLMs Finetuning with Compression using Stochastic Gates](https://mlsanity.com/paper/2412.12951/) (2024)
- [Art and Science of Quantizing Large-Scale Models: A Comprehensive Overview](https://mlsanity.com/paper/2409.11650/) (2024)
- [EchoAtt: Attend, Copy, then Adjust for More Efficient Large Language Models](https://mlsanity.com/paper/2409.14595/) (2024)
- [Fairy2i: Training Complex LLMs from Real LLMs with All Parameters in ± 1, ± i](https://mlsanity.com/paper/2512.02901/) (2025)
- [Differentially Private Subspace Fine-Tuning for Large Language Models](https://mlsanity.com/paper/2601.11113/) (2026)
- [Train Less, Infer Faster: Efficient Model Finetuning and Compression via Structured Sparsity](https://mlsanity.com/paper/2602.09169/) (2026)
- [Mapping the Schedule x Bit-Width Boundary in Sub-100M Quantisation-Aware Training](https://mlsanity.com/paper/2605.25966/) (2026)
- [Interactions Across Blocks in Post-Training Quantization of Large Language Models](https://mlsanity.com/paper/2411.03934/) (2024)
- [Coded Deep Learning: Framework and Algorithm](https://mlsanity.com/paper/2501.09849/) (2025)
- [Onboard Optimization and Learning: A Survey](https://mlsanity.com/paper/2505.08793/) (2025)
- [MLoRQ: Bridging Low-Rank and Quantization for Transformer Compression](https://mlsanity.com/paper/2507.09616/) (2025)
- [Evaluating the Safety and Skill Reasoning of Large Reasoning Models Under Compute Constraints](https://mlsanity.com/paper/2509.18382/) (2025)
- [Breaking Modality Heterogeneity in Low-Bit Quantization for Large Vision-Language Models](https://mlsanity.com/paper/2605.19929/) (2026)
- [In-Cell Learning: Language Models That Update Their Own Weights in Sequence Without Changing the File They Ship](https://mlsanity.com/paper/2608.20873/) (2026)
- [Scale-QLoRA: Code-Invariant Adapter Merging for Native 4-bit Microscaling LLMs](https://mlsanity.com/paper/2609.04526/) (2026)

## Abstract (arXiv)

Large language models (LLMs) are omnipresent, however their practical deployment is challenging due to their ever increasing computational and memory demands. Quantization is one of the most effective ways to make them more compute and memory efficient. Quantization-aware training (QAT) methods, generally produce the best quantized performance, however it comes at the cost of potentially long training time and excessive memory usage, making it impractical when applying for LLMs. Inspired by parameter-efficient fine-tuning (PEFT) and low-rank adaptation (LoRA) literature, we propose LR-QAT -- a lightweight and memory-efficient QAT algorithm for LLMs. LR-QAT employs several components to save memory without sacrificing predictive performance: (a) low-rank auxiliary weights that are aware of the quantization grid; (b) a downcasting operator using fixed-point or double-packed integers and (c) checkpointing. Unlike most related work, our method (i) is inference-efficient, leading to no additional overhead compared to traditional PTQ; (ii) can be seen as a general extended pretraining framework, meaning that the resulting model can still be utilized for any downstream task afterwards; (iii) can be applied across a wide range of quantization settings, such as different choices quantization granularity, activation quantization, and seamlessly combined with many PTQ techniques. We apply LR-QAT to LLaMA-1/2/3 and Mistral model families and validate its effectiveness on several downstream tasks. Our method outperforms common post-training quantization (PTQ) approaches and reaches the same model performance as full-model QAT at the fraction of its memory usage. Specifically, we can train a 7B LLM on a single consumer grade GPU with 24GB of memory. Our source code is available at https://github.com/qualcomm-ai-research/LR-QAT