# L4Q: Parameter Efficient Quantization-Aware Fine-Tuning on Large Language Models

arXiv: https://arxiv.org/abs/2402.04902 · HTML: https://mlsanity.com/paper/2402.04902/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 46 references that are in the map.
- First posted on arXiv 7 Feb 2024.

## Builds on (most cited first, 30 of 38)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [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)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [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)
- [Prefix-Tuning: Optimizing Continuous Prompts for Generation](https://mlsanity.com/paper/2101.00190/) (2021)
- [Finetuned Language Models Are Zero-Shot Learners](https://mlsanity.com/paper/2109.01652/) (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)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [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)
- [CommonsenseQA: A Question Answering Challenge Targeting Commonsense Knowledge](https://mlsanity.com/paper/1811.00937/) (2018)
- [SmoothQuant: Accurate and Efficient Post-Training Quantization for Large Language Models](https://mlsanity.com/paper/2211.10438/) (2022)
- [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)
- [Learned Step Size Quantization](https://mlsanity.com/paper/1902.08153/) (2019)
- [KVQuant: Towards 10 Million Context Length LLM Inference with KV Cache Quantization](https://mlsanity.com/paper/2401.18079/) (2024)
- [PACT: Parameterized Clipping Activation for Quantized Neural Networks](https://mlsanity.com/paper/1805.06085/) (2018)
- [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)
- [LLM-QAT: Data-Free Quantization Aware Training for Large Language Models](https://mlsanity.com/paper/2305.17888/) (2023)
- [Optimal Brain Compression: A Framework for Accurate Post-Training Quantization and Pruning](https://mlsanity.com/paper/2208.11580/) (2022)
- [The case for 4-bit precision: k-bit Inference Scaling Laws](https://mlsanity.com/paper/2212.09720/) (2022)

## Built on by (most cited first, 15 of 15)

- [Low-Rank Adaptation for Foundation Models: A Comprehensive Review](https://mlsanity.com/paper/2501.00365/) (2024)
- [LoTA-QAF: Lossless Ternary Adaptation for Quantization-Aware Fine-Tuning](https://mlsanity.com/paper/2505.18724/) (2025)
- [Scaling Laws for Post Training Quantized Large Language Models](https://mlsanity.com/paper/2410.12119/) (2024)
- [FreeAct: Freeing Activations for LLM Quantization](https://mlsanity.com/paper/2603.01776/) (2026)
- [Accelerating Error Correction Code Transformers](https://mlsanity.com/paper/2410.05911/) (2024)
- [Enhancing Ultra-Low-Bit Quantization of Large Language Models Through Saliency-Aware Partial Retraining](https://mlsanity.com/paper/2504.13932/) (2025)
- [Low-Resource Dialect Adaptation of Large Language Models: A French Dialect Case-Study](https://mlsanity.com/paper/2510.22747/) (2025)
- [Onboard Optimization and Learning: A Survey](https://mlsanity.com/paper/2505.08793/) (2025)
- [Every Bit Counts: A Theoretical Study of Precision-Expressivity Tradeoffs in Quantized Transformers](https://mlsanity.com/paper/2602.02707/) (2026)
- [Fine-Tuning Low-Bit Models with Gradient in Quantized Code Space](https://mlsanity.com/paper/2608.30908/) (2026)
- [Scale-QLoRA: Code-Invariant Adapter Merging for Native 4-bit Microscaling LLMs](https://mlsanity.com/paper/2609.04526/) (2026)
- [QATFactory: A Versatile, Deployment-Aligned Framework for Quantization-aware Training and Distillation of LLMs](https://mlsanity.com/paper/2609.39223/) (2026)
- [Can abstract concepts from LLM improve SLM performance?](https://mlsanity.com/paper/2512.19069/) (2025)
- [LLM Compression with Jointly Optimizing Architectural and Quantization choices](https://mlsanity.com/paper/2606.04063/) (2026)
- [BiSCo-LLM: Lookup-Free Binary Spherical Coding for Extreme Low-Bit Large Language Model Compression](https://mlsanity.com/paper/2607.08643/) (2026)

## Abstract (arXiv)

Due to the high memory and computational costs associated with large language models (LLMs), model compression techniques such as quantization, which reduces inference costs, and parameter-efficient fine-tuning (PEFT) methods like Low-Rank Adaptation (LoRA), which reduce training costs, have gained significant popularity. This trend has spurred active research into quantization-aware PEFT techniques, aimed at maintaining model accuracy while minimizing memory overhead during both inference and training. Previous quantization-aware PEFT methods typically apply post-training quantization (PTQ) to pre-trained LLMs, followed by PEFT to recover accuracy loss. Meanwhile, this approach has limitations in recovering the accuracy loss. In this paper, we propose L4Q, a method that integrates Quantization-Aware Training (QAT) with LoRA. By employing a memory-optimized layer design, L4Q significantly reduces QAT's memory overhead, making its training cost comparable to LoRA, while preserving the advantage of QAT in producing fully quantized LLMs with high accuracy. Our experiments demonstrate that this combined approach to quantization and fine-tuning achieves superior accuracy compared to decoupled fine-tuning schemes, particularly in 4-bit and 3-bit quantization, positioning L4Q as an efficient QAT solution. Using the LLaMA and Mistral models with instructional datasets, we showcase L4Q's capabilities in language tasks and few-shot learning.