# LQER: Low-Rank Quantization Error Reconstruction for LLMs

arXiv: https://arxiv.org/abs/2402.02446 · HTML: https://mlsanity.com/paper/2402.02446/

## Key facts

- Cited by 41 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 59 references that are in the map.
- First posted on arXiv 4 Feb 2024.

## Builds on (most cited first, 30 of 39)

- [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)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [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)
- [Longformer: The Long-Document Transformer](https://mlsanity.com/paper/2004.05150/) (2020)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [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)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [BLOOM: A 176B-Parameter Open-Access Multilingual Language Model](https://mlsanity.com/paper/2211.05100/) (2022)
- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [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)
- [The LAMBADA dataset: Word prediction requiring a broad discourse context](https://mlsanity.com/paper/1606.06031/) (2016)
- [LLM.int8(): 8-bit Matrix Multiplication for Transformers at Scale](https://mlsanity.com/paper/2208.07339/) (2022)
- [A White Paper on Neural Network Quantization](https://mlsanity.com/paper/2106.08295/) (2021)
- [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)
- [SpQR: A Sparse-Quantized Representation for Near-Lossless LLM Weight Compression](https://mlsanity.com/paper/2306.03078/) (2023)
- [LLM-QAT: Data-Free Quantization Aware Training for Large Language Models](https://mlsanity.com/paper/2305.17888/) (2023)
- [Estimating the Carbon Footprint of BLOOM, a 176B Parameter Language Model](https://mlsanity.com/paper/2211.02001/) (2022)
- [LoftQ: LoRA-Fine-Tuning-Aware Quantization for Large Language Models](https://mlsanity.com/paper/2310.08659/) (2023)
- [Outlier Suppression: Pushing the Limit of Low-bit Transformer Language Models](https://mlsanity.com/paper/2209.13325/) (2022)
- [Microscaling Data Formats for Deep Learning](https://mlsanity.com/paper/2310.10537/) (2023)

## Built on by (most cited first, 30 of 41)

- [Low-Rank Quantization-Aware Training for LLMs](https://mlsanity.com/paper/2406.06385/) (2024)
- [Low-Rank Adaptation for Foundation Models: A Comprehensive Review](https://mlsanity.com/paper/2501.00365/) (2024)
- [A Survey of Low-bit Large Language Models: Basics, Systems, and Algorithms](https://mlsanity.com/paper/2409.16694/) (2024)
- [QERA: an Analytical Framework for Quantization Error Reconstruction](https://mlsanity.com/paper/2410.06040/) (2024)
- [Low-Bit Quantization Favors Undertrained LLMs: Scaling Laws for Quantized LLMs with 100T Training Tokens](https://mlsanity.com/paper/2411.17691/) (2024)
- [SLiM: One-shot Quantization and Sparsity with Low-rank Approximation for LLM Weight Compression](https://mlsanity.com/paper/2410.09615/) (2024)
- [Low-bit Model Quantization for Deep Neural Networks: A Survey](https://mlsanity.com/paper/2505.05530/) (2025)
- [LittleBit: Ultra Low-Bit Quantization via Latent Factorization](https://mlsanity.com/paper/2506.13771/) (2025)
- [LLaVA-FA: Learning Fourier Approximation for Compressing Large Multimodal Models](https://mlsanity.com/paper/2602.00135/) (2026)
- [RILQ: Rank-Insensitive LoRA-based Quantization Error Compensation for Boosting 2-bit Large Language Model Accuracy](https://mlsanity.com/paper/2412.01129/) (2024)
- [ASER: Activation Smoothing and Error Reconstruction for Large Language Model Quantization](https://mlsanity.com/paper/2411.07762/) (2024)
- [A3 : an Analytical Low-Rank Approximation Framework for Attention](https://mlsanity.com/paper/2505.12942/) (2025)
- [EoRA: Fine-tuning-free Compensation for Compressed LLM with Eigenspace Low-Rank Approximation](https://mlsanity.com/paper/2410.21271/) (2024)
- [Towards Low-bit Communication for Tensor Parallel LLM Inference](https://mlsanity.com/paper/2411.07942/) (2024)
- [CDQuant: Greedy Coordinate Descent for Accurate LLM Quantization](https://mlsanity.com/paper/2406.17542/) (2024)
- [A Comprehensive Evaluation on Quantization Techniques for Large Language Models](https://mlsanity.com/paper/2507.17417/) (2025)
- [Bandwidth-Efficient Adaptive Mixture-of-Experts via Low-Rank Compensation](https://mlsanity.com/paper/2512.17073/) (2025)
- [LoPRo: Enhancing Low-Rank Quantization via Permuted Block-Wise Rotation](https://mlsanity.com/paper/2601.19675/) (2026)
- [Quant Experts: Token-aware Adaptive Error Reconstruction with Mixture of Experts for Large Vision-Language Models Quantization](https://mlsanity.com/paper/2602.24059/) (2026)
- [Scaling Laws For Mixed Quantization](https://mlsanity.com/paper/2410.06722/) (2024)
- [Low-Rank Correction for Quantized LLMs](https://mlsanity.com/paper/2412.07902/) (2024)
- [FLRQ: Faster LLM Quantization with Flexible Low-Rank Matrix Sketching](https://mlsanity.com/paper/2601.05684/) (2026)
- [EdgeRazor: A Lightweight Framework for Large Language Models via Mixed-Precision Quantization-Aware Distillation](https://mlsanity.com/paper/2605.04062/) (2026)
- [MixQuant: Adaptive Mixed-Precision Quantization for Large Language Models](https://mlsanity.com/paper/2607.23047/) (2026)
- [Efficient Large Language Model Inference with Neural Block Linearization](https://mlsanity.com/paper/2505.21077/) (2025)
- [Assigning Distinct Roles to Quantized and Low-Rank Matrices Toward Optimal Weight Decomposition](https://mlsanity.com/paper/2506.02077/) (2025)
- [On Information Geometry and Iterative Optimization in Model Compression: Operator Factorization](https://mlsanity.com/paper/2507.09428/) (2025)
- [Preserve-Then-Quantize: Balancing Rank Budgets for Quantization Error Reconstruction in LLMs](https://mlsanity.com/paper/2602.02001/) (2026)
- [SERQ: Saliency-Aware Low-Rank Error Reconstruction for LLM Quantization](https://mlsanity.com/paper/2603.08185/) (2026)
- [D-QRELO: Training- and Data-Free Delta Compression for Large Language Models via Quantization and Residual Low-Rank Approximation](https://mlsanity.com/paper/2604.16940/) (2026)

## Abstract (arXiv)

Post-training quantization of Large Language Models (LLMs) is challenging. In this work, we introduce Low-rank Quantization Error Reduction (LQER), which combines quantization and low-rank approximation to recover the model capability. LQER leverages an activation-induced scale matrix to drive the singular value distribution of quantization error towards a desirable distribution, which enables nearly-lossless W4A8 quantization on various LLMs and downstream tasks without the need for knowledge distillation, grid search, or gradient-base iterative optimization. Unlike existing methods, the computation pattern of LQER eliminates the need for specialized Scatter and Gather processes to collect high-precision weights from irregular memory locations. Our W4A8 LLMs achieve near-lossless performance on six popular downstream tasks, while using 1.36× fewer hardware resources than the leading state-of-the-art method. We open-source our framework at https://github.com/ChengZhang-98/lqer