# Norm Tweaking: High-performance Low-bit Quantization of Large Language Models

arXiv: https://arxiv.org/abs/2309.02784 · HTML: https://mlsanity.com/paper/2309.02784/

## Key facts

- Cited by 33 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 38 references that are in the map.
- First posted on arXiv 6 Sep 2023.

## Builds on (most cited first, 30 of 31)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [OPT: Open Pre-trained Transformer Language Models](https://mlsanity.com/paper/2205.01068/) (2022)
- [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)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [Root Mean Square Layer Normalization](https://mlsanity.com/paper/1910.07467/) (2019)
- [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)
- [SparseGPT: Massive Language Models Can Be Accurately Pruned in One-Shot](https://mlsanity.com/paper/2301.00774/) (2023)
- [GLM: General Language Model Pretraining with Autoregressive Blank Infilling](https://mlsanity.com/paper/2103.10360/) (2021)
- [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)
- [LLM-Pruner: On the Structural Pruning of Large Language Models](https://mlsanity.com/paper/2305.11627/) (2023)
- [FlexGen: High-Throughput Generative Inference of Large Language Models with a Single GPU](https://mlsanity.com/paper/2303.06865/) (2023)
- [ERNIE: Enhanced Language Representation with Informative Entities](https://mlsanity.com/paper/1905.07129/) (2019)
- [ZeroQuant: Efficient and Affordable Post-Training Quantization for Large-Scale Transformers](https://mlsanity.com/paper/2206.01861/) (2022)
- [DeepSpeed Inference: Enabling Efficient Inference of Transformer Models at Unprecedented Scale](https://mlsanity.com/paper/2207.00032/) (2022)
- [LLM-QAT: Data-Free Quantization Aware Training for Large Language Models](https://mlsanity.com/paper/2305.17888/) (2023)
- [LoSparse: Structured Compression of Large Language Models based on Low-Rank and Sparse Approximation](https://mlsanity.com/paper/2306.11222/) (2023)
- [ZeroQuant-V2: Exploring Post-training Quantization in LLMs from Comprehensive Study to Low Rank Compensation](https://mlsanity.com/paper/2303.08302/) (2023)
- [Compress, Then Prompt: Improving Accuracy-Efficiency Trade-off of LLM Inference with Transferable Prompt](https://mlsanity.com/paper/2305.11186/) (2023)

## Built on by (most cited first, 30 of 33)

- [KVQuant: Towards 10 Million Context Length LLM Inference with KV Cache Quantization](https://mlsanity.com/paper/2401.18079/) (2024)
- [A Survey on Efficient Inference for Large Language Models](https://mlsanity.com/paper/2404.14294/) (2024)
- [MobileVLM V2: Faster and Stronger Baseline for Vision Language Model](https://mlsanity.com/paper/2402.03766/) (2024)
- [DuQuant: Distributing Outliers via Dual Transformation Makes Stronger Quantized LLMs](https://mlsanity.com/paper/2406.01721/) (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)
- [MobileVLM : A Fast, Strong and Open Vision Language Assistant for Mobile Devices](https://mlsanity.com/paper/2312.16886/) (2023)
- [PB-LLM: Partially Binarized Large Language Models](https://mlsanity.com/paper/2310.00034/) (2023)
- [VisionLLaMA: A Unified LLaMA Backbone for Vision Tasks](https://mlsanity.com/paper/2403.00522/) (2024)
- [LORD: Low Rank Decomposition Of Monolingual Code LLMs For One-Shot Compression](https://mlsanity.com/paper/2309.14021/) (2023)
- [I-LLM: Efficient Integer-Only Inference for Fully-Quantized Low-Bit Large Language Models](https://mlsanity.com/paper/2405.17849/) (2024)
- [Oaken: Fast and Efficient LLM Serving with Online-Offline Hybrid KV Cache Quantization](https://mlsanity.com/paper/2503.18599/) (2025)
- [Low-bit Model Quantization for Deep Neural Networks: A Survey](https://mlsanity.com/paper/2505.05530/) (2025)
- [Anda: Unlocking Efficient LLM Inference with a Variable-Length Grouped Activation Data Format](https://mlsanity.com/paper/2411.15982/) (2024)
- [HiRE: High Recall Approximate Top-k Estimation for Efficient LLM Inference](https://mlsanity.com/paper/2402.09360/) (2024)
- [MorphServe: Efficient and Workload-Aware LLM Serving via Runtime Quantized Layer Swapping and KV Cache Resizing](https://mlsanity.com/paper/2506.02006/) (2025)
- [Pruning Large Language Models via Accuracy Predictor](https://mlsanity.com/paper/2309.09507/) (2023)
- [RaanA: A Fast, Flexible, and Data-Efficient Post-Training Quantization Algorithm](https://mlsanity.com/paper/2504.03717/) (2025)
- [Achieving Peak Performance for Large Language Models: A Systematic Review](https://mlsanity.com/paper/2409.04833/) (2024)
- [Deploying Foundation Model Powered Agent Services: A Survey](https://mlsanity.com/paper/2412.13437/) (2024)
- [LlamaRestTest: Effective REST API Testing with Small Language Models](https://mlsanity.com/paper/2501.08598/) (2025)
- [Qrazor: Reliable and Effortless 4-bit LLM Quantization by Significant Data Razoring](https://mlsanity.com/paper/2501.13331/) (2025)
- [Enhancing Ultra-Low-Bit Quantization of Large Language Models Through Saliency-Aware Partial Retraining](https://mlsanity.com/paper/2504.13932/) (2025)
- [Q-resafe: Assessing Safety Risks and Quantization-aware Safety Patching for Quantized Large Language Models](https://mlsanity.com/paper/2506.20251/) (2025)
- [D2Quant: Accurate Low-bit Post-Training Weight Quantization for LLMs](https://mlsanity.com/paper/2602.02546/) (2026)
- [Mobile-VideoGPT: Fast and Accurate Model for Mobile Video Understanding](https://mlsanity.com/paper/2503.21782/) (2025)
- [Integer Scale: A Free Lunch for Faster Fine-grained Quantization of LLMs](https://mlsanity.com/paper/2405.14597/) (2024)
- [Superpipeline: A Universal Approach for Reducing GPU Memory Usage in Large Models](https://mlsanity.com/paper/2410.08791/) (2024)
- [An Evaluation of LLMs Inference on Popular Single-board Computers](https://mlsanity.com/paper/2511.07425/) (2025)
- [Benford's Law as a Distributional Prior for Post-Training Quantization of Large Language Models](https://mlsanity.com/paper/2602.00165/) (2026)

## Abstract (arXiv)

As the size of large language models (LLMs) continues to grow, model compression without sacrificing accuracy has become a crucial challenge for deployment. While some quantization methods, such as GPTQ, have made progress in achieving acceptable 4-bit weight-only quantization, attempts at lower-bit quantization often result in severe performance degradation. In this paper, we introduce a technique called norm tweaking, which can be used as a plugin in current PTQ methods to achieve high precision while being cost-efficient. Our approach is inspired by the observation that rectifying the quantized activation distribution to match its float counterpart can readily restore accuracy for LLMs. To achieve this, we carefully design a tweaking strategy that includes calibration data generation and channel-wise distance constraint to update the weights of normalization layers for better generalization. We conduct extensive experiments on various datasets using several open-sourced LLMs. Our method demonstrates significant improvements in both weight-only quantization and joint quantization of weights and activations, surpassing existing PTQ methods. On GLM-130B and OPT-66B, our method even achieves the same level of accuracy at 2-bit quantization as their float ones. Our simple and effective approach makes it more practical for real-world applications.