# QuantEase: Optimization-based Quantization for Language Models

arXiv: https://arxiv.org/abs/2309.01885 · HTML: https://mlsanity.com/paper/2309.01885/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 50 references that are in the map.
- First posted on arXiv 5 Sep 2023.

## Builds on (most cited first, 30 of 32)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [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)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [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)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (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)
- [XNOR-Net: ImageNet Classification Using Binary Convolutional Neural Networks](https://mlsanity.com/paper/1603.05279/) (2016)
- [A Survey of Quantization Methods for Efficient Neural Network Inference](https://mlsanity.com/paper/2103.13630/) (2021)
- [The RefinedWeb Dataset for Falcon LLM: Outperforming Curated Corpora with Web Data, and Web Data Only](https://mlsanity.com/paper/2306.01116/) (2023)
- [Up or Down? Adaptive Rounding for Post-Training Quantization](https://mlsanity.com/paper/2004.10568/) (2020)
- [Sparsity in Deep Learning: Pruning and growth for efficient inference and training in neural networks](https://mlsanity.com/paper/2102.00554/) (2021)
- [ZeroQuant: Efficient and Affordable Post-Training Quantization for Large-Scale Transformers](https://mlsanity.com/paper/2206.01861/) (2022)
- [SpQR: A Sparse-Quantized Representation for Near-Lossless LLM Weight Compression](https://mlsanity.com/paper/2306.03078/) (2023)
- [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)
- [Learning to Prune Deep Neural Networks via Layer-wise Optimal Brain Surgeon](https://mlsanity.com/paper/1705.07565/) (2017)
- [Outlier Suppression: Pushing the Limit of Low-bit Transformer Language Models](https://mlsanity.com/paper/2209.13325/) (2022)
- [Soft-to-Hard Vector Quantization for End-to-End Learning Compressible Representations](https://mlsanity.com/paper/1704.00648/) (2017)
- [The BigScience ROOTS Corpus: A 1.6TB Composite Multilingual Dataset](https://mlsanity.com/paper/2303.03915/) (2023)
- [Understanding and Overcoming the Challenges of Efficient Transformer Quantization](https://mlsanity.com/paper/2109.12948/) (2021)
- [XNOR-Net++: Improved Binary Neural Networks](https://mlsanity.com/paper/1909.13863/) (2019)
- [ZeroQuant-V2: Exploring Post-training Quantization in LLMs from Comprehensive Study to Low Rank Compensation](https://mlsanity.com/paper/2303.08302/) (2023)

## Built on by (most cited first, 29 of 29)

- [A Survey on Efficient Inference for Large Language Models](https://mlsanity.com/paper/2404.14294/) (2024)
- [LLM Inference Unveiled: Survey and Roofline Model Insights](https://mlsanity.com/paper/2402.16363/) (2024)
- [Quantization Error Propagation: Revisiting Layer-Wise Post-Training Quantization](https://mlsanity.com/paper/2504.09629/) (2025)
- [GuidedQuant: Large Language Model Quantization via Exploiting End Loss Guidance](https://mlsanity.com/paper/2505.07004/) (2025)
- [A Survey of Low-bit Large Language Models: Basics, Systems, and Algorithms](https://mlsanity.com/paper/2409.16694/) (2024)
- [MagR: Weight Magnitude Reduction for Enhancing Post-Training Quantization](https://mlsanity.com/paper/2406.00800/) (2024)
- [Block Rotation is All You Need for MXFP4 Quantization](https://mlsanity.com/paper/2511.04214/) (2025)
- [ALPS: Improved Optimization for Highly Sparse One-Shot Pruning for Large Language Models](https://mlsanity.com/paper/2406.07831/) (2024)
- [A Comprehensive Survey of Compression Algorithms for Language Models](https://mlsanity.com/paper/2401.15347/) (2024)
- [COMQ: A Backpropagation-Free Algorithm for Post-Training Quantization](https://mlsanity.com/paper/2403.07134/) (2024)
- [Benchmarking Post-Training Quantization in LLMs: Comprehensive Taxonomy, Unified Evaluation, and Comparative Analysis](https://mlsanity.com/paper/2502.13178/) (2025)
- [Multilingual Brain Surgeon: Large Language Models Can be Compressed Leaving No Language Behind](https://mlsanity.com/paper/2404.04748/) (2024)
- [Effective Quantization of Muon Optimizer States](https://mlsanity.com/paper/2509.23106/) (2025)
- [Scaling Laws for Floating Point Quantization Training](https://mlsanity.com/paper/2501.02423/) (2025)
- [A Survey of Transformer-based Language Models with Focus on Efficiency](https://mlsanity.com/paper/2406.16893/) (2024)
- [LPCD: Unified Framework from Layer-Wise to Submodule Quantization](https://mlsanity.com/paper/2512.01546/) (2025)
- [CoreQ: Learning-Free Mismatch Correction and Successive Rounding for Quantization](https://mlsanity.com/paper/2602.05902/) (2026)
- [CLoQ: Enhancing Fine-Tuning of Quantized LLMs via Calibrated LoRA Initialization](https://mlsanity.com/paper/2501.18475/) (2025)
- [CDQuant: Greedy Coordinate Descent for Accurate LLM Quantization](https://mlsanity.com/paper/2406.17542/) (2024)
- [Achieving Peak Performance for Large Language Models: A Systematic Review](https://mlsanity.com/paper/2409.04833/) (2024)
- [DynaMo: Runtime Switchable Quantization for MoE with Cross-Dataset Adaptation](https://mlsanity.com/paper/2503.21135/) (2025)
- [TropNNC: Structured Neural Network Compression Using Tropical Geometry](https://mlsanity.com/paper/2409.03945/) (2024)
- [DiscQuant: A Quantization Method for Neural Networks Inspired by Discrepancy Theory](https://mlsanity.com/paper/2501.06417/) (2025)
- [3BASiL: An Algorithmic Framework for Sparse plus Low-Rank Compression of LLMs](https://mlsanity.com/paper/2603.01376/) (2026)
- [Semantic Retention and Extreme Compression in LLMs: Can We Have Both?](https://mlsanity.com/paper/2505.07289/) (2025)
- [OSAQ: Outlier Self-Absorption for Accurate Low-bit LLM Quantization](https://mlsanity.com/paper/2605.04738/) (2026)
- [SchurQuant: Groupwise Discrete Optimization for Layer-Wise LLM Quantization](https://mlsanity.com/paper/2608.15567/) (2026)
- [JARQ: Joint Alternating Refinement for Quantization](https://mlsanity.com/paper/2609.38599/) (2026)
- [DualQuant: Dual-scale Calibration-free Weight-and-Activation Quantization for LLMs](https://mlsanity.com/paper/2610.13767/) (2026)

## Abstract (arXiv)

With the rising popularity of Large Language Models (LLMs), there has been an increasing interest in compression techniques that enable their efficient deployment. This study focuses on the Post-Training Quantization (PTQ) of LLMs. Drawing from recent advances, our work introduces QuantEase, a layer-wise quantization framework where individual layers undergo separate quantization. The problem is framed as a discrete-structured non-convex optimization, prompting the development of algorithms rooted in Coordinate Descent (CD) techniques. These CD-based methods provide high-quality solutions to the complex non-convex layer-wise quantization problems. Notably, our CD-based approach features straightforward updates, relying solely on matrix and vector operations, circumventing the need for matrix inversion or decomposition. We also explore an outlier-aware variant of our approach, allowing for retaining significant weights (outliers) with complete precision. Our proposal attains state-of-the-art performance in terms of perplexity and zero-shot accuracy in empirical evaluations across various LLMs and datasets, with relative improvements up to 15% over methods such as GPTQ. Leveraging careful linear algebra optimizations, QuantEase can quantize models like Falcon-180B on a single NVIDIA A100 GPU in ~3 hours. Particularly noteworthy is our outlier-aware algorithm's capability to achieve near or sub-3-bit quantization of LLMs with an acceptable drop in accuracy, obviating the need for non-uniform quantization or grouping techniques, improving upon methods such as SpQR by up to two times in terms of perplexity.