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Linear regression is a widely used technique to fit linear models and finds widespread applications across different areas such as machine learning and statistics. In most real-world scenarios, however, linear regression problems are often…

Quantum Physics · Physics 2023-05-02 Shantanav Chakraborty , Aditya Morolia , Anurudh Peduri

Recent work in machine learning community proposed multiple methods for performing lossy compression (quantization) of large matrices. This quantization is important for accelerating matrix multiplication (main component of large language…

Information Theory · Computer Science 2025-10-16 Or Ordentlich , Yury Polyanskiy

Post-training quantization (PTQ) techniques applied to weights, activations, and the KV cache greatly reduce memory usage, latency, and power consumption of Large Language Models (LLMs), but may lead to large quantization errors when…

We study Sigma-Delta quantization methods coupled with appropriate reconstruction algorithms for digitizing randomly sampled low-rank matrices. We show that the reconstruction error associated with our methods decays polynomially with the…

Information Theory · Computer Science 2018-04-18 Eric Lybrand , Rayan Saab

As large language models become standard backends for content generation, practical provenance increasingly requires multi-bit watermarking. In provider-internal deployments, a key requirement is message symmetry: the message itself should…

Computation and Language · Computer Science 2026-04-16 Junlin Zhu , Baizhou Huang , Xiaojun Wan

Layer-wise quantization is a key technique for efficiently compressing large models without expensive retraining. Previous methods typically quantize the weights of each layer by "uniformly" optimizing the layer reconstruction loss across…

Machine Learning · Computer Science 2025-03-04 Yi-Lin Sung , Prateek Yadav , Jialu Li , Jaehong Yoon , Mohit Bansal

Post-Training Quantization (PTQ) is crucial for efficient model deployment, yet its effectiveness on Ascend NPU remains under-explored compared to GPU architectures. This paper presents a case study of representative PTQ baselines applied…

Machine Learning · Computer Science 2026-02-23 Yuchen Luo , Fangyue Zhu , Ruining Zhou , Mingzhe Huang , Jian Zhu , Fanyu Fan , Wei Shao

Large Language Models (LLMs) have greatly advanced the natural language processing paradigm. However, the high computational load and huge model sizes pose a grand challenge for deployment on edge devices. To this end, we propose APTQ…

Machine Learning · Computer Science 2024-04-17 Ziyi Guan , Hantao Huang , Yupeng Su , Hong Huang , Ngai Wong , Hao Yu

Quantization is a key method for deploying deep neural networks on edge devices with limited memory and computation resources. Recent improvements in Post-Training Quantization (PTQ) methods were achieved by an additional local optimization…

Computer Vision and Pattern Recognition · Computer Science 2024-09-27 Ofir Gordon , Elad Cohen , Hai Victor Habi , Arnon Netzer

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…

Machine Learning · Computer Science 2024-05-31 Cheng Zhang , Jianyi Cheng , George A. Constantinides , Yiren Zhao

We introduce GPTAQ, a novel finetuning-free quantization method for compressing large-scale transformer architectures. Unlike the previous GPTQ method, which independently calibrates each layer, we always match the quantized layer's output…

Machine Learning · Computer Science 2025-05-15 Yuhang Li , Ruokai Yin , Donghyun Lee , Shiting Xiao , Priyadarshini Panda

Quantization is an effective strategy to reduce the storage and computation footprint of large language models (LLMs). Post-training quantization (PTQ) is a leading approach for compressing LLMs. Popular weight quantization procedures,…

Machine Learning · Computer Science 2026-05-13 Ryan Lucas , Mehdi Makni , Xiang Meng , Adam Deng , Rahul Mazumder

Quantization of neural networks has become common practice, driven by the need for efficient implementations of deep neural networks on embedded devices. In this paper, we exploit an oft-overlooked degree of freedom in most networks - for a…

Machine Learning · Computer Science 2019-02-07 Eldad Meller , Alexander Finkelstein , Uri Almog , Mark Grobman

Low-bit quantization is challenging to maintain high performance with limited model capacity (e.g., 4-bit for both weights and activations). Naturally, the distribution of both weights and activations in deep neural network are…

Computer Vision and Pattern Recognition · Computer Science 2019-08-06 Haibao Yu , Tuopu Wen , Guangliang Cheng , Jiankai Sun , Qi Han , Jianping Shi

Low-bit post-training quantization (PTQ) is a practical route to deploy reasoning-capable LLMs under tight memory and latency budgets, yet it can markedly impair mathematical reasoning (drops up to 69.81% in our harder settings). We address…

Machine Learning · Computer Science 2026-01-21 Zhen Li , Yupeng Su , Songmiao Wang , Runming Yang , Congkai Xie , Aofan Liu , Ming Li , Jiannong Cao , Yuan Xie , Ngai Wong , Hongxia Yang

For large language models (LLMs), post-training quantization (PTQ) can significantly reduce memory footprint and computational overhead. Model quantization is rapidly evolving. Though many papers report breakthrough results, they are often…

Machine Learning · Computer Science 2026-01-30 Yutong Liu , Cairong Zhao , Guosheng Hu

We consider the problem of model compression for Large Language Models (LLMs) at post-training time, where the task is to compress a well-trained model using only a small set of calibration input data. In this work, we introduce a new…

Machine Learning · Statistics 2024-12-12 Meyer Scetbon , James Hensman

Diffusion models have achieved remarkable success in image generation but come with significant computational costs, posing challenges for deployment in resource-constrained environments. Recent post-training quantization (PTQ) methods have…

Computer Vision and Pattern Recognition · Computer Science 2025-07-18 Dongyeun Lee , Jiwan Hur , Hyounguk Shon , Jae Young Lee , Junmo Kim

Large Language Models (LLMs) suffer severe performance degradation when facing extremely low-bit (sub 2-bit) quantization. Several existing sub 2-bit post-training quantization (PTQ) methods utilize a mix-precision scheme by leveraging an…

Machine Learning · Computer Science 2025-08-07 Jiaqi Zhao , Miao Zhang , Ming Wang , Yuzhang Shang , Kaihao Zhang , Weili Guan , Yaowei Wang , Min Zhang

The advancements of hardware technology in recent years has brought many possibilities for low-precision applications. However, the use of low precision can introduce significant computational errors, posing a considerable challenge to…

Mathematical Software · Computer Science 2024-09-30 Hongyaoxing Gu