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Finding the densest sphere packing in $d$-dimensional Euclidean space $\mathbb{R}^d$ is an outstanding fundamental problem with relevance in many fields, including the ground states of molecular systems, colloidal crystal structures, coding…

Statistical Mechanics · Physics 2013-06-12 Étienne Marcotte , Salvatore Torquato

Several post-training quantization methods have been applied to large language models (LLMs), and have been shown to perform well down to 8-bits. We find that these methods break down at lower bit precision, and investigate quantization…

Computation and Language · Computer Science 2023-05-30 Zechun Liu , Barlas Oguz , Changsheng Zhao , Ernie Chang , Pierre Stock , Yashar Mehdad , Yangyang Shi , Raghuraman Krishnamoorthi , Vikas Chandra

Recently, video language models (VLMs) have been applied in various fields. However, the visual token sequence of the VLM is too long, which may cause intolerant inference latency and GPU memory usage. Existing methods propose…

Computer Vision and Pattern Recognition · Computer Science 2026-05-05 Wei Tao , Xiaoyang Qu , Peiqiang Wang , Guokuan Li , Jiguang Wan , Kai Lu , Jianzong Wang

Multimodal Large Language Models (MLLMs) have demonstrated impressive capabilities in cross-modal understanding, but remain vulnerable to adversarial attacks through visual inputs despite robust textual safety mechanisms. These…

Cryptography and Security · Computer Science 2025-11-21 Wei Zhao , Zhe Li , Yige Li , Jun Sun

Post-training quantization (PTQ) is a promising approach to reducing the storage and computational requirements of large language models (LLMs) without additional training cost. Recent PTQ studies have primarily focused on quantizing only…

Machine Learning · Computer Science 2026-02-17 Reena Elangovan , Charbel Sakr , Anand Raghunathan , Brucek Khailany

Large language models (LLMs) have shown remarkable performance in various domains, but they are constrained by massive computational and storage costs. Quantization, an effective technique for compressing models to fit resource-limited…

Computation and Language · Computer Science 2026-04-14 Han Liu , Haotian Gao , Xiaotong Zhang , Changya Li , Feng Zhang , Wei Wang , Fenglong Ma , Hong Yu

Post-training quantization is essential for deploying Large Language Models (LLMs) on resource-constrained devices. However, standard integer quantization (e.g., INT4) fundamentally degrades performance by imposing a uniform grid on the…

Machine Learning · Computer Science 2026-01-13 Vladimer Khasia

The present work surveys problems in $n$-dimensional space with $n$ large. Early development in the study of packing and covering in high dimensions was motivated by the geometry of numbers. Subsequent results, such as the discovery of the…

Metric Geometry · Mathematics 2022-02-24 Gábor Fejes Tóth

Large language models (LLMs) have shown promising performance across various tasks. However, their autoregressive decoding process poses significant challenges for efficient deployment on existing AI hardware. Quantization alleviates memory…

Machine Learning · Computer Science 2025-12-01 Guanxi Lu , Hao Mark Chen , Zhiqiang Que , Wayne Luk , Hongxiang Fan

Recently, sharing key-value (KV) cache across layers has been found effective in efficient inference of large language models (LLMs). To systematically investigate different techniques of cross-layer KV sharing, we propose a unified…

Computation and Language · Computer Science 2025-02-06 You Wu , Haoyi Wu , Kewei Tu

Post-training quantization (PTQ) is an effective technique for compressing large language models (LLMs). However, while uniform-precision quantization is computationally efficient, it often compromises model performance. To address this, we…

Machine Learning · Computer Science 2025-05-27 Wei Huang , Haotong Qin , Yangdong Liu , Yawei Li , Qinshuo Liu , Xianglong Liu , Luca Benini , Michele Magno , Shiming Zhang , Xiaojuan Qi

We reveal that low-bit quantization favors undertrained large language models (LLMs) by observing that models with larger sizes or fewer training tokens experience less quantization-induced degradation (QiD) when applying low-bit…

Machine Learning · Computer Science 2024-11-28 Xu Ouyang , Tao Ge , Thomas Hartvigsen , Zhisong Zhang , Haitao Mi , Dong Yu

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

Large language models (LLMs) show impressive performance in solving complex language tasks. However, its large number of parameters presents significant challenges for the deployment. So, compressing LLMs to low bits can enable to deploy on…

Vector Quantization (VQ) is essential for discretizing continuous representations in unsupervised learning but suffers from representation collapse, causing low codebook utilization and limiting scalability. Existing solutions often rely on…

Machine Learning · Computer Science 2025-10-06 Yongxin Zhu , Bocheng Li , Yifei Xin , Zhihua Xia , Linli Xu

Autoregressive decoding in large language models (LLMs) requires caching a growing list of past key-value (KV) pairs, making long-context inference a memory-bound problem. While recent methods have explored quantizing the cache, evicting…

Computation and Language · Computer Science 2025-10-08 Harshil Vejendla

The quadratic complexity of the attention mechanism and the substantial memory footprint of the Key-Value (KV) cache present severe computational and memory challenges for Large Language Models (LLMs) processing long contexts. Existing…

Machine Learning · Computer Science 2026-03-10 Dongfang Li , Zixuan Liu , Gang Lin , Baotian Hu , Min Zhang

Goal-oriented de novo molecule design, namely generating molecules with specific property or substructure constraints, is a crucial yet challenging task in drug discovery. Existing methods, such as Bayesian optimization and reinforcement…

Computational Engineering, Finance, and Science · Computer Science 2025-02-28 Chuanliu Fan , Ziqiang Cao , Zicheng Ma , Nan Yu , Yimin Peng , Jun Zhang , Yiqin Gao , Guohong Fu

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

As large language models (LLMs) grow in size and deployment scale, quantization has become an essential technique for reducing memory footprint and improving inference efficiency. However, existing quantization toolkits often lack…

Machine Learning · Computer Science 2025-12-01 Dong Liu , Yanxuan Yu