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IEEE ASSP Magazine 1984年第2期1卷 4-29页

作者： Gray, Robert M. Stanford University Stanford CA USA

A vector quantizer is a system for mapping a sequence of continuous or discrete vectors into a digital sequence suitable for communication over or storage in a digital channel. The goal of such a system is data compression: to reduce the bit rate so as to minimize communication channel capacity or digital storage memory requirements while maintaining the necessary fidelity of the data. The mapping for each vector may or may not have memory in the sense of depending on past actions of the coder, just as in well established scalar techniques such as PCM, which has no memory, and predictive quantization, which does. Even though information theory implies that one can always obtain better performance by coding vectors instead of scalars, scalar quantizers have remained by far the most common data compression system because of their simplicity and good performance when the communication rate is sufficiently large. In addition, relatively few design techniques have existed for vector quantizers. During the past few years several design algorithms have been developed for a variety of vector quantizers and the performance of these codes has been studied for speech waveforms, speech linear predictive parameter vectors, images, and several simulated random processes. It is the purpose of this article to survey some of these design techniques and their applications. © 1984, IEEE. All rights reserved.

关键词： vector quantization Data compression Speech processing Speech coding Communication channels Channel capacity Phase change materials Information theory

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vector quantization-driven image compression through multi-objective evolutionary algorithms

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EXPERT SYSTEMS WITH APPLICATIONS 2025年 261卷

作者： Camacho-Gonzalez, Francisco David Lima-Lopez, Daniel Zapotecas-Martinez, Saul Altamirano-Robles, Leopoldo Inst Nacl Astrofis Opt & Electr Comp Sci Dept Tonantzintla 72840 Puebla Mexico

In recent years, information consumption among the population has increased, especially through the widespread use of digital images and videos. Consequently, the demand for efficient compression methods has escalated, aiming to facilitate both data storage and transmission while adapting to the unique requirements of diverse problems. The image compression problem has been explored in several works through the lens of vector quantization (VQ) by adopting a single-objective approach to achieve optimal quality results but with a fixed compression level. In contrast, this investigation introduces a groundbreaking multi-objective compression approach that simultaneously optimizes image quality and compression level. This is achieved by selecting the most representative information to construct an adequate codebook while minimizing its size. The proposed method was evaluated on a curated selection of well-known public domain images, using different types of multi-objective evolutionary algorithms, including Pareto-, indicator- and decomposition-based approaches. The compressed images produced were assessed through the application of established quality indicators drawn from the expansive realm of image processing literature, ensuring the reliability and validity of our findings. The results demonstrate the proposed method's ability to adapt to the intrinsic characteristics of each image, removing the maximum amount of redundant information presented. Furthermore, the multi-objective nature of the proposed approach allows us to obtain solutions with different levels of trade-off between quality and compression, opening up new possibilities in the field and demonstrating the potential to address the evolving challenges posed by the escalating volume of information in the digital landscape.

关键词： Image compression vector quantization Multi-objective optimization Evolutionary multi-objective algorithms

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Representing domain-mixing optical degradation for real-world Computational Aberration Correction via vector quantization

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OPTICS AND LASER TECHNOLOGY 2025年 183卷

作者： Jiang, Qi Yi, Zhonghua Gao, Shaohua Gao, Yao Qian, Xiaolong Shi, Hao Sun, Lei Niu, Jinxing Wang, Kaiwei Yang, Kailun Bai, Jian Zhejiang Univ Coll Opt Sci & Engn State Key Lab Extreme Photon & Instrumentat Hangzhou 310027 Peoples R China Hunan Univ Natl Engn Res Ctr Robot Visual Percept & Control T Changsha 410082 Peoples R China Zhejiang Univ Jiaxing Res Inst Intelligent Opt & Photon Res Ctr Jiaxing 314031 Peoples R China North China Univ Water Resources & Elect Power Sch Mech Engn Zhengzhou 450045 Peoples R China

Relying on paired synthetic data, existing learning-based Computational Aberration Correction (CAC) methods are confronted with the intricate and multifaceted synthetic-to-real domain gap, which leads to suboptimal performance in real-world applications. In this paper, in contrast to improving the simulation pipeline, we deliver a novel insight into real-world CAC from the perspective of Unsupervised Domain Adaptation (UDA). By incorporating readily accessible unpaired real-world data into training, we formalize the Domain Adaptive CAC (DACAC) task, and then introduce a comprehensive Real-world aberrated images (Realab) dataset to benchmark it. The setup task presents a formidable challenge due to the intricacy of understanding the target optical degradation domain. To this intent, we propose a novel Quantized Domain-Mixing Representation (QDMR) framework as a potent solution to the issue. Centering around representing and quantizing the optical degradation which is consistent across different images, QDMR adapts the CAC model to the target domain from three key aspects: (1) reconstructing aberrated images of both domains by a VQGAN to learn a Domain-Mixing Codebook (DMC) characterizing the optical degradation;(2) modulating the deep features in CAC model with DMC to transfer the target domain knowledge;and (3) leveraging the trained VQGAN to generate pseudo target aberrated images from the source ones for convincing target domain supervision. Extensive experiments on both synthetic and real-world benchmarks reveal that the models with QDMR consistently surpass the competitive methods in mitigating the synthetic-to-real gap, which produces visually pleasant real-world CAC results with fewer artifacts. Codes and datasets are made publicly available at https://***/zju-jiangqi/QDMR.

关键词： Optical aberration Optical information processing Computational imaging Computational Aberration Correction vector quantization Unsupervised Domain Adaptation

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Enhanced vector quantization for Embedded Machine Learning: A Post-Training Approach With Incremental Clustering

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IEEE ACCESS 2025年 13卷 17440-17456页

作者： Flores, Thommas K. S. Medeiros, Morsinaldo Silva, Marianne Costa, Daniel G. Silva, Ivanovitch Univ Fed Rio Grande do Norte PPgEEC BR-59078970 Natal Brazil Univ Fed Alagoas SI BR-57200000 Penedo Brazil Univ Porto Fac Engn SYSTEC ARISE P-4200465 Porto Portugal

TinyML enables the deployment of Machine Learning (ML) models on resource-constrained devices, addressing a growing need for efficient, low-power AI solutions. However, significant challenges remain due to strict memory, processing, and energy limitations. This study introduces a novel method to optimize Post-Training quantization (PTQ), a widely used technique for reducing model size, by integrating vector quantization (VQ) with incremental clustering. While VQ is a technique that reduces model size by grouping similar parameters, incremental clustering, implemented via the AutoCloud K-Fixed algorithm, preserves accuracy during compression. This combined approach was validated on an automotive dataset predicting CO2 emissions from vehicle sensor measurements such as mass air flow, intake pressure, temperature, and speed. The model was quantized and deployed on Macchina A0 hardware, demonstrating over 90% compression with negligible accuracy loss. Results show improved performance and deployment efficiency, showcasing the potential of this combined technique for real-world embedded applications.

关键词： Clustering algorithms Computational modeling Accuracy Adaptation models Training Embedded systems Computational efficiency Automotive engineering vector quantization Data models post-training quantization vector quantization automotive sensors pollution

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CSI Acquisition in Internet of Vehicle Network: Federated Edge Learning With Model Pruning and vector quantization

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INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS 2025年第1期2025卷

作者： Wang, Yi Zhi, Junlei Mei, Linsheng Huang, Wei Zhengzhou Univ Aeronaut Sch Elect & Informat Zhengzhou 450046 Henan Peoples R China Zhengzhou Univ Aeronaut Henan Key Lab Gen Aviat Technol Zhengzhou 450046 Henan Peoples R China Hefei Univ Technol Sch Comp Sci & Informat Engn Hefei 230601 Anhui Peoples R China

The conventional machine learning (ML)-based channel state information (CSI) acquisition has overlooked the potential privacy disclosure and estimation overhead problem caused by transmitting pilot datasets during the estimation stage. In this paper, we propose federated edge learning for CSI acquisition to protect the data privacy in the Internet of vehicle network with massive antenna array. To reduce the channel estimation overhead, the joint model pruning and vector quantization algorithm for network gradient parameters is presented to reduce the amount of exchange information between the centralized server and devices. This scheme allows for local fine-tuning to adapt the global model to the channel characteristics of each device. In addition, we also provide theoretical guarantees of convergence and quantization error bound in closed form, respectively. Simulation results demonstrate that the proposed FL-based CSI acquisition with model pruning and vector quantization scheme can efficiently improve the performance of channel estimation while reducing the communication overhead.

关键词： CSI acquisition federated learning Internet of vehicle model pruning vector quantization

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An Efficient vector quantization-Based Semantic Communication System for Virtual Reality Video Transmission

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IEEE Wireless Communications Letters 2025年

作者： Miao, Yongyi Hu, Die Wang, Yang Fudan University School of Information Science and Technology Shanghai200433 China

The large volume of data associated with virtual reality (VR) video presents significant challenges for wireless transmission. This letter proposes an efficient transmission system for VR video, based on semantic vector quantization (VQ) and moving object tracking, termed SeVQ-VR. This system not only substantially reduces the transmission data volume but also ensures full compatibility with existing communication systems. Specifically, it prioritizes the transmission of semantically significant moving objects, optimizing bandwidth utilization. Additionally, it utilizes semantic vector quantization to further compress video feature data by transmitting only the feature indices, while maintaining accurate reconstruction of the content. Simulation results indicate that SeVQ-VR outperforms the H.265 standard in terms of both Multi-Scale Structural Similarity (MS-SSIM) and Learned Perceptual Image Patch Similarity (LPIPS) metrics, especially under low channel signal-to-noise ratio (SNR) in multi-path channels. © 2012 IEEE.

关键词： vector quantization

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Compressing 3D Gaussian Splatting by Noise-Substituted vector quantization

arXiv

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arXiv 2025年

作者： Wang, Haishan Vali, Mohammad Hassan Solin, Arno Department of Computer Science Aalto University Espoo Finland

3D Gaussian Splatting (3DGS) has demonstrated remarkable effectiveness in 3D reconstruction, achieving high-quality results with real-time radiance field rendering. However, a key challenge is the substantial storage cost: reconstructing a single scene typically requires millions of Gaussian splats, each represented by 59 floating-point parameters, resulting in approximately 1 GB of memory. To address this challenge, we propose a compression method by building separate attribute codebooks and storing only discrete code indices. Specifically, we employ noise-substituted vector quantization technique to jointly train the codebooks and model features, ensuring consistency between gradient descent optimization and parameter discretization. Our method reduces the memory consumption efficiently (around 45×) while maintaining competitive reconstruction quality on standard 3D benchmark scenes. Experiments on different codebook sizes show the trade-off between compression ratio and image quality. Furthermore, the trained compressed model remains fully compatible with popular 3DGS viewers and enables faster rendering speed, making it well-suited for practical applications. © 2025, CC BY.

关键词： vector quantization

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VQ-LLM: High-performance Code Generation for vector quantization Augmented LLM Inference

VQ-LLM: High-performance Code Generation for Vector Quantiza...

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IEEE Symposium on High-Performance Computer Architecture

作者： Zihan Liu Xinhao Luo Junxian Guo Wentao Ni Yangjie Zhou Yue Guan Cong Guo Weihao Cui Yu Feng Minyi Guo Yuhao Zhu Minjia Zhang Chen Jin Jingwen Leng Shanghai Jiao Tong University Shanghai Qi Zhi Institute Duke University National University of Singapore University of Rochester University of Illinois Urbana-Champaign Magik Compute

ISBN: (数字)9798331506476

ISBN: (纸本)9798331506483

vector quantization (VQ), which treats a vector as a compression unit, gains increasing research interests for its potential to accelerate large language models (LLMs). Compared to conventional element-wise quantization methods, VQ algorithms can compress weight and KV cache tensors in LLMs with a greater ratio while maintaining the high model accuracy. However, translating a VQ algorithm’s memory reduction into the actual latency improvement is challenging. We profile and analyze the current approach of integrating VQ into computation kernels and show that its major inefficiency lies in the poor access efficiency of codebooks in VQ algorithms and uncoordinated computation dataflow. Meanwhile, the diversity of VQ algorithms (e.g., different vector sizes and entry counts) and LLMs, computation kernels (e.g matrix-matrix/vector multiplication and attention computation) makes it impractical to manually craft efficient kernel implementations for each specific case. In this work, we design and implement VQ-LLM, an efficient fused VQ kernel generation framework. We first introduce a software abstraction called codebook cache to optimize codebook access efficiency and support the integration of VQ with various computations. The codebook cache adaptively stores different entries across the GPU’s memory hierarchy, including off-chip global memory, on-chip shared memory, and registers. Centered around the codebook cache, we design an efficient computation engine that optimizes memory traffic during computations involving codebooks. This compute engine adopts the codebook-centric dataflow and fusion optimizations. Additionally, we provide adaptive heuristics to tailor parameter selection in our optimizations to diverse VQ configurations. Our optimizations achieve the latency reduction of $\mathbf{6 4. 3 6 \%}$ to $\mathbf{9 9. 1 \%}$ compared to existing open-source implementations. A final comparison with state-of-the-art element-wise quantization methods like AWQ and QoQ sho

关键词： Codes Accuracy Translation vector quantization vectors Computational efficiency System-on-chip Kernel Optimization Engines

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A2ATS: Retrieval-Based KV Cache Reduction via Windowed Rotary Position Embedding and Query-Aware vector quantization

arXiv

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arXiv 2025年

作者： He, Junhui Xing, Junna Wang, Nan Xu, Rui Wu, Shangyu Zhou, Peng Liu, Qiang Xue, Chun Jason Li, Qingan Wuhan University China Alibaba Cloud Computing China Jinan University China City University of Hong Kong Hong Kong MBZUAI United Arab Emirates

Long context large language models (LLMs) pose significant challenges for efficient serving due to the large memory footprint and high access overhead of KV cache. Retrieval-based KV cache reduction methods can mitigate these challenges, typically by offloading the complete KV cache to CPU and retrieving necessary tokens on demand during inference. However, these methods still suffer from unsatisfactory accuracy degradation and extra retrieval overhead. To address these limitations, this paper proposes A2ATS, a novel retrieval-based KV cache reduction method. A2ATS aims to obtain an accurate approximation of attention scores by applying the vector quantization technique to key states, thereby enabling efficient and precise retrieval of the top-K tokens. First, we propose Windowed Rotary Position Embedding, which decouples the positional dependency from query and key states after position embedding. Then, we propose query-aware vector quantization that optimizes the objective of attention score approximation directly. Finally, we design the heterogeneous inference architecture for KV cache offloading, enabling long context serving with larger batch sizes. Experimental results demonstrate that A2ATS can achieve a lower performance degradation with similar or lower overhead compared to existing methods, thereby increasing long context serving throughput by up to 2.7×. © 2025, CC BY.

关键词： vector quantization

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SSVQ: Unleashing the Potential of vector quantization with Sign-Splitting

arXiv

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arXiv 2025年

作者： Li, Shuaiting Deng, Juncan Wang, Chengxuan Xu, Kedong Deng, Rongtao Gu, Hong Shen, Haibin Huang, Kejie Zhejiang University China vivo Mobile Communication Co. Ltd China

vector quantization (VQ) has emerged as a prominent weight compression technique, showcasing substantially lower quantization errors than uniform quantization across diverse models, particularly in extreme compression scenarios. However, its efficacy during fine-tuning is limited by the constraint of the compression format, where weight vectors assigned to the same codeword are restricted to updates in the same direction. Consequently, many quantized weights are compelled to move in directions contrary to their local gradient information. To mitigate this issue, we introduce a novel VQ paradigm, Sign-Splitting VQ (SSVQ), which decouples the sign bit of weights from the codebook. Our approach involves extracting the sign bits of uncompressed weights and performing clustering and compression on all-positive weights. We then introduce latent variables for the sign bit and jointly optimize both the signs and the codebook. Additionally, we implement a progressive freezing strategy for the learnable sign to ensure training stability. Extensive experiments on various modern models and tasks demonstrate that SSVQ achieves a significantly superior compression-accuracy trade-off compared to conventional VQ. Furthermore, we validate our algorithm on a hardware accelerator, showing that SSVQ achieves a 3× speedup over the 8-bit compressed model by reducing memory access. Copyright © 2025, The Authors. All rights reserved.

关键词： vector quantization

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