Vector Quantization

Also known as VQ

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8 papers in the last four weeks, level with the four weeks before. 0.1% of all new papers.

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Jul 17, 2026cs.CV

Distributional Matching for Vector Quantization: A Unified Theoretical and Empirical Framework

The effectiveness of modern visual representation learning and autoregressive models critically depends on vector quantization (VQ), which discretizes continuous feature representations using a learnable codebook. Despite its widespread use, existing VQ methods often suffer from training instability and codebook collapse, arising from gradient mismatch induced by the straight-through estimator and the under-utilization of code vectors. In this work, we show that both issues can be traced to a fundamental mismatch between the distributions of feature vectors and code vectors, leading to inefficient representation and information loss. Building on this observation, we propose a distributional matching framework for vector quantization. We introduce principled criteria for desirable VQ behavior and demonstrate through theoretical analysis and empirical evaluation that aligning feature and code vector distributions provides a unifying mechanism for mitigating training instability and codebook collapse. We instantiate this framework using a Wasserstein-based objective with an efficient closed-form under a mild Gaussian approximation, and further show that a nonparametric alternative based on maximum mean discrepancy yields comparable performance. Extensive experiments on visual tokenization benchmarks support the effectiveness and robustness of the proposed approach.

Xianghong Fang, Litao Guo, Hengchao Chen +8

University of Toronto · The Hong Kong University of Science and Technology · Lehigh University +2

Distribution Matching Vector Quantization

Jul 14, 2026cs.LG

AVQ-Attention: Adaptive Vector-Quantized Attention

The

\mathcal{O}(N^2)

complexity of attention over

N

tokens remains a computational bottleneck in transformer models. Vector-Quantized (VQ) attention reduces this to

\mathcal{O}(MN)

by representing keys with

M

codewords, but applies uniform codebook capacity regardless of where attention mass concentrates: high-attention regions of key space may be coarsely approximated while low-attention regions waste representational capacity. We propose Adaptive Vector-Quantized (AVQ) Attention, which adaptively allocates codebook capacity based on attention importance. Starting from a small set of codewords, our method identifies the most important codes during the forward pass and refines them with pre-learned child codewords, achieving fine-grained quantization where it matters most while maintaining coarse quantization elsewhere. We develop an implementation using custom Triton kernels that enables the full adaptive refinement process, including importance scoring, child codeword insertion, and parent contribution replacement, to be carried out within the tiled computation paradigm of Flash Attention with minimal overhead. Our approach maintains

\mathcal{O}(MN)

complexity while achieving improved accuracy-efficiency trade-offs compared to fixed-codebook VQ-attention.

Winfried van den dool, Patrick Forré, Amir Habibian +2

QUVA Lab, University of Amsterdam, The Netherlands · AMLab, Informatics Institute, University of Amsterdam, The Netherlands · AI4Science Lab, University of Amsterdam, The Netherlands +3

Transformer Attention Vector Quantization Efficient Attention Attention Quantization

Jul 6, 2026cs.CV

Clustered Codebook Quantization for 2D Gaussian-based Image Compression

Gaussian-based image representations effectively model image content using compact parametric primitives while preserving high visual fidelity, yet storing a large number of floating-point parameters per primitive degrades rate-distortion efficiency at higher fidelity targets. To improve the rate-distortion performance in Gaussian representation, we present our Cluster-Guided Vector Quantization (CGVQ), a Gaussian primitive based image compression method. Our key idea is to partition Gaussian parameters further into homogeneous groups prior to quantization, enabling higher compression efficiency and accurate parameter reconstruction. In practice, our extensive experiments show that CGVQ decreases the bpp by 20% with respect to our baseline, while maintaining on-par visual quality

Runze Cheng, Yicheng Zhan, Josef Spjut +1

University College London · London, UK · NVIDIA +1

Learned Image Compression Vector Quantization

Jul 2, 2026cs.CV

Sparse-Aware Vector Quantization for Bandwidth-Efficient Collaborative 3D Semantic Occupancy Prediction

Collaborative perception extends single-agent perception by enabling multiple vehicles to exchange complementary perceptual information. However, it introduces an inherent trade-off between perception gain and communication overhead, which is particularly severe for 3D semantic occupancy prediction that relies on fine-grained spatial structures. Existing methods typically compress 3D features into 2D, causing severe spatial information loss, or transmit dense 3D representations, hindering real-world deployment. To overcome these limitations, we propose a bandwidth-efficient collaborative Vector Quantization Semantic Occupancy Prediction (VQSOP) framework. VQSOP employs a Sparse-Aware Vector Quantization (SAVQ) mechanism that exploits 3D scene sparsity to compactly encode informative regions, drastically reducing communication overhead while preserving complete geometric context. Furthermore, to enhance structural consistency and feature continuity, we design a Dual-Branch Adaptive Spatial Refinement (ASR) module that dynamically fuses local high-frequency details with broad contextual semantics. Extensive experiments demonstrate that our approach achieves state-of-the-art performance while reducing communication volume by up to 82x.

Feng Li, Chaokun Zhang, Gong Chen

School of Computer Science and Technology, Tianjin University, Tianjin, China · School of Cybersecurity, Tianjin University, Tianjin, China

Communication-Efficient Collaborative Perception 3D Occupancy Prediction Vector Quantization Cooperative Perception

Jul 1, 2026cs.LG

GSRQ: Gain-Shape Residual Quantization for Sub-1-bit KV Cache

The deployment of Large Language Models (LLMs) with extended context windows is increasingly constrained by the linear growth of Key-Value (KV) cache memory. Vector Quantization (VQ), particularly Residual Quantization (RQ), is a promising approach for pushing KV cache storage toward the sub-1-bit regime by progressively encoding residuals with small codebooks. However, most VQ methods still rely on standard

\ell_2

K

-means as the core codebook-learning primitive. We identify a subtle high-dimensional issue of this primitive: Euclidean centroid averaging can induce centroid shrinkage, which weakens the angular alignment term in the

\ell_2

distortion and makes directional preservation harder. To address this issue, we propose Gain-Shape

K

-means (GSKM), a drop-in replacement for

K

-means that improves directional fidelity while matching, and in some regimes improving,

\ell_2

distortion. We then build Gain-Shape Residual Quantization (GSRQ) by incorporating a weighted extension of GSKM into an RQ pipeline. On LLaMA-3-8B, GSRQ substantially improves over strong KV cache quantization baselines across bit rates. At 1-bit, it improves the average accuracy across LongBench tasks from 11.34 to 33.54, a gain of 22.20 percentage points over VQLLM.

Soosung Kim, Minjae Park, Eui-Young Chung +1

Department of Electrical and Electronic Engineering, Yonsei University, Seoul, Republic of Korea · Department of Systems Semiconductor Engineering, Yonsei University, Seoul, Republic of Korea

LLM Compression Residual VQ KV Caching Clustering Vector Quantization KV-Cache Quantization+1

Jun 30, 2026cs.CV

GEAR: Guided End-to-End AutoRegression for Image Synthesis

Visual generative models are typically trained in two stages. A tokenizer is first trained for reconstruction and then frozen, after which a generator is trained on its discrete indices or continuous latents. This decoupling leaves the tokenizer unaware of what the generator finds easy to model. We present GEAR (Guided End-to-end AutoRegression), which trains a vector-quantized (VQ) tokenizer and an autoregressive (AR) generator jointly and end-to-end, guided by representation alignment. The key obstacle is that the VQ index fed to the AR model is non-differentiable, so gradients cannot reach the tokenizer, and a straight-through estimator collapses. GEAR resolves this with a dual read-out of the codebook assignment. A hard, one-hot branch trains the AR with next-token prediction, while a differentiable soft branch carries a representation-alignment loss that flows back to guide only the tokenizer. The AR model thereby steers its tokenizer toward an index distribution it can predict more easily. This shifts the alignment burden from the tokenizer to the AR: the tokenizer's own features become less DINOv2-like while the AR's become more so, the opposite of diffusion-side recipes that make the latent itself semantic. GEAR speeds up ImageNet gFID convergence by up to 10x relative to the strong LlamaGen-REPA baseline, learns markedly better patch-level and spatially-coherent features, and generalizes across quantizers (VQVAE, LFQ, IBQ) and to text-to-image generation.

Bin Lin, Zheyuan Liu, Chenguo Lin +8

Peking University · Tencent Hunyuan

Vector Quantization Autoregressive Image Generation Representation Alignment

Jun 26, 2026cs.CV

CascadeOcc: Rethinking 3D Occupancy World Models with Cascaded VQ Representations

This letter proposes CascadeOcc, a novel occupancy world model that prioritizes intrinsic structural hierarchy over extrinsic auxiliary modalities for autonomous driving. Occupancy world models -- forecasting the future driving environment and planning the driving trajectory -- effectively bridge perception and planning, but current approaches often heavily rely on external modalities or large language models, failing to fully exploit the inherent structural potential of occupancy representations themselves. To enhance representational capacity for complex 3D scenes, we integrate a cascaded Vector Quantized (VQ) mechanism into an autoregressive framework. Following a coarse-to-fine principle, CascadeOcc progressively refines fine-grained details from global structures through a multi-scale architecture. Additionally, we incorporate a TimeMixer to capture multi-scale temporal dependencies, establishing a dual-hierarchy mechanism in both space and time. Experimental results on 4D occupancy forecasting and motion planning benchmarks demonstrate that CascadeOcc achieves superior performance among vision-centric approaches, validating that optimizing inherent representations is a powerful alternative to relying on external foundation models.

Kyumin Hwang, Wonhyeok Choi, Jaeyeul Kim +3

Daegu Gyeongbuk Institute of Science and Technology (DGIST), Daegu 42988, South Korea

World Model Learning 3D Occupancy Prediction Vector Quantization World Models for Autonomous Driving Autonomous Driving Planning

Jun 25, 2026cs.CV

Safe Autoregressive Image Generation with Iterative Self-Improving Codebooks

Unlike diffusion-based models that operate in continuous latent spaces, autoregressive unified multimodal models produce images by sequentially predicting discretized visual tokens. These tokens are derived from a codebook that maps embeddings to quantized visual patterns. The language-like architecture enables unified multimodal models to effectively capture text conditional information for generation, making them promising for text-to-image tasks. This also raises an interesting question: how safe are the images generated in such an autoregressive way? In this work, we propose iterative self-improving codebooks for safe autoregressive generation. We leverage the understanding and judgment capabilities of the unified multimodal model itself to identify unsafe generated images without human annotation. Subsequently, the inherent representations in the codebook are fixed to eliminate harmful mappings. Our method comprises two steps: first, we use the unified model to identify unsafe generations and construct corresponding harmful and safe image-text pairs. These pairs are used to construct the Harmful Space and guide updates to the codebook, thereby eliminating harmful outputs. Second, we perform adaptive fine-tuning on the codebook within the harmless space using safe image-text pairs to ensure the quality of generated images. These two steps are repeated until no further improvement is observed, producing a safety-enhanced model codebook. Without additional external feedback, the safety of models is improved iteratively.

Yunqi Xue, Zhijiang Li, Philip Torr +1

School of Information Management, Wuhan University, Wuhan, China · Torr Vision Group, University of Oxford, Oxford, United Kingdom

T2I Generation Image Generation Safe T2I Generation Vector Quantization Autoregressive Image Generation

Jun 24, 2026cs.SD

Enhancing BEST-RQ Pseudo-Label Quality through Online Refinement for Automatic Speech Recognition

BEST-RQ is a simple and effective self-supervised training method for speech representation learning that performs well on automatic speech recognition (ASR) tasks. It generates pseudolabels using a fixed online quantization scheme, which simplifies training but provides weaker supervision than HuBERT-style models that iteratively refine pseudo-labels. In this work, we improve online pseudo-label generation while preserving simplicity. We propose three modifications: replacing the quantizer's linear projection with Principal Component Analysis (PCA), updating the codebook via iterative codebook refinement, and introducing an additional codebook updated via codebook distillation. We pre-train on the LibriSpeech 960-hour dataset and fine-tune using 100 hours of supervised LibriSpeech data. With all three modifications enabled, we achieve a 12% relative reduction in word error rate (WER) on the LibriSpeech test-other set, improving from 10.1% to 8.8%.

Jingjing Xu, Zijian Yang, Mohammad Zeineldeen +3

Machine Learning and Human Language Technology Group, RWTH Aachen University, Germany · Apptek GmbH, Aachen, Germany

Automatic Speech Recognition Vector Quantization Pseudo-Labeling Self-Supervised Speech Representation Learning

Jun 19, 2026cs.RO

VQActFlow: Vector-Quantized Action Mode Steering for Multi-Task Robot Manipulation

Multi-task robot manipulation policies are challenging to learn from demonstration because traditionally a single network must select among qualitatively different action modes from a multimodal demonstration distribution, conditioned on language and visual context. A wrong mode selection means executing the wrong task or an action infeasible in the scene. Tokenizing continuous actions into a learned discrete codebook separates these modes at the representation level, offering structural advantages for multi-task learning. We propose VQActFlow, a multi-task manipulation policy that tokenizes action chunks and generates code sequences via Variational Flow Matching. VQActFlow maintains an explicit preference over action modes throughout generation. Inference-time guidance acts on this preference to steer mode commitment. We instantiate this with classifier-free guidance over language conditioning, which steers the policy toward the instructed action mode, and a learned codebook critic that supplies a complementary feasibility signal. We evaluate VQActFlow on three platforms: the LIBERO simulation benchmarks, a Unitree G1 humanoid performing whole-body pick-and-place, and an ALOHA-style bimanual platform performing contact-rich tasks. Across these benchmarks, VQActFlow outperforms both continuous and discrete baselines.

Zhigen Zhao, Mark Leggiero, Yipu Chen +5

Institute for Robotics and Intelligent Machines (IRIM), Georgia Institute of Technology, Atlanta, GA 30332

Latent Action Learning Language-Conditioned Robot Manipulation Multi-Task Robotic Manipulation Vector Quantization Robotic Manipulation Robot Imitation Learning

Jun 19, 2026cs.LG

Fast-TurboQuant: A Multiplier-Free Online Vector Quantization Approach

As large language models scale, memory bandwidth for key-value caches and retrieval-augmented generation systems becomes a critical bottleneck. While 1-bit quantization addresses this constraint, recent TurboQuant relies on dense random rotation matrices to condition the vector distribution before quantization. This projection demands millions of floating-point multiplications per embedding, making it difficult to deploy on constrained edge silicon. We introduce Fast-TurboQuant, a multiplier-free projection architecture that replaces the dense matrix with a structured fast Johnson-Lindenstrauss transform. By applying a Rademacher phase inversion followed by a fast Walsh-Hadamard transform (FWHT), the method leverages sub-Gaussian concentration to satisfy the prerequisites of scalar Lloyd-Max quantization without Gaussian projections. This substitution reduces the arithmetic complexity to only additions, eliminating hardware multipliers. Evaluation on DBpedia OpenAI-3 Large embeddings demonstrates a 19.7 times algorithmic speedup under sequential execution. Furthermore, the dimension expansion due to the FWHT zero-padding reduces the mean squared error and improves Recall@10.

Pedro M. R. Pereira, Felipe A. P. de Figueiredo, Rausley A. A. de Souza

National Institute of Telecommunications (Inatel), Santa Rita do Sapucaí, MG 37536-001, Brazil

LLM Quantization Rotation-Based Quantization Vector Quantization Randomized Sketching Embedding Compression

Jun 15, 2026eess.AS

Towards Robust Generative Speech Enhancement Using Vector Quantisation-Based Neural Audio Codec

This work investigates modelling strategies in continuous and discrete latent spaces in the vector quantisation (VQ)-based neural audio codec (NAC) speech enhancement (SE), along with the role of VQ regularisation. We propose cNAC-SE and dNAC-SE frameworks that predict continuous representations and discrete tokens in latent space, respectively. Theoretical analysis and visualisations in latent space are performed to exhibit their inherent modelling mechanisms. Experimental results show that the fully fine-tuned cNAC-SE model consistently outperforms all dNAC-SE variants across diverse test conditions and achieves leading performance among established generative approaches in DNS-MOS metrics. Comparison with the discriminative counterpart shows that VQ enhances robustness through an intrinsic effect of clean-prior-constrained regularisation, independent of discrete token processing. This highlights the transferable value of VQ regularisation to other continuous modelling methods.

Haixin Zhao, Nilesh Madhu

IDLab, Ghent University - imec, Belgium

Neural Audio Codecs Vector Quantization Speech Enhancement

Jun 12, 2026cs.NE

VQ4SNN: Vector Quantization for Memory-Efficient FPGA Spiking Neural Networks

Spiking Neural Networks (SNNs) offer an energy-efficient paradigm for edge AI, making them attractive for hardware acceleration. However, deploying dense SNNs on FPGAs is constrained by limited on-chip memory for synaptic weight storage. To address this bottleneck, we propose VQ4SNN, a hardware-aware architecture that reduces memory requirements through Vector Quantization (VQ)-based weight sharing. To the best of our knowledge, this is the first application of VQ to pipelined spatial-dataflow SNN accelerators on FPGAs. VQ4SNN replaces conventional weight storage with a two-level memory organization consisting of compact pointers and a shared codebook of quantized weight vectors. The proposed design integrates FPGA-aware memory mapping with analytical VQ parameter selection, enabling efficient deployment on such accelerators while preserving inference accuracy. The experimental results show a reduction of 52-61% in the total number of BRAMs compared to the state-of-the-art uncompressed FPGA SNNs without increasing overall logic utilization.

Dimitrios Sekertzis, Giorgos Dimitrakopoulos

Integrated Circuits Lab, Electrical and Computer Engineering, Democritus University of Thrace (DUTH), Greece

Memory-Efficient Inference Vector Quantization Spiking Neural Networks FPGA-Based Neural Network Acceleration Neural Network Compression

Jun 9, 2026cs.CV

NSVQ: Mitigating Codebook Collapse by Stabilizing Encoder Drift in Vector Quantization

Vector quantization is central to modern generative modeling pipelines, but large-codebook VQ models often suffer from codebook collapse. We identify encoder drift as a key driver of this failure: as the encoder moves the latent distribution, sparsely updated code vectors can lag behind, lose assignments, and increase quantization error, creating a feedback loop through the straight-through estimator. We propose NSVQ, a non-stationary-aware VQ training strategy that combines a dense non-stationary embedding loss, codebook replacement, and stage-wise encoder freezing. NSVQ first helps the codebook track encoder drift during early training, then freezes the encoder to consolidate the codebook under a fixed latent geometry, and finally reintroduces adversarial refinement. Experiments on ImageNet-1k show that NSVQ improves reconstruction quality while maintaining full codebook utilization. On ImageNet-1k at 128

\times

128 with 65,536 codes, NSVQ reduces rFID from 2.39 to 2.10 compared with SimVQ, while both methods maintain 100% utilization. Additional latent diffusion experiments show that NSVQ also improves downstream ImageNet generation FID.

Hao Lu, Yongxin Guo, Onur Koyun +3

Wake Forest University School of Medicine / Advocate Health · Wake Forest University School of Medicine · Advocate Health

Vector Quantization

Jun 9, 2026cs.CL

UniSVQ: 2-bit Unified Scalar-Vector Quantization

Post-training quantization at the 2-bit level enables low-cost deployment and inference acceleration for large language models (LLMs). Scalar quantization (SQ) and vector quantization (VQ) are two primary quantization methods, however, the former suffers from significant performance degradation, and the latter incurs computational and storage overhead. We propose UniSVQ, a unified 2-bit quantization framework that bridges scalar and vector quantization by parameterizing codewords as an affine transform of integer lattices. This structure preserves compatibility with optimized integer kernels while retaining much of VQ's flexibility. We further introduce a data-driven block-wise fine-tuning strategy to directly minimize quantization reconstruction error. Extensive experiments across multiple LLM families and zero-shot benchmarks demonstrate that UniSVQ consistently outperforms state-of-the-art SQ methods and achieves performance comparable to advanced VQ methods, while providing higher inference throughput. Codes are publicly available at https://github.com/AI9Stars/UniSVQ.

Haoyu Wang, Haiyan Zhao, Xingyu Yu +4

Department of Computer Science and Technology, Tsinghua University, Beijing, China · School of Software and Microelectronics, Peking University, Beijing, China · School of Physics, Beihang University, Beijing, China

LLM Quantization Vector Quantization Post-Training Quantization Low-Bit Quantization Neural Network Quantization

Jun 4, 2026cs.IR

ColBERTSaR: Sparsified ColBERT Index via Product Quantization

While ColBERT is an effective neural retrieval architecture, it requires a heavy index structure to support candidate set retrieval based on approximated token embeddings, gathering and decompressing document token embeddings, and applying the MaxSim operation. Indexes in PLAID and similar ColBERT implementations require five to ten times the disk storage of the original raw text, which limits their scalability. Furthermore, prior work has identified that the gathering and decompression stages are the primary inefficiencies at query time. Limiting the number of document tokens that must be gathered by thresholding and score approximation does not eliminate the need for the entire index to support ad hoc queries. In this work, we propose an embedding quantization approach that turns a ColBERT index into a true inverted index. We show that, theoretically, ColBERT with embedding quantization is equivalent to learned-sparse retrieval except for the scoring mechanism. Empirically, we demonstrate that our index is 50-70% smaller than a one-bit PLAID index while retaining retrieval effectiveness.

Eugene Yang, Andrew Yates, Dawn Lawrie +3

Johns Hopkins University, Baltimore, MD, USA

Vector Quantization Multi-Vector Retrieval Embedding Compression Product Quantization Dense Retrieval

Jun 1, 2026cs.CV

Adversarial Attacks on Robot Localization Systems via Deep Feature Perturbation

Robot localization systems are critical for autonomous navigation and safety. Adversarial perturbations can mislead these systems, resulting in mislocalization, navigation errors, or unsafe interactions, especially in mission-critical scenarios. This paper investigates the vulnerability of deep learning based localization pipelines to adversarial attacks. We propose a novel framework for generating adversarial queries that specifically target Product Quantization (PQ) in visual localization systems. Our method employs a Lightweight Product Quantization Network (LPQN) to perturb query feature encodings, misleading the retrieval process by returning semantically irrelevant database entries. Adversarial queries are generated via a two-phase procedure: a forward pass that perturbs feature distributions and a backward pass that refines the perturbation through optimization. The lightweight design of LPQN allows the creation of subtle yet highly effective perturbations with minimal computational overhead. Extensive experiments in both controlled and real-world robotic environments demonstrate that our approach substantially degrades PQN performance, exposing critical vulnerabilities in practical applications.

Zhenyu Li, Tianyi Shang

Shandong Academy of Sciences · Fuzhou University

Adversarial Attacks Vector Quantization Adversarial Perturbations Product Quantization Robot Localization

May 31, 2026cs.CV

HiTokSR: A Coarse-to-Fine Tokenizer with Hierarchical Codebooks for High-Fidelity Real-World Image Super-Resolution

Vector-quantized (VQ) generative models have shown promising results in real-world image super-resolution (Real-ISR). However, existing methods typically rely on a monolithic latent space that entangles low-frequency structures with high-frequency textures. This entanglement forces a single codebook to capture a combinatorially complex set of structure-texture pairings, which constrains representational capacity and limits codebook utilization. To address this issue, we present HiTokSR, a hierarchical token prediction framework. Instead of using a single codebook, HiTokSR partitions the latent space along the channel dimension into frequency-aware groups, quantizing each with an independent sub-codebook. This coarse-to-fine design disentangles global structures from fine details, enhancing combinatorial expressiveness while circumventing the optimization instability of high-dimensional nearest-neighbor lookups. To further improve semantic consistency, our generator integrates priors from a vision foundation model via adaptive feature modulation, multi-scale class tokens, and a representation alignment loss. Additionally, we introduce an index-level perturbation strategy during decoder fine-tuning to bridge the train-test discrepancy in discrete token prediction. Extensive experiments on real-world benchmarks demonstrate that HiTokSR achieves state-of-the-art performance in both perceptual quality and reconstruction fidelity.

Mingxi Li

Image Tokenization Vector Quantization Image Super-Resolution

May 29, 2026cs.LG

Inner Product Aware Quantization: Provably Fast, Accurate, and Adaptive Algorithms

Quantization is a fundamental tool used to compress datasets, neural network weights, and memory usage in a range of computational tasks. Many downstream applications of vector quantization perform inner products with arbitrary inputs. This motivates the study of inner product aware quantization schemes that approximately preserve inner products with unseen vectors -- in contrast to simply minimizing the mean-squared error. In this work, we formulate objectives that capture natural desiderata and develop adaptive and unbiased quantization methods that approximately preserve inner products with worst-case and average-case inputs. An analysis of these objectives shows a tight connection with the well-studied notion of Adaptive Stochastic Quantization (ASQ). We develop provably fast exact and approximate algorithms for our objectives. Our theoretical results inspire efficient practical algorithms that perform well across a variety of workload distributions. They also lead to practical algorithms for standard ASQ which are 2-10

\times

faster than prior state-of-the-art methods while maintaining quality. These theoretical and empirical results contribute towards making adaptive quantization techniques more efficient and tractable in practical settings.

Nathan White, Krish Singal

University of Pennsylvania

Vector Quantization Neural Network Quantization

May 29, 2026cs.CV

MergeTok: Unified Continuous and Discrete Visual Tokenization via Token Merging

Most visual tokenizers for image generation are bifurcated into two families with complementary limitations: continuous VAEs offer high-fidelity reconstruction but suffer from dense, entangled latents that are poorly suited for semantic control, whereas discrete VQ-based models enable autoregressive generation yet struggle with gradient sparsity, unstable training, and codebook collapse. In this work, we introduce MergeTok, a unified tokenizer that jointly optimizes continuous (VAE) and discrete (VQ) tokenizers within a encoder-decoder architecture, leveraging token merging techniques as a semantic bridge. By clustering similar tokens during encoding, MergeTok establishes a structural prior that provides dual supervision signals: (i) it imposes merged-token semantic alignment in the VAE branch, regularizing its latent space toward disentangled, semantic-aware representations; (ii) it derives group-wise constraints, promoting intra-group diversity and inter-group exclusivity that stabilize VQ training. MergeTok shows competitive reconstruction and generation performance on ImageNet-256, with substantially lower rFID than strong VAE and VQ models under matched token budgets, while producing semantically-organized token representations compatible with both autoregressive and diffusion generators. This shows that a single architecture can endow visual tokenizers with robust semantic organization and generator-friendly discreteness.

Luyuan Zhang, Siyuan Li, Zedong Wang +7

1Tsinghua University · 2Westlake University · 3Zhejiang University +3

Variational Autoencoders Token Merging Image Tokenization Visual Tokenization Vector Quantization Visual Token Merging

May 25, 2026cs.LG

QAM-W: Joint 2D Codebook Quantization for LLM Weights via Hadamard Rotation and Activation-Aware Scaling

Scalar post-training quantizers discard pairwise coordinate structure within weight rows. We introduce QAM-W (Quadrature Amplitude Modulation for Weights), a codec that recovers this structure: each row is L2-normalized, block-Hadamard rotated, paired into 2D coordinates, and quantized against a single Lloyd-Max codebook trained on the unit circular Gaussian, with activation-aware per-channel scaling. In a cross-model study spanning five LLMs from four families (1.1B--13B parameters) and eight quantized configurations, the activation-aware variant at

\approx 5.5

bpw stays within

\pm 0.4\%

of BF16 WikiText-2 perplexity on every model, matching the SmoothQuant W8A8 quality envelope at

32\%

fewer weight bits. Joint 2D coding outperforms polar (amplitude

\times

phase) coding by 2--15pp $Δ$ PPL at equal bitrate, and paired KL against BF16 tracks $Δ$ PPL% at Spearman $ρ= 0.99$ across 37 (method, model) rows, consistent with a monotone composite bound from codec distortion to KL divergence. A 3.5bpw variant is competitive on quantization-tolerant architectures. At strict 4~~bpw, the rotated-codebook frontier method QTIP outperforms QAM-W; the contribution is the quality-preserving 5--6~~bpw band.

Preetam Sharma, Kacper Dobek

Independent Research · Institute of Computing Science Poznan University of Technology, Poznan, Poland

LLM Quantization Rotation-Based Quantization Vector Quantization Weight-Only Quantization Post-Training Quantization

May 25, 2026cs.CV

Channel-wise Vector Quantization

We present Channel-wise Vector Quantization (CVQ), a novel image tokenization paradigm that replaces patch-wise tokens with channel-wise tokens. Unlike conventional vector quantization, which assigns a discrete token to each patch feature vector, CVQ quantizes each channel of the feature map. This formulation represents an image as discrete levels of visual details, rather than as a grid of spatial patches. Based on CVQ, we introduce a new visual autoregressive framework with "next-channel prediction". Instead of rendering images patch by patch in raster order, our Channel-wise Autoregressive (CAR) model predicts image channels sequentially, producing progressively enriched visual details. Specifically, it first sketches global structure and then refines fine-grained attributes, akin to a human artist's workflow. Empirically, we show that: (1) CVQ achieves 100% codebook utilization with a 16K+ codebook size without any bells and whistles, and substantially improves reconstruction quality over conventional VQ; and (2) CAR attains a DPG score of 86.7 and a GenEval score of 0.79, demonstrating strong effectiveness for text-to-image generation.

Wei Song, Tianhang Wang, Yitong Chen +5

Shanghai Innovation Institute · Westlake University · Zhejiang University +2

Image Tokenization Visual Tokenization T2I Generation Vector Quantization Autoregressive Image Generation Visual Token Compression

May 22, 2026cs.AR

EVA: Accelerating LLM Decoding via an Efficient Vector Quantization Architecture

Large Language Models (LLMs) have achieved impressive performance across diverse domains but remain inefficient during the autoregressive decoding phase. Unlike the prefill stage, which employs compute-bound GEMM operations, decoding executes a sequence of small GEMV-like computations that are memory-bound and underutilize modern accelerators. Weight-only vector quantization (VQ) has emerged as an effective compression technique that clusters model weights into a shared codebook and replaces the original weight matrix with low-precision indices, enabling 2-bit-level weight compression. While this approach substantially reduces model size and memory bandwidth, it still suffers from two critical inefficiencies: the low utilization of GEMV computation and frequent memory conflicts during codebook lookups. This paper presents EVA, an efficient vector-quantization-based architecture that addresses both computational and memory bottlenecks in LLM decoding. EVA builds on a simple yet effective insight that combines input-codebook computation with conflict-free memory access. Instead of reconstructing quantized weights from indices, EVA directly performs dot products between input vectors and the weight codebook, transforming LLM decoding from GEMV to GEMM computation. It then performs structured lookups from an intermediate output buffer, eliminating memory bank conflicts. We further design a hardware-software co-optimized architecture specialized for LLM decoding while remaining compatible with conventional prefill execution. Evaluations show that EVA achieves up to 11.17

\times

speedup and 7.17

\times

higher energy efficiency compared with the SOTA lookup-based architecture, while preserving arithmetic precision after vector quantization. Our code is available at https://github.com/dbw6/Eva.git.

Bowen Duan, Cong Guo, Chiyue Wei +8

Duke University, USA

Vector Quantization LLM Inference Acceleration Weight-Only Quantization Hardware-Software Co-Design Autoregressive Decoding

May 22, 2026eess.IV

Efficient Learned Image Compression without Entropy Coding

Entropy coding is widely used in typical learned image compression (LIC) that converts latents into a compact bitstream. However, entropy coding is typically sequential and becomes the coding latency bottleneck. To overcome it, we present Entropy-Coding Free Learned Image Compression (EF-LIC), a multi-rate framework that generates compact representation by removing statistical and correlation redundancy with low coding latency. First, we introduce unconstrained vector quantization and prove that its index distribution approaches the maximum-entropy bound, yielding minimal statistical redundancy. Second, we propose a context-conditioned autoregressive transform that directly reparameterizes the latents to reduce inter-dependency. Theoretical analysis shows that EF-LIC can remove correlation redundancy as effectively as typical LIC with entropy coding, leading to comparable compression performance. Experiments show EF-LIC achieves up to 67.86% bitrate reduction over MS-ILLM on Kodak with LPIPS. Ablation studies further show EF-LIC matches the compression performance of its entropy-coding based variant while achieving over

3\times

faster encoding and

5\times

faster decoding.

Hao Cao, Wenqi Guo, Zhijin Qin +1

Department of Electronic Engineering, Tsinghua University · Department of Automation, Tsinghua University · State Key Laboratory of Space Network and Communications +1

Learned Image Compression Vector Quantization

May 20, 2026cs.LG

OCTOPUS: Optimized KV Cache for Transformers via Octahedral Parametrization Under optimal Squared error quantization

The key-value (KV) cache dominates memory bandwidth and footprint in long-context autoregressive inference. Recent rotation-preconditioned codecs (TurboQuant, PolarQuant) show that a structured random rotation followed by a per-coordinate scalar quantizer matched to an analytically tractable marginal is a near-optimal recipe for KV compression. OCTOPUS advances this paradigm through joint quantization of rotated coordinate triplets. Each triplet's direction is mapped to a square via an octahedral parameterization, and the two resulting coordinates and the triplet norm are Lloyd-Max quantized against implementation-matched marginals. Optimizing the per-triplet squared error gives a strictly non-uniform bit allocation depending only on the total dimensionality of the keys. We find the finite-dimensional quality optimum with sweeps to be constant on every real decoder we test. The codec is data-oblivious, online, and deterministic given a seed. Across text, video, and audio, OCTOPUS matches or beats every prior rotation codec at every reported bit width and metric, with a lead that grows as bits drop for extreme compression. Furthermore, a fused Triton implementation reconstructs keys on the fly without materializing the uncompressed key, so the codec adds no decode-time bandwidth or latency over the existing dequantization. Project Page: https://octopus-quant.github.io/

Mark Boss, Vikram Voleti, Simon Donné +1

Stability AI

KV Caching Memory-Efficient Optimization Rotation-Based Quantization Vector Quantization KV-Cache Compression KV-Cache Quantization

May 20, 2026cs.CV

MGVQ: Synergizing Multi-dimensional Sensitivity-Aware and Gradient-Hessian Fusion for Vector Quantization

Vision-Language Models (VLMs) achieve outstanding performance, yet their huge model size severely hinders deployment on edge devices with limited resources. As an efficient model compression technique, vector quantization (VQ) excels in ultra-low-bit representation, which maps model weights to discrete codewords in a compact codebook to cut memory consumption and transmission overhead while preserving model capability. Direct VQ application to VLMs still has two core limitations. First, cross-modality weight distribution differences brought by visual and textual inputs cannot be well fitted by a single unified codebook. Second, current second-order error compensation ignores first-order gradient information, causing weight deviation from pre-trained optimal states, gradient drift and biased compensation results. This work proposes MGVQ, a novel vector quantization framework integrating multi-dimensional sensitivity perception and gradient-Hessian fusion. It consists of two core modules: sensitivity-guided structured mixed-precision quantization dynamically assigns different bit-widths according to channel sensitivity via combined global and local sensitivity analysis for refined resource allocation; gradient-aware second-order error compensation embeds first-order gradients into error correction, and adopts Kronecker and Block-LDL decomposition to ensure low computational cost. Extensive experiments on mainstream VLMs including LLaVA-onevision, InternVL2 and Qwen2-VL verify the effectiveness of MGVQ. In 2-bit quantization settings, MGVQ surpasses existing advanced post-training quantization methods significantly, achieving a maximum accuracy improvement of 4.9 points (71.4% vs 67.0% on InternVL2-26B). The proposed method realizes stable and efficient ultra-low-bit VLM quantization, greatly promoting the practical deployment of multimodal large models in resource-limited environments.

Zhong Wang, Zukang Xu, Xing Hu +1

Bauman Moscow State Technical University · Houmo AI

Mixed-Precision Quantization Vision-Language Models VLM Quantization Vector Quantization Post-Training Quantization Neural Network Quantization

May 19, 2026cs.LG

Block-Sphere Vector Quantization

Vector quantization is a fundamental primitive for scalable machine learning systems, enabling memory-efficient storage, fast retrieval, and compressed inference. Recent rotation-based quantizers such as EDEN, RabitQ, and TurboQuant have introduced strong guarantees and empirical performance, but the surrounding comparisons have been difficult to interpret because they rely on different distortion criteria, probability regimes, and implementation assumptions. As our first contribution, we provide a unified theoretical comparison of these methods and show that their relative advantages are criterion-dependent rather than absolute: EDEN and TurboQuant are favorable for MSE distortion, EDEN is also effective for expected inner-product distortion, and RabitQ provides strong high-probability control. This comparison further clarifies that EDEN provides particularly strong guarantees for expected distortion measures. As our second contribution, we introduce Block-Sphere Quantization (BlockQuant), a new rotation-based block quantization algorithm designed around the spherical geometry of randomly rotated vectors. Unlike coordinate-wise quantizers, BlockQuant quantizes blocks on the sphere, preserving the geometry of rotated embeddings more faithfully. We prove that this block-spherical design theoretically improves over the baselines considered in this paper for both reconstruction MSE and expected inner-product distortion. Our experiments on real embedding datasets and long-context LLM inference tasks show practical gains that are consistent with our theoretical improvements.

Heesang Ann, Joongkyu Lee, Min-hwan Oh

Seoul National University

Rotation-Based Quantization Vector Quantization Neural Network Quantization

May 17, 2026cs.LG

IVF-TQ: Calibration-Free Streaming Vector Search via a Codebook-Free Residual Layer

Approximate nearest neighbor (ANN) indexes deployed against streaming corpora silently lose recall over weeks. The standard diagnosis is distribution shift, but under shuffled-i.i.d. ingestion -- no shift at all -- product quantization still degrades -3.8pp at sub-matched bit budgets. The dominant production compression methods (PQ, OPQ, ScaNN) all fit a codebook to an initial sample and reuse it as the database grows by orders of magnitude. This paper presents IVF-TQ, an inverted-file index whose residual compression layer is data-independent: a fixed random rotation followed by a precomputed Lloyd-Max scalar quantizer parameterised only by the bit width b and dimension d. Only the IVF coarse k-means partition is trained. A uniform-over-sphere inner-product error bound depending only on (b, d, delta) provides a structural guarantee no learned-codebook method admits. The same codebook-free design enables an IVF-amplification effect that closes the gap to Extended RaBitQ to within statistical noise (+17.7pp over flat TQ at matched bit budget), and an Adaptive variant that refreshes the partition without touching the compression layer. Across nine controlled cells (three 10M datasets, three PQ memory regimes, three seeds), per-batch PQ codebook retraining never recovers the streaming gap; IVF-PQ streaming stability requires per-dataset bit-budget tuning, while IVF-TQ holds at one fixed (b, d) configuration on all three datasets with Delta in [-0.80, +0.56]pp. The contribution is operational: no codebook to train, no per-dataset bit-budget tuning, no retraining cycle that ever closes the gap.

Tarun Sharma

Independent Researcher USA

Vector Quantization Approximate Nearest Neighbor Search

May 16, 2026cs.LG

VQ-Atom: Semantic Discretization of Local Atomic Environments for Molecular Representation Learning

Large language models succeed by combining large-scale pretraining with meaningful discrete tokens. In molecular machine learning, SMILES is widely used as a token representation, but it is primarily a linearization format for molecular graphs rather than a semantic decomposition of chemistry. We propose VQ-Atom, a semantic tokenization framework that assigns discrete atom-level tokens based on local chemical environments via vector quantization. Unlike SMILES tokens, VQ-Atom tokens encode graph-local chemical context and are aligned with molecular structure. On protein-cold drug--target interaction prediction using the KIBA dataset, VQ-Atom substantially improves global ranking performance, achieving AUROC of 0.79 while substantially outperforming both SMILES-based and continuous molecular representations under an identical downstream architecture. Furthermore, VQ-Atom enables approximately 3 times faster downstream training than continuous atom-level representations by replacing per-atom continuous features with reusable discrete tokens. These results suggest that molecular tokenization is not merely a preprocessing step, but a central design choice. In particular, well-structured tokens can encode substantial chemical semantics, reducing the burden on downstream learning. VQ-Atom can be interpreted as defining a molecular language, where tokens correspond to chemically meaningful atomic environments, suggesting that token design may constitute an additional axis of machine learning research alongside architecture, objectives, and optimization.

Takayuki Kimura

Atoms as Language, LLC

Vector Quantization Molecular Representation Learning

May 15, 2026cs.IT

PrismQuant: Rate-Distortion-Optimal Vector Quantization for Gaussian-Mixture Sources

For a Gaussian source under mean-squared error (MSE), classical transform coding is rate--distortion (RD) optimal: the Karhunen--Loeve transform (KLT) diagonalizes the covariance, reverse waterfilling allocates the bits, and scalar quantization closes the loop. This elegant story breaks down for multimodal sources, where no single covariance can capture heterogeneous local geometries, and the RD function loses its closed form. We revisit this problem through Gaussian-mixture sources and develop a constructive RD theory for them. Our key finding is that the mixture structure incurs only a component label cost. Conditioned on the active mixture component, each branch is Gaussian; the challenge is allocating bits across heterogeneous branches. We prove that the genie-aided conditional RD function is governed by a single global reverse-waterfilling level shared across all components and eigenmodes. Building on this result, we introduce PrismQuant, which transmits the component label losslessly and encodes the residual using the component-matched KLT, followed by scalar quantization, achieving a rate of H(C)/n bits per source dimension of the converse, with a vanishing asymptotic gap. We further develop a practical implementation based on EM-driven Gaussian-mixture learning, component-adaptive KLTs, and entropy-constrained scalar quantization (ECSQ). Experiments on synthetic Gaussian mixtures show that PrismQuant closely approaches the theoretical RD bound, while experiments on real-world channel-state-information (CSI) data demonstrate competitive or superior performance compared with transformer-based learned codecs at more than one order of magnitude smaller model size.

Bumsu Park, Chanho Park, Youngmok Park +1

Department of Electrical Engineering POSTECH Pohang, South Korea

Rate-Distortion Theory Gaussian Mixture Models Vector Quantization Rate-Distortion Optimization Information-Theoretic Lower Bounds