Calibration-Free Low-Bit Vector Quantization

Residual vector quantization (RVQ) turns physiological waveforms into compact token sequences, but conventional masked modeling treats every incorrect token as equally costly. We propose GeoRVQ, a coarse-to-fine masked token model whose objective reflects the local response of a frozen waveform decoder. Decoder-induced costs define geometry-aware soft targets and expected distortion, while quantizer-causal prediction follows residual dependencies from coarse to fine levels. In a descriptive aggregate over MIMIC-IV Waveform, VitalDB, and CODE-15%, GeoRVQ increases exact token accuracy from $.133\pm.004$ to $.143\pm.003$, reduces decoded distance from $.606\pm.006$ to $.393\pm.007$, and increases R-peak F1 from $.784\pm.004$ to $.837\pm.008$ under matched model and training conditions. Across 45 held-out code substitutions, decoder-induced cost has a Spearman correlation of $.85$ with realized decoded cost, compared with $.54$ for Euclidean codeword distance. These results indicate that decoder-aware objectives can improve waveform and event preservation without requiring a large increase in exact token accuracy.

Speech-to-speech translation (S2ST) has advanced significantly with speech LLMs, offering the potential for joint optimization and preserving non-linguistic information. However, these models struggle with predicting high-bitrate speech tokens in LLMs, and face the challenge of relying on S2ST training data with ideally aligned speaker identity and prosody. We propose using low-bitrate tokens based on single-layer vector quantization, trained to reconstruct self-supervised learning (SSL) features. We also employ a separate token-to-waveform decoder named Autowave-X, which is also conditioned on the source speech to improve non-linguistic transfer, thereby relaxing the training data constraints. With the integration of these techniques, we propose an S2ST model named Kraken, which augments a pre-trained LLM with speech feature inputs and the low-bitrate token outputs, followed by Autowave-X vocoder. We built the model upon Qwen3-8B and trained it using 150k hours of multilingual and multitask speech data. We demonstrated that our model exhibited better translation quality than SeamlessM4T-Large v2 and Qwen2.5-Omni, along with improved speaker and prosody transfer capabilities.

Residual Vector Quantization (RVQ)-based neural audio codecs (NACs) enable high-fidelity audio distribution at unprecedentedly low bitrates through discrete token-based representations. However, this shift disrupts traditional forensics, as non-linear neural transcoding obscures the underlying traces of legacy compression. This study defines the forensic gap and proposes a Transformer-based framework designed to leverage the hierarchical and temporal dependencies inherent in RVQ sequences. By modeling inter-layer causal relationships and dynamic forensic significance, our model effectively disentangles superimposed artifacts from legacy-to-neural transcoding. Experimental results achieve 97%+ accuracy for codec identification and robust joint identification performance across 32-128 kbps. These results demonstrate that traditional codec traces persist even after neural transcoding, supporting the feasibility and necessity of neural-codec-aware audio forensics.

Low-bit quantization can achieve high recall on some vector representations and fail sharply on others, while average distortion and global rank correlation do not explain the difference. We study quantized vector search at the level of the comparisons consumed by ranking and graph-pruning algorithms. Our first result is a distribution-free decomposition: the probability that a comparison flips is bounded by the probability mass of exact margins near zero plus the tail probability of the calibrated residual. We then account for dependence between residuals that share a query or graph node, and derive covariance-aware second-moment identities and tail bounds under a joint MGF proxy. For a frozen candidate permutation, we prove a deterministic coupling theorem for Vamana neighbour selection: the approximate replay returns the exact neighbour list exactly when all candidate-level pruning actions agree on the frozen exact states. We connect these results to representation geometry through an exact Gaussian oracle, establish a strict correlation gain from a deterministic magnitude bit in an aligned bilinear model, and give a rare-contamination construction showing why marginal Gaussian diagnostics do not imply the required residual tails. When analytical assumptions are unavailable, a held-out block certificate bounds the selective failure risk of a frozen quantized rule. Across learned, classical, and synthetic embeddings, standardized exact margins predict held-out ranking and pruning flip rates substantially better than global rank correlation. The framework applies to coordinate binary codes, RaBitQ, Lucene BBQ, and product quantizers through a common decision interface.

Vector-quantization based image compression has achieved strong rate--distortion performance, yet most of them still produce a separate compressed representation for each target bitrate. Such variable-rate behavior allows one model to operate at multiple rates, but it does not necessarily provide a progressive bitstream whose prefixes are themselves decodable and can be refined by appending additional bits. We propose \textbf{Tree-VQ}, a progressive tree-structured vector quantization framework for learned image compression. Tree-VQ organizes discrete codewords as a hierarchical binary tree and represents each latent token by a routed root-to-leaf path. Crucially, every prefix of this path corresponds to a valid quantized representation, so shallow internal nodes serve as coarse reconstruction codes and deeper nodes provide successive refinements. This allows a compressed image to be decoded from an early prefix and progressively improved as more branch symbols are received, rather than being re-encoded for different target rates. To make this structure practical for compression, we introduce a prefix-compatible tree entropy model that codes progressive continuation decisions and routed branch refinements using only causally available decoded contexts. We further use rate-aware refinement scheduling to decide which spatial blocks should receive additional tree bits under a given prefix budget, and hierarchical prefix supervision to ensure that internal nodes are directly decodable at low rates. Experiments show that Tree-VQ achieves a superior performance--efficiency trade-off, delivering the best perceptual compression results with much fewer parameters and lower latency than competing methods.

This paper proposes PACodec, a novel low-bitrate neural speech codec based on parallel additive vector quantization (PAVQ). Unlike the mainstream residual vector quantization (RVQ) used in most neural speech codecs, where vector quantizers (VQs) are sequentially dependent, the PAVQ strategy adopted in PACodec aggregates parallel quantization results to optimize bitrate usage. Specifically, the PAVQ adopts a "global-local-global" (GLG) design: the global encoded features are quantized in parallel by multiple independent VQs, each attending to a local component of the representation, and their outputs are aggregated through addition to yield the final global quantization result for decoding. Experimental results show that PACodec, as each VQ focuses only on local information, supports smaller codebooks and reduces bitrate by 30% compared with baselines at the same decoding quality, with only minor model complexity. Further analysis shows that, owing to the GLG framework of PAVQ, the proposed PACodec is disentanglement-friendly, and each independent VQ captures different aspects of speech, e.g., content, timbre, and acoustic details, suggesting potential for application to downstream tasks such as voice conversion.

Neural audio codecs (NACs) convert speech into discrete token sequences, and prior work has reported that these sequences follow language-like statistical laws. This paper analyzes the token statistics of 13 NACs spanning multi-codebook residual vector quantization (RVQ), single-codebook VQ, and non-VQ designs, evaluated on three corpora under clean, white-noise, and real-world DEMAND-noise conditions. Zipf and Heaps parameters, unigram entropy, codebook occupancy, and Jensen-Shannon divergence (JSD) are estimated from matched token samples with explicit fit-validity safeguards and family-conditional $n$-gram orders. Corpus identity explains little variance in any metric, whereas acoustic condition and quantizer meta-category dominate in a metric-dependent way, and unigram entropy is the metric most strongly associated with meta-category. Clean-to-noise JSD computed at a common unigram order is associated with mel-cepstral distortion most clearly under DEMAND noise. The collapse and explosion degradation signatures previously reported for RVQ codecs concentrate in RVQ cells under white and DEMAND noise, respectively; explosion also occurs in non-VQ codecs, and single-codebook VQ codecs shift in occupancy and distribution shape without either signature. These results provide architecture-conditioned conventions for applying language-statistical analysis to NAC tokens.

By introducing RSLM (Rotated Scaled Lloyd-Max), a family of training-free vector quantization codecs compressing embeddings to 1--4 bits per dimension, we reduce memory cost and memory bandwidth of a typical large-scale Approximate Nearest Neighbor (ANN) search system, while reducing its complexity and keeping or improving recall across multiple benchmark datasets. State-of-the-art systems filter candidates using coarse partitions, approximately score them to narrow the set, and then rescore the best with higher precision representations (often >=8 bits per dimension). Our relativized codecs can bring this down to 2--4 bits per dimension. We use the properties of the ANN system to encode residual vectors instead of full vectors, both for the approximate scoring phase and the rescoring phase. Since Maximum Inner Product Search (MIPS) is very sensitive to vector norms, we correct the $L_2$ norms of quantized vectors. Our major innovation is that we correct the $L_2$ norm of the final reconstructed vector rather than just the residual. Our rescaling replaces more complicated schemes, such as Anisotropic loss. The residualization scheme gives us a more favorable quality vs size trade-off than generic quantization methods. Our high-performance implementation leverages a block-wise cascaded Fast Walsh-Hadamard Transform (FWHT) with linear-like complexity, AVX SIMD-optimized codebooks, and a steganographic encoding of scaling factors for perfect cache-line alignment.

Achieving local differential privacy in distributed optimization while maintaining low communication cost remains challenging. Existing vector quantization methods, such as vqSGD, use high-dimensional geometric constructions but incur unfavorable dimension-dependent variance. In this work, we propose Subsampled Stochastic TurboQuant (SSTQ), a framework that combines overcomplete equal-norm tight frames, coordinate subsampling, and privacy-aware one-dimensional quantization. SSTQ includes two variants: a Flat Randomized Response version and a Metric-Aware Laplace version, the latter being better suited to higher codebook bit-width regimes. We show that SSTQ achieves optimal mean squared error scaling while using only $\lceil \log_2 N \rceil + b$ bits per client, where $N = Θ(d)$ is the frame size. We also derive a surrogate privacy-aware codebook objective that reduces the codebook-dependent MSE scaling from $O(4^b)$ to $O(2^b)$. Finally, we empirically evaluate SSTQ against established baselines on federated learning tasks using CIFAR-10 and Fashion-MNIST, demonstrating favorable utility and communication efficiency. Some of the analytical derivations were first obtained using a fully automated Gemini-based agentic system developed internally at Google. The authors have verified those derivations and edited them for clarity of presentation.

Long-context LLM decoding reads the key-value (KV) cache at every step. Loading it takes longer than computing attention over it, so throughput is bandwidth-bound. Hence, reducing the cache size can raise both decoding speed and serving capacity. The challenge is to reduce cache size while preserving the attention products, keeping reconstruction cheap, and using a fixed per-token bit count. At two bits per element, the most competitive methods rely on orthogonal transforms. However, existing techniques are either data-oblivious or use the query statistics without deriving the transform from a distortion criterion. Moreover, they rely on transforms built on top of random or Hadamard rotations, which equalize variances across entries rather than compacting energy, and fixed-width scalar quantizers, which are suboptimal at low rates. In this paper, we formulate KV cache quantization as a transform coding problem in which distortion is the error in the attention products. We derive closed-form optimal transforms for keys and values from calibration statistics, under a high-resolution model. We show that the optimal key transform is not orthogonal and satisfies a generalized Parseval relation: the attention-aware distortion becomes mean-squared error (MSE) in the transform domain. Thus, we can use MSE-optimal vector quantizers applied directly to the transformed key coefficients. To meet the fixed-width layout requirement, we show that grouping coefficients into equal-volume partitions makes equal-size codebooks attain the variable-rate optimum under the same high-resolution model. At two bits per element, our method, termed NOVA-KV, recovers most of the long-context retrieval accuracy lost by scalar quantization methods at comparable throughput.

A fundamental challenge of vector search is achieving consistently high recall while minimizing computational costs. Fixed search parameters cause significant performance variance across queries, and conventional evaluation on average recall masks these per-query disparities. We introduce QASP (Query-Adaptive robust vector Search Policy), which predicts the complete recall progression curve per query via a single upfront supervised regression, from which a search policy is derived for any recall target; this avoids iterative model invocations during search or separate predictors per target. By predicting normalized recall values with scale-invariant features and pre-search inference, QASP generalizes across recall targets, index configurations, and datasets. Its fine-grained progress predictions further enable a lightweight reactive complement that adjusts search depth based on predicted-versus-observed deviations without additional inference. We prove that QASP requires a finite training sample independent of dataset size and dimensionality, that its loss exceeds the irreducible lower bound of any fixed policy by a vanishing margin, and that its data access savings over fixed probing grow exponentially in intrinsic dimensionality. Experimentally, QASP achieves significantly lower recall variance and deviation from target, higher query satisfaction rate, and scales to large data and hierarchical indices without retraining, achieving 99% recall with 80% less data access.

Vector quantization is an old problem but has recently become central to AI infrastructure. It is therefore experiencing a surge of renewed engineering and research activity. This paper provides a unified framework for developing and benchmarking new quantization algorithms. We describe 7 common conceptual quantization primitives and show how to compose them arbitrarily. We then re-express 25 common quantizers as pipelines of these primitives. Finally, we publish VQ-bench as open-source to be extended further and make reproducible benchmarks publicly available.

Synthetic tabular data is increasingly used in privacy-preserving data sharing, data augmentation, and to mitigate downstream classifier bias. State-of-the-art tabular diffusion models such as TabDDPM and TabSyn achieve excellent distributional fidelity but offer no mechanism for fairness; conversely, fairness-aware tabular generators (DECAF, FairTGAN, FairTabDDPM) impose explicit fairness penalties at training time, yielding modest fairness gains at substantial cost to either sample quality or downstream utility. We introduce FairDiffuseVQVAE, a two-stage architecture that decouples fidelity from fairness: a vector-quantized autoencoder with a row-level discriminator (Stage1, no fairness terms) is followed by a DiffuseVAE-style continuous diffusion refiner that conditions on both the Stage-1 reconstruction and the protected attribute via classifier-free guidance (Stage2). Fairness emerges as a property of the sampling distribution -- uniform sampling of the protected attribute at inference time enforces demographic parity by construction, rather than from competing loss terms. On the Adult, Bank and COMPAS datasets, FairDiffuseVQVAE achieves the highest mean Demographic Parity Ratio ($0.702$, $+47\%$ over FairTabDDPM) and Equalized Odds Ratio ($0.686$, $+100\%$). It also attains the lowest mean pair-wise correlation error ($0.034$) of any published method, while explicitly trading \sim$$15 AUC points for these fairness gains.

Vision-Language-Action (VLA) models have demonstrated strong potential for embodied AI, yet their high inference latency on GPUs limits real-time deployment. Existing accelerators, such as Dadu-Corki, improve efficiency but treat VLA models as full-precision workloads, leaving substantial redundancy in both memory and computation underexploited. In this paper, we propose VQVLA, an algorithm-hardware co-design framework that accelerates VLA inference by exploiting weight similarity and execution dynamics. We first introduce MotionVQ, a motion-aware vector quantization scheme that dynamically adjusts quantization precision based on the robot's execution state, reducing memory access while preserving task success rate. We then propose a merged-centroid vectorized GEMM paradigm that operates on the codebook-index representation, eliminating redundant multiplications through spatial aggregation and temporal reuse of centroids. To realize these optimizations, we design an accelerator that efficiently supports dynamic precision selection and centroid-reuse computation. Experimental results show that VQVLA achieves 6.5x, 2.8x, 1.9x, 3.3x, and 4.3x speedup over the A100 GPU, Dadu-Corki, LUT-DLA, CodeGEMM, and ShiftAddLLM, respectively, with negligible accuracy degradation.

Vector Quantization (VQ) underpins modern discrete visual tokenization. However, training quantization modules for state-of-the-art VQ-based models requires significant computational resources which, in practice, all but prevents the development of novel, cutting-edge VQ techniques under resource constraints. To address this limitation, we propose {\bf VQ-Transplant}, a simple framework that enables plug-and-play integration of new VQ modules into frozen, pre-trained tokenizers by replacing their native VQ modules. Crucially, the proposed transplantation process preserves all encoder-decoder parameters, obviating the need for costly end-to-end retraining when modifying the quantization method. To mitigate decoder-quantization mismatch, we introduce a lightweight decoder adaptation strategy (trained for only 5 epochs on ImageNet-1k) to align feature priors with the new quantization space. In our empirical evaluation, we find that VQ-Transplant allows obtaining near state-of-the-art reconstruction fidelity for industry-level models like VAR while reducing the training cost by 95%. VQ-Transplant democratizes quantization research by enabling resource-efficient integration of novel VQ techniques while matching industry-level reconstruction performance.

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.

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

Efficient large-scale image retrieval requires compact representations that preserve semantic similarity under fast Hamming-space search. Deep hashing is appealing, but most existing CNN- and ViT-based methods still follow a post-quantization paradigm, where continuous visual features are first learned and binary codes are then produced by a terminal hash projection or binarization operation. This late code generation creates a feature-to-code discrepancy between the continuously optimized representation space and the discrete Hamming space used for retrieval. To address this limitation, we propose HashViT, a Vision Transformer framework for native hash token learning. Instead of treating hashing as a terminal readout, HashViT introduces a dedicated HASH token that serves as a persistent, hash-oriented retrieval state inside the transformer. The HASH token is structurally decomposed into a Hash Register for direct binary code generation and a Semantic Workspace for preserving auxiliary continuous semantics. To enable effective workspace-to-register interaction, we further design a lightweight Hash Refinement Adapter that progressively refines the Hash Register across transformer layers. As a result, binary-oriented representations are formed through token evolution within the backbone, rather than being abruptly induced by an output-level projection. HashViT is optimized with a unified objective that combines learnable semantic center supervision, class-token similarity distillation, and quantization regularization, encouraging the HASH token to encode semantically structured and compact binary representations. Extensive experiments on three widely used benchmarks demonstrate that HashViT achieves state-of-the-art or highly competitive retrieval performance while preserving the efficiency of compact Hamming codes. Code is available at https://github.com/Xinze919/HashViT.

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.

Communication systems designed for reliable data reconstruction, rather than task-oriented communication, typically rely on separate source and channel coding and incur high latency under limited spectrum availability and fading channels. To address this, we propose a transmission framework with opportunistic spectrum access, in which the transmitter sends discrete latent representations learned via a vector-quantized variational autoencoder (VQ-VAE) over idle licensed channels using standard digital modulation. The AI-powered receiver is still able to reconstruct task-related information from the heavily compressed data. We develop a cross-layer latency model that accounts for compression, block errors, retransmissions, and stochastic channel access. Results on latency-accuracy trade-offs show that the proposed scheme achieves at least 79- and 3.3-fold latency reductions with only 5.7% and 2.4% drops in classification accuracy compared to benchmarks using conventional source and channel coding. The framework enables low-latency communication and reliable task execution even under limited spectrum availability and challenging channel conditions.

Learned video codecs based on continuous latent representations struggle to operate reliably below 0.1 bits per pixel~(bpp): without a differentiable rate signal, Lagrangian optimisation cannot effectively trade reconstruction quality for bitrate at extreme compression ratios. We demonstrate that discrete latent representations sidestep this limitation entirely. In a vector-quantized~(VQ) codec, the codebook size~$K$ imposes a hard information ceiling of $\log_2 K$ bits per symbol; a learned autoregressive prior then exploits the non-uniform distribution of code usage -- which we show follows a power law -- to push actual bitrates well below this ceiling, without any rate-penalty tuning. Building on the MS-VQ-VAE architecture introduced in~\cite{kotthapalli2026msvqvae}, we sweep $K \in \{128, 256, 512, 1024\}$ under a uniform training protocol to trace four operating points on the rate-distortion~(RD) curve. We identify and resolve a critical training instability: gradient-based VQ collapses catastrophically at $K \leq 512$, whereas EMA-stabilised codebook updates with dead-code restart maintain full utilisation across all configurations. On 500 UCF101 test clips ($64\!\times\!64$, 32frames), our models operate at 0.043-0.064bpp -- 3.3-5$\times$ below H.264's practical floor and $5$-$7.6\times$ below H.265's floor at this resolution. Every MS-VQ-VAE configuration outperforms H.265 CRF,36 on perceptual quality (LPIPS) despite using $5$-$7.6\times$ fewer bits. At $K{=}1024$, the model surpasses H.265 CRF,36 on LPIPS by a margin of 0.072 absolute while using $5.1\times$ fewer bits. Codebook analysis confirms power-law index distributions and 70-85% entropy efficiency, establishing the pipeline as a principled learned entropy coder.

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.

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.

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.

This study systematically compares Turbo-Quant and SpectralQuant KV-cache compression, evaluating non-dominated schemes, including WHT rotation with Beta Lloyd-Max and QJL, through a statistical validation methodology that separates systematic codec differences from implementation variance. Key findings reveal that while eigenbasis-based methods fail on heavy-tailed data due to covariance instability, they excel in structured regimes, with the effective semantic dimension ($d_{eff}$) adapting to calibration budgets rather than true data rank. (this is an abstract of the abstract thank you )

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.

We present ViP-VL, an efficient Vietnamese Self-supervised speech Pretraining model leveraging Vector-quantization Learning. To bridge the gap between high-resolution audio and efficient processing, ViP-VL incorporates Acoustic Stacking and Receptive Field Alignment to enable a synchronized 8x subsampling rate within the ChunkFormer architecture, while further enhancing representation robustness through a specialized Mask Selection Strategy during pretraining on the BEST-RQ framework. Pretrained on 17,000 hours of unlabeled Vietnamese speech, our model establishes new state-of-the-art results across four major downstream tasks: Automatic Speech Recognition, Speech Emotion Recognition, Dialect Classification, and Speaker Verification. To facilitate future research and the development of high-performance Vietnamese speech technologies, we publicly release our pretrained weights and implementation at github.com/khanld/chunkformer.

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.

Text-to-motion generation requires modeling both global action structure and fine-grained motion dynamics from natural language. Existing approaches typically rely on either continuous diffusion models or vector-quantized discrete representations. Diffusion models generate smooth motions but lack explicit compositional structure for temporal planning, while discrete token-based methods improve controllability but compress motion into finite codebooks, losing fine-grained dynamics. We argue that this limitation stems from a representation mismatch: action semantics such as intent, phase transitions, and temporal layout are inherently discrete and compositional, whereas joint trajectories and motion dynamics are continuous and locally correlated. To address this, we propose DC-Motion, a discrete-continuous factorized framework for human motion generation. DC-Motion decomposes motion into discrete structural tokens capturing global action layout and continuous residual latents modeling fine-grained dynamics. A text-conditioned structure generator predicts discrete tokens via iterative masked modeling, and a diffusion-based residual generator produces continuous motion conditioned on the structure. Experiments on HumanML3D and KIT-ML demonstrate that DC-Motion achieves strong performance in both FID and R-Precision, outperforming representative diffusion-based and discrete-token baselines.

Clark Hash is a small method for storing neural embeddings in less space. It normalizes each database vector, applies a deterministic sparse signed Johnson-Lindenstrauss projection, clips the result, and stores a fixed-width scalar-quantized code. Queries stay in floating point and are scored against the stored sketches. In the default 384-dimensional sentence-embedding setting, Clark Hash stores a cosine-search vector in 48 bytes instead of 1536 bytes for dense f32 storage. This is 32x smaller. The method does not need a training pass, learned codebooks, rotations, or corpus statistics before new vectors can be stored. We describe the codec, the Rust implementation, and a multilingual sentence-similarity evaluation on 9,304 labeled pairs from 29 subsets. With a multilingual MiniLM encoder, the 48-byte sketches reached 0.910 and 0.946 macro Pearson correlation with dense cosine scores on STS17 and STS22. Clark Hash is not a new Johnson-Lindenstrauss theorem and it is not a replacement for approximate nearest-neighbor indexes. It is a simple stateless codec for compact embedding storage.

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.

A central challenge in electroencephalography (EEG) foundation modeling is learning transferable representations across recordings with diverse tasks, montages, references, and spectral characteristics. Existing masked modeling approaches often rely on broadband continuous patches or a single discrete representation, which may underrepresent frequency-specific activity. This paper proposes BandVQ, a band-wise vector-quantized EEG foundation model that decomposes EEG into delta, theta, alpha, beta, and gamma bands, trains an independent VQ-VAE tokenizer for each band, and pretrains a shared Transformer encoder on the resulting discrete VQ code indices. The encoder uses masked code tokens, quantized absolute log-power tokens, channel and temporal embeddings, and metadata prefix tokens representing reference, band, task family, and phase. Region-based masking is also introduced to reduce the trivial reconstruction of spatially adjacent electrodes. The model is pretrained on 71 public EEG corpora comprising over 9,200 subjects and 357,000 single-channel hours and evaluated on six subject-independent classification datasets. Under the current evaluation setting, the proposed model achieves strong transfer performance, with the highest reported results on three cognitive tasks and competitive performance on three motor imagery tasks.

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.

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.

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.

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.

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.

Vector quantization is a fundamental tool for compressing high-dimensional embeddings, yet existing multi-codebook methods rely on static codebooks that limit expressiveness under heterogeneous data geometry. While recent dynamic quantizers like QINCo adapt codebooks to individual inputs and improve expressiveness, their strict sequential dependencies create decoding bottlenecks. We propose Residual Quantization via Mixture of Experts (RQ-MoE), a framework combining a two-level MoE with dual-stream quantization to enable input-dependent codebook adaptation for efficient vector quantization. RQ-MoE enables dynamic codebook construction and decouples instruction from quantization, facilitating parallel decoding. Theoretically, we show that standard Residual Quantization and QINCo can be recovered as constrained special cases of RQ-MoE, and derive a guideline for setting expert dimensionality in RQ-MoE. Extensive experiments show that RQ-MoE achieves state-of-the-art or on-par performance in reconstruction and retrieval, while providing 6x-14x faster decoding than prior vector quantization methods. The implementation is available at https://github.com/KDEGroup/RQ-MoE.

Vector quantization via random projection followed by scalar quantization is a fundamental primitive in machine learning, with applications ranging from similarity search to federated learning and KV cache compression. While dense random rotations yield clean theoretical guarantees, they require $Θ(d^2)$ time. The randomized Hadamard transform $HD$ reduces this cost to $O(d \log d)$, but its discrete structure complicates analysis and leads to weaker or purely empirical compression guarantees. In this work, we study a variant of this approach: dithered quantization with a single randomized Hadamard transform. Specifically, the quantizer applies $HD$ to the input vector and subtracts a random scalar offset before quantizing, injecting additional randomness at negligible cost. We prove that this approach is unbiased and provides mean squared error bounds that asymptotically match those achievable with truly random rotation matrices. In particular, we prove that a dithered version of TurboQuant achieves mean squared error $\bigl(π\sqrt{3}/2 + o(1)\bigr) \cdot 4^{-b}$ at $b$ bits per coordinate, where the $o(1)$ term vanishes uniformly over all unit vectors and all dimensions as the number of quantization levels grows.

Vector Quantized Variational Autoencoder (VQ-VAE) has become a fundamental framework for learning discrete representations in image modeling. However, VQ-VAE models must tokenize entire images using a finite set of codebook vectors, and this capacity limitation restricts their ability to capture rich and diverse representations. In this paper, we propose ArcCosine Additive Margin VQ-VAE (ArcVQ-VAE), a novel vector quantization framework that introduces a spherical angular-margin prior (SAMP) for the codebook of a conventional VQ-VAE. The proposed SAMP consists of Ball-Bounded Norm Regularization, which constrains all codebook vectors within a time-dependent Euclidean ball, and ArcCosine Additive Margin Loss, which encourages greater angular separability among latent vectors. This formulation promotes more discriminative and uniformly dispersed latent representations within the constrained space, thereby improving effective latent-space coverage and leading to improved codebook utilization. Experimental results on standard image reconstruction and generation tasks show that ArcVQ-VAE achieves competitive performance against baseline models in terms of reconstruction accuracy, representation diversity, and sample quality. The code is available at: https://github.com/goals4292/ArcVQ-VAE

Predicting cross-sectional stock returns is challenging due to low signal-to-noise ratios and evolving market regimes. Classical factor models offer interpretability but limited flexibility, while deep learning models achieve strong performance yet often underutilize financial priors. We address this gap with PRISM-VQ (PRior-Informed Stock Model with Vector Quantization), a dynamic factor framework that integrates expert prior factors, vector-quantized discrete latent factors learned from cross-sectional structure, and a structure-conditioned Mixture-of-Experts to generate time-varying factor loadings. Vector quantization acts as an information bottleneck that suppresses noise while capturing robust market structure, with discrete codes serving both as latent factors and as routing signals for temporal expert specialization. Experiments on CSI 300 and S&P 500 show consistent improvements in cross-sectional return prediction and portfolio performance over strong baselines while preserving interpretability. Our code is available at https://github.com/finxlab/PRISM-VQ.

Differentiable vector graphics have enabled powerful gradient-based optimization of vector primitives directly from raster images. However, existing frameworks formulate this as a flat optimization problem, forcing hundreds to thousands of randomly initialized curves to blindly compete for pixel-level error reduction. This disordered optimization leads to topology collapse, where macroscopic structures are distorted by internal high-frequency noise, resulting in a redundant and uneditable "polygon soup" that limits practical editability. To address this limitation, we propose Vector Scaffolding, a novel hierarchical optimization framework that shifts from flat pixel-matching to structured topological construction tailored for vector graphics. By identifying a key cause of topology collapse as the mathematical imbalance between area and boundary gradients, we introduce Interior Gradient Aggregation to stabilize the learning dynamics of multi-scale curve mixtures. Upon this stabilized landscape, we employ Progressive Stratification and Rapid Inflation Scheduling to progressively densify vector primitives with extremely high learning rates ($\times 50$). Experiments demonstrate that our approach accelerates optimization by $2.5\times$ while simultaneously improving PSNR by up to 1.4 dB over the previous state of the art.

Long-context inference is increasingly a memory-traffic problem. The culprit is the key--value (KV) cache: it grows with context length, batch size, layers, and heads, and it is read at every decoding step. Rotation-based scalar codecs meet this systems constraint by storing a norm, applying a shared random rotation, and quantizing one coordinate at a time. They are universal and random-access, but they discard the geometry created by the normalization step. After a Haar rotation, a block of $k$ consecutive coordinates is not a product source; it is a spherical-Beta source on the unit ball. We introduce \textsc{FibQuant}, a universal fixed-rate vector quantizer that keeps the same normalize--rotate--store interface while replacing scalar tables by a shared radial--angular codebook matched to this canonical source. The codebook combines Beta-quantile radii, Fibonacci,/,Roberts--Kronecker quasi-uniform directions, and multi-restart Lloyd--Max refinement. We prove that the resulting vector code strictly improves on its scalar product specialization at matched rate, with a high-rate gain that separates into a cell-shaping factor and a density-matching factor. The same construction gives a dense rate axis, including fractional-bit and sub-one-bit operating points, without calibration or variable-length addresses. On GPT-2 small KV caches, \textsc{FibQuant} traces a memory--fidelity frontier from $5\times$ compression at $0.99$ attention cosine similarity to $34\times$ at $0.95$. End-to-end on TinyLlama-1.1B, it is within $0.10$ perplexity of fp16 at $4\times$ compression and has $3.6\times$ lower perplexity than scalar \textsc{TurboQuant} at $b = 2$ ($8\times$ compression), where scalar random-access quantization begins to fail.

Low-precision number formats are widely used in modern machine learning systems due to their efficiency. Accurate direction representation is key to the accuracy of vector operations. This work precisely explores the extent to which the direction of a vector can be represented by selecting its scalar elements from a common finite alphabet of a given size. This is standard practice in machine learning, where low-precision significands may be narrow-width floating-point or integer values. A geometric framework is introduced for analyzing the directional coverage of such product-structured codes. This work analytically quantifies the suboptimality gap between such product-structured codes and spherical codes for the vector as a whole, in both low and asymptotically high dimensions. Furthermore, within the product code class, it is proven that the standard formats of two's complement, fixed-point, and floating-point are suboptimal, again with quantified gap, pointing to the potential to develop new scalar number formats. Such scalar alphabets are numerically optimized across multiple block dimensions for directional coverage, including the dimension used in NVIDIA's NVFP4 format. Experimental results are presented comparing the performance of standard formats and the optimized alphabet. We find that for four bits, NVIDIA's choice of E2M1 closely approximates the optimized alphabet, providing a geometric explanation for its strong performance in low-precision machine learning workloads and an analytical understanding of the link between that superiority and block size. We provide open-source formal proofs in Lean for the theorems in this work, along with the experimental code and the optimized alphabets obtained.

Uniform random rotations (URRs) are a common preprocessing step in modern quantization approaches used for gradient compression, inference acceleration, KV-cache compression, model weight quantization, and approximate nearest-neighbor search in vector databases. In practice, URRs are often replaced by randomized Hadamard transforms (RHTs), which preserve orthogonality while admitting fast implementations. The remaining issue is the performance for worst-case inputs. With a URR, each coordinate is individually distributed as a shifted beta distribution, which converges to a Gaussian distribution in high dimensions. Generally, one RHT is not suitable in the worst case, as individual coordinates can be far from these distributions. We show that after composing two RHTs on any $d$-sized input vector, the marginal distribution of every fixed coordinate of the normalized rotated vector is within $O(d^{-1/2})$ of a standard Gaussian both in Kolmogorov distance and in $1$-Wasserstein distance. We then plug these bounds into the analyses of modern compression schemes, namely DRIVE and QUIC-FL, and show that two RHTs achieve performance that asymptotically matches URRs. However, we show that two RHTs may not be sufficient for Vector Quantization (VQ), which often requires weak correlation across fixed-size blocks of coordinates (as opposed to only marginal distribution convergence for single coordinates). We prove that a composition of three RHTs leads to decaying coordinate covariance. This ensures that any fixed, bounded, multi-dimensional VQ codebook optimized for URRs has the same expected error when using three RHTs, up to an additive term that vanishes with the dimension. Finally, because practical inputs are rarely adversarial, we propose a linear-time ${O}(d)$ check on the input's moments to dynamically adapt the number of RHTs used at runtime to improve performance.

Vector quantization (VQ) with autoregressive (AR) token modeling is a widely adopted and highly competitive paradigm for time-series generation. However, such models are fundamentally limited by exposure bias: during inference, errors can accumulate across sequential predictions, leading to pronounced quality degradation in long-horizon generation. To address this, we propose SDFlow ($\textbf{S}$imilarity-$\textbf{D}$riven $\textbf{Flow}$ Matching), a non-autoregressive framework that operates entirely in the frozen VQ latent space and enables parallel sequence generation via flow matching. We tackle three key challenges in making this transition: (1) eliminating exposure bias by replacing step-wise token prediction with a global transport map; (2) mitigating the high-dimensionality of VQ token spaces via a low-rank manifold decomposition with a learned anchor prior over the latent manifold; and (3) incorporating discrete supervision into continuous transport dynamics by introducing a categorical posterior over codebook indices within a variational flow-matching formulation. Extensive experiments show that SDFlow achieves state-of-the-art performance, improving Discriminative Score and substantially reducing Context-FID, particularly for challenging long-sequence generation. Moreover, SDFlow provides significant inference speedups over autoregressive baselines, offering both high fidelity and computational efficiency. Code is available at https://anonymous.4open.science/r/SDFlow-D6F3/

In this work, we developed and tested 3 techniques for vector quantization (VQ) based model weight compression. To mitigate codebook collapse and enable end-to-end training, we adopted cosine similarity-based assignment. Building on ideas from attention-based formulations in Differentiable K-Means (DKM), we further improved this approach by using cosine similarity for assignment combined with top-1 sampling and a straight-through estimator, thereby eliminating the need for weighted-average reconstruction. Finally, we investigated the use of differentiable neural architecture search (NAS) to adaptively select layer-wise quantization configurations, further optimizing the compression process. Although our method does not consistently outperform existing approaches across all quantization levels, it provides useful insights into the design trade-offs and behaviors of VQ-based model compression methods.

We propose a novel hierarchical spatiotemporal vector quantization framework for unsupervised skeleton-based temporal action segmentation. We first introduce a hierarchical approach, which includes two consecutive levels of vector quantization. Specifically, the lower level associates skeletons with fine-grained subactions, while the higher level further aggregates subactions into action-level representations. Our hierarchical approach outperforms the non-hierarchical baseline, while primarily exploiting spatial cues by reconstructing input skeletons. Next, we extend our approach by leveraging both spatial and temporal information, yielding a hierarchical spatiotemporal vector quantization scheme. In particular, our hierarchical spatiotemporal approach performs multi-level clustering, while simultaneously recovering input skeletons and their corresponding timestamps. Lastly, extensive experiments on multiple benchmarks, including HuGaDB, LARa, and BABEL, demonstrate that our approach establishes a new state-of-the-art performance and reduces segment length bias in unsupervised skeleton-based temporal action segmentation.

Vector Symbolic Architectures (VSAs) provide a well-defined algebraic framework for compositional representations in hyperdimensional spaces. We introduce HyperSpace, an open-source framework that decomposes VSA systems into modular operators for encoding, binding, bundling, similarity, cleanup, and regression. Using HyperSpace, we analyze and benchmark two representative VSA backends: Holographic Reduced Representations (HRR) and Fourier Holographic Reduced Representations (FHRR). Although FHRR provides lower theoretical complexity for individual operations, HyperSpaces modularity reveals that similarity and cleanup dominate runtime in spatial domains. As a result, HRR and FHRR exhibit comparable end-to-end performance. Differences in memory footprint introduce additional deployment trade-offs where HRR requires approximately half the memory of FHRR vectors. By enabling modular, system-level evaluation, HyperSpace reveals practical trade-offs in VSA pipelines that are not apparent from theoretical or operator-level comparisons alone.

Scalar quantization of large language models (LLMs) is fundamentally limited by information-theoretic bounds. While vector quantization (VQ) overcomes these limits by encoding blocks of parameters jointly, practical implementations must avoid the need for expensive lookup mechanisms or other explicit codebook storage. Lattice approaches address this through highly structured and dense packing. This paper explores the Leech lattice, which, with its optimal sphere packing and kissing configurations at 24 dimensions, is the highest dimensional lattice known with such optimal properties. To make the Leech lattice usable for LLM quantization, we extend an existing search algorithm based on the extended Golay code construction, to i) support indexing, enabling conversion to and from bitstrings without materializing the codebook, ii) allow angular search over union of Leech lattice shells, iii) propose fully-parallelisable dequantization kernel. Lastly, we provide a geometric reinterpretation of combining shape--gain quantization with GPTQ-style Hessian corrections: the standard scale-correction step of shape--gain acts as a retraction onto a product of spheres, yielding a Spherical GPTQ primarily acting on directions. We find that low-angular-distortion LLVQ reduces sensitivity to Hadamard/rotation preprocessing, and enables a strong Hadamard-free PTQ in practice. LLVQ delivers state-of-the-art LLM quantization performance, outperforming recent methods such as Quip#, QTIP, and PVQ. The results highlight the effectiveness of high-dimensional lattices for scalable, theoretically grounded model compression.

The rapid advancement of large language models (LLMs) has intensified the need for effective mechanisms to transform continuous multimodal data into discrete representations suitable for language-based processing. Discrete tokenization, with vector quantization (VQ) as a central approach, offers both computational efficiency and compatibility with LLM architectures. Despite its growing importance, there is a lack of a comprehensive survey that systematically examines VQ techniques in the context of LLM-based systems. This work fills this gap by presenting the first structured taxonomy and analysis of discrete tokenization methods designed for LLMs. We categorize 8 representative VQ variants that span classical and modern paradigms and analyze their algorithmic principles, training dynamics, and integration challenges with LLM pipelines. Beyond algorithm-level investigation, we discuss existing research in terms of classical applications without LLMs, LLM-based single-modality systems, and LLM-based multimodal systems, highlighting how quantization strategies influence alignment, reasoning, and generation performance. In addition, we identify key challenges including codebook collapse, unstable gradient estimation, and modality-specific encoding constraints. Finally, we discuss emerging research directions such as dynamic and task-adaptive quantization, unified tokenization frameworks, and biologically inspired codebook learning. This survey bridges the gap between traditional vector quantization and modern LLM applications, serving as a foundational reference for the development of efficient and generalizable multimodal systems. A continuously updated version is available at: https://github.com/jindongli-Ai/LLM-Discrete-Tokenization-Survey.

Large Language Model (LLM) inference is typically memory-intensive, especially when processing large batch sizes and long sequences, due to the large size of key-value (KV) cache. Vector Quantization (VQ) is recently adopted to alleviate this issue, but we find that the existing approach is susceptible to distribution shift due to its reliance on calibration datasets. To address this limitation, we introduce NSNQuant, a calibration-free Vector Quantization (VQ) technique designed for low-bit compression of the KV cache. By applying a three-step transformation-1) a token-wise normalization (Normalize), 2) a channel-wise centering (Shift), and 3) a second token-wise normalization (Normalize)-with Hadamard transform, NSNQuant effectively aligns the token distribution with the standard normal distribution. This alignment enables robust, calibration-free vector quantization using a single reusable codebook. Extensive experiments show that NSNQuant consistently outperforms prior methods in both 1-bit and 2-bit settings, offering strong generalization and up to 3$\times$ throughput gain over full-precision baselines. Code is available at https://github.com/DHdroid/NSNQuant.

Recently, numerous end-to-end optimized image compression neural networks have been developed and proved themselves as leaders in rate-distortion performance. The main strength of these learnt compression methods is in powerful nonlinear analysis and synthesis transforms that can be facilitated by deep neural networks. However, out of operational expediency, most of these end-to-end methods adopt uniform scalar quantizers rather than vector quantizers, which are information-theoretically optimal. In this paper, we present a novel Lattice Vector Quantization scheme coupled with a spatially Adaptive Companding (LVQAC) mapping. LVQ can better exploit the inter-feature dependencies than scalar uniform quantization while being computationally almost as simple as the latter. Moreover, to improve the adaptability of LVQ to source statistics, we couple a spatially adaptive companding (AC) mapping with LVQ. The resulting LVQAC design can be easily embedded into any end-to-end optimized image compression system. Extensive experiments demonstrate that for any end-to-end CNN image compression models, replacing uniform quantizer by LVQAC achieves better rate-distortion performance without significantly increasing the model complexity. Code is available at: https://github.com/xzhang9308/LVQAC.