Vector Quantization

Understanding how deep neural networks process information remains a central challenge. Existing interpretability methods often compromise structural fidelity, rely on prespecified corpora, or explain models post-hoc. We propose Polytopal Neural Networks (PNNs), a framework that extracts distinct layer-wise aspects by enforcing a polytope-based structure that is used directly in subsequent information processing. We scale our approach using learned corpus representations and an amortized simplex inference procedure and highlight how the framework also gives a direct route to vector quantized (VQ) training. In PNNs, observations are explicitly described by their alignment with layer-specific aspects. Empirical results show that imposing polytopal constraints on neural network representations preserves meaningful structures in the latent space with minimal degradation in performance, favorable compressed representations when compared to VQ representations in unsupervised learning, while also providing a performant new approach to VQ deep learning training. Our findings suggest that deep networks can enforce interpretable polytope-based representations, offering a principled path toward more transparent AI systems with minimal performance compromise.

Zador's celebrated theorem is a cornerstone of optimal quantisation: it establishes both the weak limit of the empirical distribution of an optimal $n$-point quantiser in $R^d$ and the decay rate of the associated $L_s$-mean quantisation error. In large dimension, however, observing this asymptotic behaviour requires an astronomically large sample size. We prove that, for spherically symmetric target distributions, optimisation over all spherically symmetric distributions is a convex problem and derive an equivalence theorem that both characterises global optimality and yields a constructive algorithm. We show that, for moderate $n$, random quantisers uniformly distributed on a sphere of suitably chosen radius $R$ perform exceptionally well and, over a broad range of values of $n$, are numerically certified to be optimal among all random quantisers. Their expected distortion has an explicit integral representation that can be evaluated to arbitrary precision, and we prove concentration across random quantisers: the distortion variance tends to zero as $n\to\infty$ for fixed $d$. For $s=2$, both the optimal radius and the associated minimum expected distortion admit exact expressions. For general $s$, the optimal radius can be determined efficiently, and extreme-value theory provides useful approximations when $n$ grows with $d$. Depending on this growth rate, $R$ either converges to zero or approaches a positive limit that is independent of $s$.

Embedding tables are among the largest components of modern language models. Most compression methods fix a coding geometry such as coordinate blocks, low-rank subspaces, or unrestricted codebooks, and optimize within it. We instead ask whether the coding geometry can itself be discovered. We introduce \emph{OrBIT}, a structure-guided embedding compression framework that learns reusable local geometry from orbit dynamics and uses it to constrain a small set of shared codewords. The global reconstruction residual then decides where the fixed coding budget is spent, while redundant overlapping charts let local errors compensate one another after gluing. Our theory shows how tight-chart geometry controls distortion, how the global residual directs sequential allocation, and how data-geometry-guided refinement improves the codec. The resulting orbit machinery is compiled away, leaving a compact decoder in which the learned structure governs what is stored, where capacity is allocated, and how local information is assembled globally. Across four LLM embedding tables, OrBIT achieves $37.9\times$ compression on GPT-2 and over $23\times$ on each 7B table relative to 16-bit storage, while delivering competitive rate-distortion performance against established quantization and low-rank baselines.

Generative Information Retrieval (GIR) has emerged as a transformative paradigm, shifting document retrieval from a traditional "retrieve-and-rank" workflow to sequence-to-sequence generation, where a model directly predicts document identifiers (DocIDs). While the semantic design of these DocIDs is known to be critical for performance, a fundamental question remains under-explored: what makes a good DocID? Current approaches rely heavily on computationally expensive downstream evaluations, hindering systematic analysis and rapid iteration. In this work, we address this challenge by presenting a comprehensive study on the properties, metrics, and trade-offs that define effective numerical DocIDs. Specifically, our contributions are threefold: First, we propose a unified framework that unifies Product Quantization (PQ) and Residual Quantization (RQ), and their hybrid variants within a single design space. This enables us to systematically study key DocID properties, such as hierarchy versus parallelism, as well as the impact of hyperparameters like DocID length and codebook size. Second, we define a suite of training-free, intrinsic metrics, to quantify DocID quality and evaluate structural fidelity without the overhead of full model training. Through extensive experiments on MS MARCO 300K and NQ320K, we analyze how these structural properties influence retrieval effectiveness.

Hyperdimensional computing and vector symbolic architectures often represent quantized scalar levels by dense binary codebooks whose level-to-level similarity is intended to follow a prescribed function of scalar separation. At finite dimensionality, randomized scalar codebook constructions deviate from this target because of sampling noise, random-start imbalance, update-count fluctuations, component dependence, and finite-capacity effects. We develop a transition-based derandomization framework for dense binary scalar codebooks across two target-similarity families, with similarity decaying exponentially or linearly with level separation. The framework separates the target similarity law, the derandomization variant, and the concrete generator construction, making explicit how initialization, selection, update, and capacity-handling mechanisms shape the induced similarity profile. We formalize derandomization variants that separately constrain initial Hamming weight, update-count variability, and update balance, thereby controlling distinct sources of finite-dimensional error. For each family and variant, we derive the induced mean similarity, identify realization-wise and mean target-matching regimes, and derive exact finite-dimensional expressions for bias, variance, and root-mean-square error. Simulations across dimensions, quantization ranges, reference scalar levels, and generator constructions validate the theory and show how each constraint removes or reduces a specific source of similarity mismatch. The results provide practical guidance for choosing scalar codebook generators that more closely match a desired similarity law under finite-dimensional and hardware-relevant constraints.

A critical prerequisite of generative recommendation is designing semantic identifiers (SIDs) that are both scalable to large item sets and efficiently learnable. Existing SID learning methods fundamentally rely on Top-1 hard assignment during vector quantization. While heuristic strategies -- such as clustering-based initialization or forced post-hoc collision resolution -- can artificially inflate codebook coverage, they often disrupt end-to-end semantic alignment and fail to address the underlying optimization bottleneck: sparse gradient propagation. In standard Top-1 assignment, gradients concentrate on a narrow subset of frequently selected codewords, leaving the majority inherently under-trained and causing severe SID collisions. To overcome this limitation natively without relying on complex initialization priors, we propose FineSID, a unified quantization framework that moves beyond Top-1 assignment by enabling fine-grained gradient propagation across the entire codebook. Instead of updating only a single selected codeword, FineSID distributes learning signals to all codewords in a soft, differentiable manner. This design promotes globally balanced codebook optimization while strictly preserving semantic consistency, effectively alleviating SID collisions and stabilizing training in large, high-dimensional codebooks. Extensive experiments on multiple public benchmarks demonstrate that FineSID is robust to initialization configurations and consistently improves both codebook utilization and recommendation accuracy. Our work provides a principled, initialization-agnostic solution for semantic identifier learning, advancing the practicality of generative recommendation.

Uniform random rotations are an effective preprocessing step for quantization: they make normalized coordinate distributions approximately Gaussian, enabling the use of codebooks optimized offline. We introduce TORQUE, a framework that improves on previous quantization works that use random rotations by jointly optimizing how many and which coordinates to preserve at high precision both before and after rotation, under a fixed overall expected bit budget. Intuitively, before rotation, preserving large input coordinates at high precision can reduce overall error by preventing the rotation from spreading their values across many coordinates. Likewise, after rotation, preserving a small fraction of the largest-magnitude coordinates at high precision allows the remaining values to be quantized more accurately using codebooks optimized offline for the resulting truncated Gaussian distribution. We derive a quantization error upper bound and prove that top-$k$ pre-rotation retention minimizes it for each $k$. This reduces the search over coordinate subsets to an optimization over $k$, enabling a fast optimizer that uses offline codebooks and parallel parameter selection for practical implementation. We demonstrate an improved tradeoff between reconstruction accuracy and storage cost through numerical evaluation under the Gaussian model and experiments on nearest-neighbor retrieval, KV-cache compression, and activation compression.

Recent foundation models are moving toward native multimodal Vision-Language Models (VLMs), making VLMs a central form of next-generation foundation models. However, their large language backbones make edge deployment difficult due to high memory footprint and memory-bound autoregressive decoding. Weight-only post-training quantization is a practical solution, but pushing VLMs to extreme low bit-widths remains challenging: existing rotation-free methods suffer from outliers at 2-3 bits, while rotation-based methods improve accuracy at the cost of additional runtime overhead. We propose SPHQuant, a rotation-free spherical weight-only quantization framework for VLMs. Instead of quantizing weights directly in Cartesian coordinates, SPHQuant decomposes each 8D weight vector into coordinate signs, radius, and a positive unit direction. This representation isolates outlier magnitude into the radius while keeping directions bounded and statistically regular. Based on this insight, SPHQuant allocates extra precision to the radius to mitigate accuracy degradation induced by outliers. It further uses a compact positive-direction codebook and fine-tunes codebook entries through angular parameterization to preserve the unit-sphere constraint. We also design a hardware-friendly GEMV kernel that keeps the direction codebook small enough for shared-memory lookup and packs radial bits efficiently. Experiments show that SPHQuant matches the performance of state-of-the-art extreme low-bit quantization methods while improving decode throughput over QTIP by 30.3% on RTX A6000. Code will be released in https://github.com/Pushazf/SPHQuant.

Action tokenizers play a central role in autoregressive vision-language-action (VLA) models, determining both the targets for policy training and the executable commands recovered from predicted tokens. Their fidelity is commonly evaluated using pointwise reconstruction metrics such as mean squared error (MSE), yet small individual errors do not fully characterize how faithfully action adjustments across demonstrations are preserved. After compression, similar actions may still cluster around a representative motion, while the adjustments needed for different contexts are diminished, distorted, or even reversed. We introduce physical rank consistency (PRC) to measure how well tokenization preserves local physical distance rankings after reconstruction. Evaluating decoded actions provides a common reference across token vocabularies and decoder architectures, complementing pointwise accuracy with a measure of relational fidelity. We further present ActionPiece, which preserves physical action relationships through joint supervision of representation learning and quantization. Physical rank preservation supervises near-far ordering in encoder and quantized feature distances, while quantization regularization applies the same ordering to codeword assignment distributions. Both objectives augment reconstruction, producing discrete action tokens for standard autoregressive policy learning and execution through a frozen decoder. Under the same Qwen3-VL-4B policy training setup, ActionPiece achieves 94.8% on LIBERO and 68.8% on unseen LIBERO-Plus, with additional evaluations reaching 71.9% on SimplerEnv and 51.5% across VLA-Arena L0-L2. Component ablations show that the two objectives jointly improve PRC and policy success, demonstrating the value of physical relationship supervision for action tokenization.

Recent advancements have successfully adapted autoregressive language models to process multimodal signals, such as images and actions. Since raw action signals are continuous, effective tokenization is essential to map high-dimensional inputs into compact discrete tokens for autoregressive processing. However, existing discrete action tokenizers often suffer from high reconstruction loss, failing to preserve the fine-grained dynamics required for precise control. This "discretization bottleneck" significantly limits the performance ceiling of downstream Vision-Language-Action (VLA) models. To address this, we propose ${M}^2$Tok, a Multi-head Multi-codebook Action Tokenizer designed to minimize reconstruction error and enhance policy performance. Our approach introduces two key structural innovations: (1) we decompose the latent action features into multiple heads, enabling the model to implicitly align specific heads with distinct action dimensions; (2) we assign independent codebooks to each head for quantization. By leveraging the combinatorial nature of multiple codebooks, we significantly expand the representational expressivity of the tokenizer, leading to substantially lower reconstruction loss compared to previous methods. We evaluate the ${M}^2$Tok-based VLA on the RoboTwin, Simpler-Env, and 3 zero-shot real-world tasks. Experimental results demonstrate our method not only achieves superior reconstruction fidelity but also significantly boosts the success rate of VLA models. Comprehensive ablation studies further confirm the effectiveness of the multi-head and multi-codebook mechanisms. Code is available at https://github.com/cpaaax/M2Tok.

Existing knowledge-base-assisted semantic communication schemes commonly adopt either single knowledge-base quantization (SKBQ) or multi-knowledge-base residual quantization (MKBQ). SKBQ incurs limited storage overhead but has restricted quantization capacity, whereas MKBQ supports progressive refinement by assigning an independent knowledge base (KB) to each stage, causing the KB storage to grow linearly with the transmission depth. To address this problem, we propose storage-scalable knowledge-base reuse quantization (SSKBQ), which reuses a compact set of KBs across multiple residual refinement stages and thereby decouples the number of transmission stages from the number of maintained KBs. A stage-aware residual supervision mechanism is further introduced to regularize intermediate quantized representations and encourage progressive refinement. Experimental results demonstrate that KB reuse provides an effective solution to the storage scalability problem while maintaining competitive progressive reconstruction performance.

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.

Progressive image compression requires a single embedded representation whose received prefixes can be decoded without re-encoding the source. Modern vector-quantized (VQ) image models provide strong discrete endpoint representations, but conventional flat codeword indices do not define meaningful intermediate states for a neural decoder. We present Tree-VQ, a post-hoc conversion of a pretrained flat VQ tokenizer into a fine-grained, arbitrary-prefix progressive representation while preserving its encoder assignments and every learned leaf vector. The key idea is to organize the original codebook into a balanced binary hierarchy, associate explicit representations with internal nodes, and transmit branch decisions in depth-major order. Consequently, once the image header is available, every payload prefix uniquely specifies a valid latent state: each additional branch bit refines exactly one token, and transmission can therefore be truncated at essentially any payload position rather than only at a small number of stage boundaries. We further adapt one shared decoder on the complete-depth and mixed-depth latent states encountered under such arbitrary truncation, making these densely spaced prefixes useful for reconstruction rather than merely syntactically decodable. On Kodak, Tree-VQ achieves a DISTS-based BD-rate saving of 52.1% relative to ProGIC, while exposing thousands of valid arbitrary-prefix operating points from a single embedded bitstream.

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.

Leech-lattice vector quantization holds the strongest reported 2-bit quality under its own evaluation protocol. Its kernel decodes one shell; we found no implementation of the multi-shell decoder the rate requires. This paper supplies one and measures its serving cost for decode-phase GEMV at batch 1. First, a serving path for the full 301-class codebook: an offline expansion into GPU layouts and a fused dequantize-plus-matvec kernel reading them without warp divergence, verified against f64. Second, the in-VRAM rate is a design axis distinct from the on-disk rate. Four bit-exact layouts timed in one process show binary bit planes beating one-hot masks on size and speed at constant bandwidth (4.80 bits per weight, 2.15x FP16). Below 4.3 bits a second, irregular stream enters; at 3.6 the decode stops being shifts and masks. Third, deployed four-bit (AWQ) and two-bit (QTIP) GEMV kernels run in the same process. The trellis kernel reads 2.40x fewer bytes than our served layout and runs 2.27x faster at near-equal fractions of their byte bounds: the time gap tracks the traffic gap, the price of unfolding a codebook too large for a lookup table. Fourth, the validity envelope: the trellis kernel outruns our no-weights control, so our launch geometry sets that floor, and on a second memory hierarchy every lattice arm falls below FP16. With the output head held identical across arms, the kernel-and-format path gains 1.11x, 1.29x and 1.41x end to end at 4B, 8B and 14B; with an int8 output head the served 4B reaches 87.0 tok/s in 2.60 GB. The quality cost, 1.38x perplexity and 14.7 MMLU points at 4B, shrinks across the three sizes measured.

Discrete visual tokenization, predominantly driven by vector, scalar, and product quantization, lacks a unified conceptual framework for understanding quantization tradeoffs. In this paper, we propose a unified rate--distortion perspective on modern discrete visual tokenization. By viewing quantization as lossy compression, we characterize the nominal fixed-length coding rate through token count and codebook size, and quantization error as the distortion. Within this framework, we resolve three central questions. First, we theoretically and empirically show that minimizing distortion, rather than maximizing codebook utilization, is the primary intrinsic objective for reconstruction fidelity, with a direct connection to the STE-induced gradient discrepancy. Second, we establish two critical fairness conditions for intrinsic quantization comparison: controlling latent feature statistics and enforcing identical coding rates. Third, under these conditions, we recover the VQ--PQ--SQ distortion hierarchy in modern visual tokenization and show empirically that modern VQ methods achieve the lowest distortion. This work provides a foundational rate--distortion reframing of modern discrete visual tokenization, resolves ambiguities in quantizer evaluation, and provides a controlled framework for isolating intrinsic quantization effectiveness under fixed-rate constraints.

Speech codecs serve as bridges between continuous speech signals and large language models, yet face an inherent conflict between acoustic fidelity and semantic preservation. To mitigate this conflict, recent works increasingly adopt dual-tower architectures to decouple semantic and acoustic modeling with separate encoders. However, these dual-tower designs incur substantial architectural overhead. To avoid such complexity, we revisit the single-tower paradigm and propose BiMTokenizer, a low-bitrate speech codec (around 1.1 kbps) combining a bidirectional state-space backbone with Residual Spherical Leech Quantization (RSLQ). The bidirectional backbone strengthens temporal modeling, while RSLQ offers a fixed, well-separated lattice bottleneck for robust semantic and acoustic tokenization without learned-codebook collapse. Experiments show that BiMTokenizer achieves superior acoustic reconstruction and the lowest WER among low-bitrate codec baselines across both clean and noisy environments, while using less than half the parameters of recent dual-tower baselines. Furthermore, its robust semantic representations yield strong performance on downstream speech understanding tasks, confirming that a well-designed single-tower codec can preserve the semantic-acoustic balance at low bitrates. The code and model weights are available at https://github.com/ZhangXinWhut/BiMTokenizer.

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.

Unsupervised skeleton-based temporal action segmentation is a crucial task for understanding human behavior in long untrimmed sequences. Recent approaches often rely on discrete quantization to discover action boundaries from motion representations. However, when spatial masking is introduced for representation learning, it can introduce representation ambiguity, while discrete quantization further amplifies small fluctuations in the latent space. The interaction between these two factors often leads to unstable code switching and severe temporal jitter near action boundaries.To address these limitations, we propose a novel Mask-aware Action Spatiotemporal Quantization (MASQ) framework. Our framework decouples the conflicting tasks of spatial feature inference and temporal smoothing.In the spatial dimension, we introduce a Joint-Level Structured Dropout (JLSD) mechanism that masks the entire temporal trajectory of selected joints, to encourage the model to learn discriminative inter-joint coordination patterns. In the temporal dimension, we design a mask-aware velocity loss that enforces motion consistency only on visible joints, that prevents gradient conflicts caused by masked signals and stabilizing temporal predictions. Extensive experiments on three widely used skeleton datasets, including HuGaDB, LARa, and BABEL, demonstrate that the proposed MASQ framework significantly outperforms existing state-of-the-art unsupervised methods. In particular, our model establishes a comprehensive and substantial leading advantage in the Mean over Frames accuracy.

Clustering is a fundamental class of data analysis techniques with the most important representatives being centroid-based methods like $k$-means. Such methods are strongly connected to quantization problems, which aim to approximate general probability measures with discrete ones. For example, $k$-means corresponds to quantization with respect to the Wasserstein distance. While Wasserstein quantization clusters points within a fixed space, this paper studies Gromov-Wasserstein (GW) quantization, which additionally aims at clustering the ambient geometry of the space. We show existence of solutions to the GW quantization problem and give a characterization that justifies an analogue to the $k$-means algorithm (Lloyd's algorithm) to approximate them numerically. We further calculate the quantization rate for usual Euclidean geometries that are used in the GW context, and relate it to standard Wasserstein quantization rates. Finally, numerical experiments show that GW quantization opens up many modeling possibilities beyond normal clustering methods (e.g., for geodesic distances of 3D shapes or structured pruning of neural networks) and that the introduced algorithm leads to useful numerical solutions with approximation quality often in line with theoretically optimal rates.

Achieving local differential privacy in distributed optimization while maintaining low communication cost remains challenging. Existing vector quantization methods, such as vqSGD, rely on high-dimensional geometric constructions but incur unfavorable dimension-dependent variance. In this work, we propose Subsampled Stochastic TurboQuant (SSTQ), a framework that combines a bounded Kashin representation, data-independent coordinate subsampling, and privacy-aware one-dimensional quantization. SSTQ includes two variants: (1) a Flat Randomized Response variant that is unbiased and, for a fixed codebook bit-width, frame redundancy, and dimension-independent Kashin level, achieves reconstruction MSE that scales linearly with the ambient dimension $d$, while using only $\lceil \log_2 N \rceil + b$ bits per message. Here, $N = Θ(d)$ denotes the frame size in the Kashin transform and $b$ is the codebook bit-width; and (2) a metric-aware truncated-Laplace variant that removes the exponential dependence on bit-width at the cost of a non-vanishing bias. We also derive a convex uniform-surrogate codebook objective whose worst-case codebook-dependent upper bound improves from $O(4^b)$ to $O(2^b)$. Experiments on synthetic regression, Fashion-MNIST, and CIFAR-10 compare the per-message privacy-utility and uplink-communication trade-offs of SSTQ with those of established baselines, demonstrating favorable utility and communication efficiency.

Video Anomaly Detection (VAD) is inherently challenging due to the scarcity of anomalies and the large visual variability in surveillance footage, including changes in lighting, viewpoint, and human appearance. To mitigate visual noise and address privacy concerns, recent work has shifted to pose-based VAD, which focuses on motion dynamics rather than raw video data. However, existing pose-based approaches model human behavior in continuous latent spaces, limiting their ability to learn compact motion patterns necessary for robust behavior analysis. We address this by proposing Vector-Quantized Video Anomaly Detection (VQ-VAD), a novel human-centric anomaly detection framework that learns discrete motion representations. VQ-VAD adapts Vector-Quantized GAN (VQ-GAN), originally developed for image generation, to operate on keypoint sequences and construct a motion codebook of normal behavior. Trained exclusively on normal motion sequences, VQ-VAD detects anomalies by identifying high reconstruction errors when an observed motion sequence cannot be mapped to the learned codebook. We conduct extensive experiments across three complementary evaluation settings, including in-domain, cross-domain, and cross-dataset generalization, on four anomaly detection benchmarks. VQ-VAD achieves strong in-domain accuracy (81.83% on HR-SHT [15]), effective cross-domain transfer from CMU Panoptic [14] (76.69% on HR-SHT [15] without retraining), and competitive cross-dataset robustness. The code base for this work is available at https://github.com/TeCSAR-UNCC/VQ-VAD.

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.

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.

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.

Learned video codecs based on continuous latent representations typically require resolution-specific retraining or rate-distortion (RD) recalibration when scaling to new spatial resolutions, because entropy models and Lagrangian weights are tightly coupled to the operating point. We investigate whether hierarchical discrete latent codecs exhibit the same sensitivity. Using a controlled empirical study of MS-VQ-VAE video compression across codebook sizes $K \in \{128,256,512,1024\}$ and resolutions $64\times64$, $128\times128$, and $256\times256$ on UCF101, we show that perceptual quality (LPIPS) depends strongly on codebook capacity but only negligibly on spatial resolution. Fitting a log-linear model $Q(K,r) = α\log_2 K + β\log_2 r + γ$ to all 12 operating points yields $α=-0.0094$ ($t=-6.6$, $p<0.001$) and $β=-0.0009$ ($t=-0.43$, $p=0.68$, not significant), with $R^2=0.82$. Codebook capacity is therefore roughly $10\times$ more influential than spatial resolution per log-unit increase. In parallel, bottom-level entropy efficiency $η=H(z)/\log_2 K$ remains stable or improves with resolution (84-87% at $64\times64$; 92-94% at $256\times256$), confirming that larger spatial grids are utilized more efficiently rather than less. Across all resolutions and codebook sizes, our models outperform H.264 on LPIPS at matched or lower bitrate, with gains of 25-52% at $128\times128$ and 21-37% over H.265 at $256\times256$. These findings suggest that codebook size $K$, not spatial resolution, is the dominant design variable governing perceptual compression quality in hierarchical discrete video codecs -- a property that may simplify multi-resolution deployment and inform the design of scalable discrete tokenizers for generative video models.

In this work, we aim to discretize the high-dimensional visual representations to bridge the gap with language models - a non-trivial challenge, as existing quantization methods suffer from codebook collapse, failing to scale while preserving semantic coherence. We identify the root cause as metric mismatch: standard Euclidean codebook objectives are fundamentally misaligned with the anisotropic geometry of representation space, leading to codebook embeddings with high-variance magnitude scales and uneven angular distributions that hinder scalability. To address this, we propose Hyper-Spherical Quantization (HSQ), which decouples semantic content from feature magnitude via angular routing, preventing code assignment from being dominated by scale rather than meaning. The resulting discrete Representation Autoencoder (dRAE) achieves high-fidelity reconstruction while preserving semantic integrity and supporting scalable codebook budget. Extensive experiments demonstrate consistent performance gains as the vocabulary size scales to 131{,}072, along with 100% codebook utilization, simplified training pipeline, and strong performance across understanding and generation tasks.

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.

Retrieval-Augmented Generation (RAG) systems increasingly power enterprise LLM applications, yet the vector retrieval layer introduces two underexplored challenges: (1) trained codebook quantizers may expose corpus statistics during index construction, creating a leakage channel in multi-tenant deployments, and (2) post-hoc filtering for tenant isolation degrades recall on selective queries. We study TurboVec, an open-source vector index built on TurboQuant - a codebook-oblivious scalar quantizer requiring no corpus-dependent training. On the DBpedia OpenAI embeddings benchmark (d=1536, 100K-999K vectors), TurboQuant 4-bit outperforms trained FAISS Product Quantization at the same memory budget by 8.5-8.9 percentage points in Recall@5 across all scales. Compared to HNSW (R@5=0.991) and IVF-PQ (R@5=0.840), TurboQuant occupies a distinct design point: higher recall than IVF-PQ without training, at 4-8x less memory than HNSW. Deployed on Snowpark Container Services, TurboVec achieves 11ms median query latency at 100K vectors versus 707ms for warehouse brute-force scan. Kernel-level allowlist filtering maintains 0.86-0.93 Recall@10 across 10-1000 tenant workloads versus 0.09-0.19 for post-filter baselines. Codebook-oblivious design reduces membership inference accuracy to near-random (50.0%) versus 57.3% for PQ codebooks. Limitations include single dataset evaluation, uncompressed HNSW comparison, and privacy evaluation on synthetic data only.

Neural audio codecs with residual vector quantization (RVQ) normally treat all frequencies uniformly, so their codebooks become spectrally entangled. Truncating stages then removes an unpredictable mix of frequencies. Parallel band decomposition addresses this by splitting audio into independent bands, but fragments the latent space and loses cross-frequency coherence. We introduce HARP (Harmonic-Aware Residual Partitioning), a training strategy that partitions RVQ stages into frequency-ordered groups where each group refines its target band while the decoder retains access to all lower frequencies. Overtones are reconstructed in the context of their fundamentals, preserving coherence that parallel methods lose. HARP requires no architectural changes; it only modifies the training loss, leaving inference identical to standard RVQ. On speech, music, and general audio, HARP outperforms both standard RVQ and parallel decomposition. MUSHRA listening tests also show perceptual improvements.