This work introduces principled criteria for desirable VQ behavior and demonstrates that aligning feature and code vector distributions provides a unifying mechanism for mitigating training instability and codebook collapse, and instantiate this framework using a Wasserstein-based objective with an efficient closed-form under a mild Gaussian approximation.
Abstract
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.
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.
Xianghong Fang, Wen-Long Mou, Yuan Yuan et al.· 0 citations
Numerical experiments show that GW quantization opens up many modeling possibilities beyond normal clustering methods and that the introduced algorithm leads to useful numerical solutions with approximation quality often in line with theoretically optimal rates.
This work proposes 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.
Tianren Ma, Lin Long, Chu-Yan Chen et al.· arXiv.org· 0 citations
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.
Hadamard-Transform-domain Quantization (HaTQ), which uses orthogonal Hadamard reparameterization before quantization to redistribute weight and activation responses in the original domain across channels, and is compatible with integer-only execution.
Jun-Qi Shi, Chongzhi Wang, Yiwen He et al.· 0 citations
BaKron is an efficient solver that combines anti-diagonal parallelism with a recursive divide-and-conquer construction that matches the cubic scaling of GPTQ while exploiting richer curvature information.
Johann Birnick, R. Saab· 1 citation· ⚡1
We use cookies to run the site and, with your consent, for analytics and to show ads.
See our Cookie Policy.
