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

• URL: http://arxiv.org/abs/2607.15933v1
• Date: Fri, 17 Jul 2026 13:18:23 GMT
• Title: Distributional Matching for Vector Quantization: A Unified Theoretical and Empirical Framework
• Abstract summary: We propose a distributional matching framework for vector quantization.<n>We show that both issues can be traced to a fundamental mismatch between the distributions of feature vectors and code vectors.
• Score: 19.918485811165425
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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