arXiv Machine Learning By Xianghong Fang, Wenlong Mou, Yuan Yuan, Dehan Kong, Tim G. J. Rudner

A Unified Rate-Distortion Perspective on Vector, Product, and Scalar Quantization

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The paper introduces a unified rate–distortion framework for discrete visual tokenization, encompassing vector, product, and scalar quantization. It shows that minimizing distortion, rather than maximizing codebook utilization, is the key objective for reconstruction fidelity and establishes fairness conditions for comparing quantizers. Under these conditions, the study confirms the distortion hierarchy VQ–PQ–SQ and demonstrates that modern VQ methods achieve the lowest distortion.

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