Block-Sphere Vector Quantization
Heesang Ann, Joongkyu Lee, Min-hwan Oh

TL;DR
This paper compares existing rotation-based vector quantizers theoretically, introduces a new spherical block quantizer called BlockQuant, and demonstrates its practical advantages for embedding compression and language model inference.
Contribution
It provides a unified theoretical comparison of rotation-based quantizers and introduces BlockQuant, a novel spherical block quantizer with improved theoretical and practical performance.
Findings
Unified comparison clarifies criterion-dependent advantages of existing methods.
BlockQuant preserves spherical geometry, improving reconstruction and inner-product distortion.
Experiments show practical gains in embedding compression and language model tasks.
Abstract
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…
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