Block Sphere Vector Quantization

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: TurboQuant is favorable for MSE distortion, EDEN is effective for expected inner-product distortion, and RabitQ provides strong high-probability control. This comparison clarifies the design principles behind each advantage and shows that no existing method uniformly dominates across the relevant measures. As our second contribution, we introduce Block-Sphere Quantization (BlockQuant), a new rotation-based block quantization algorithm designed around the spherical geometry of randomly rotated vectors. Unlike coordinate-wise quantizers, BlockQuant quantizes blocks on the sphere, preserving the geometry of rotated embeddings more faithfully. We prove that this block-spherical design improves expected distortion performance, including both reconstruction MSE and expected inner-product distortion. Experiments on real embedding data support these theoretical improvements.