# Block-Sphere Vector Quantization

arXiv: https://arxiv.org/abs/2605.19972 · HTML: https://mlsanity.com/paper/2605.19972/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 27 references that are in the map.
- First posted on arXiv 19 May 2026.

## Builds on (most cited first, 17 of 17)

- [Billion-scale similarity search with GPUs](https://mlsanity.com/paper/1702.08734/) (2017)
- [LongBench: A Bilingual, Multitask Benchmark for Long Context Understanding](https://mlsanity.com/paper/2308.14508/) (2023)
- [BEIR: A Heterogenous Benchmark for Zero-shot Evaluation of Information Retrieval Models](https://mlsanity.com/paper/2104.08663/) (2021)
- [KIVI: A Tuning-Free Asymmetric 2bit Quantization for KV Cache](https://mlsanity.com/paper/2402.02750/) (2024)
- [TurboQuant: Online Vector Quantization with Near-optimal Distortion Rate](https://mlsanity.com/paper/2504.19874/) (2025)
- [Image and Video Tokenization with Binary Spherical Quantization](https://mlsanity.com/paper/2406.07548/) (2024)
- [EDEN: Communication-Efficient and Robust Distributed Mean Estimation for Federated Learning](https://mlsanity.com/paper/2108.08842/) (2021)
- [DRIVE: One-bit Distributed Mean Estimation](https://mlsanity.com/paper/2105.08339/) (2021)
- [QJL: 1-Bit Quantized JL Transform for KV Cache Quantization with Zero Overhead](https://mlsanity.com/paper/2406.03482/) (2024)
- [RaBitQ: Quantizing High-Dimensional Vectors with a Theoretical Error Bound for Approximate Nearest Neighbor Search](https://mlsanity.com/paper/2405.12497/) (2024)
- [Practical and Asymptotically Optimal Quantization of High-Dimensional Vectors in Euclidean Space for Approximate Nearest Neighbor Search](https://mlsanity.com/paper/2409.09913/) (2024)
- [Optimized Cartesian K-Means](https://mlsanity.com/paper/1405.4054/) (2014)
- [A Note on TurboQuant and the Earlier DRIVE/EDEN Line of Work](https://mlsanity.com/paper/2604.18555/) (2026)
- [RaanA: A Fast, Flexible, and Data-Efficient Post-Training Quantization Algorithm](https://mlsanity.com/paper/2504.03717/) (2025)
- [Deep Spherical Quantization for Image Search](https://mlsanity.com/paper/1906.02865/) (2019)
- [Pyramid Vector Quantization for LLMs](https://mlsanity.com/paper/2410.16926/) (2024)
- [Revisiting RaBitQ and TurboQuant: A Symmetric Comparison of Methods, Theory, and Experiments](https://mlsanity.com/paper/2604.19528/) (2026)

## Abstract (arXiv)

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 expected distortion 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 theoretically improves over the baselines considered in this paper for both reconstruction MSE and expected inner-product distortion. Our experiments on real embedding datasets and long-context LLM inference tasks show practical gains that are consistent with our theoretical improvements.