用球坐标压缩向量，速度和精度双优。
Embedding Compression via Spherical Coordinates
- 利用高维单位向量球坐标集中在π/2的特性，压缩浮点数存储。
- 实现1.5倍压缩率，比现有无损方法提升25%。
- 适用于文本、图像等嵌入，检索性能零损失。
我们提出一种ε有界压缩方法，用于单位范数嵌入，实现1.5倍压缩率，优于最佳现有无损方法25%。该方法利用高维单位向量球坐标集中于π/2的特性，导致IEEE 754指数坍缩为单一值，高阶尾数位可预测，从而对两者进行熵编码。重构误差被限制在float32机器精度（1.19×10⁻⁷）以内，使得重构值在float32精度下与原值不可区分。在涵盖文本、图像及多向量嵌入的26种配置上评估，结果一致显示压缩性能提升，且在BEIR基准测试中检索性能无显著下降。
原文摘要 · Abstract (English)
We present an $ε$-bounded compression method for unit-norm embeddings that achieves 1.5$\times$ compression, 25% better than the best prior lossless method. The method exploits that spherical coordinates of high-dimensional unit vectors concentrate around $π/2$, causing IEEE 754 exponents to collapse to a single value and high-order mantissa bits to become predictable, enabling entropy coding of both. Reconstruction error is bounded by float32 machine epsilon ($1.19 \times 10^{-7}$), making reconstructed values indistinguishable from originals at float32 precision. Evaluation across 26 configurations spanning text, image, and multi-vector embeddings confirms consistent compression improvement with zero measurable retrieval degradation on BEIR benchmarks.
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