Embedding Compression via Spherical Coordinates

Han Xiao

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arXiv · 2602.00079

Embedding Compression via Spherical Coordinates

Han Xiao

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Abstract

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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BibTeX RIS

Han Xiao. 2026-03-25. Embedding Compression via Spherical Coordinates. https://arxiv.org/abs/2602.00079

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