Embedding Compression via Spherical Coordinates

Abstract

We present a compression method for unit-norm embeddings that achieves 1.5 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 below 1e-7, under float32 machine epsilon. Evaluation across 26 configurations spanning text, image, and multi-vector embeddings confirms consistent improvement.

Reproductions