Embedding Compression via Spherical Coordinates

Han Xiao

Track: long paper (up to 8 pages)

Keywords: embedding compression, spherical coordinates, floating-point compression, entropy coding, vector retrieval

TL;DR: 1.5x compression for unit-norm embedding vectors using spherical coordinates.

Abstract: We present a 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 $\pi/2$, 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.

Anonymization: This submission has been anonymized for double-blind review via the removal of identifying information such as names, affiliations, and identifying URLs.

Presenter: ~Han_Xiao8

Format: Yes, the presenting author will definitely attend in person because they attending ICLR for other complementary reasons.

Funding: No, the presenting author of this submission does *not* fall under ICLR’s funding aims, or has sufficient alternate funding.

Serve As Reviewer: ~Han_Xiao8

Submission Number: 7