# Embedding Compression via Spherical Coordinates

arXiv: https://arxiv.org/abs/2602.00079 · HTML: https://mlsanity.com/paper/2602.00079/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 22 references that are in the map.
- First posted on arXiv 22 Jan 2026.

## Builds on (most cited first, 12 of 12)

- [ColBERT: Efficient and Effective Passage Search via Contextualized Late Interaction over BERT](https://mlsanity.com/paper/2004.12832/) (2020)
- [Matryoshka Representation Learning](https://mlsanity.com/paper/2205.13147/) (2022)
- [TurboQuant: Online Vector Quantization with Near-optimal Distortion Rate](https://mlsanity.com/paper/2504.19874/) (2025)
- [SZ3: A Modular Framework for Composing Prediction-Based Error-Bounded Lossy Compressors](https://mlsanity.com/paper/2111.02925/) (2021)
- [PolarQuant: Quantizing KV Caches with Polar Transformation](https://mlsanity.com/paper/2502.02617/) (2025)
- [70% Size, 100% Accuracy: Lossless LLM Compression for Efficient GPU Inference via Dynamic-Length Float (DFloat11)](https://mlsanity.com/paper/2504.11651/) (2025)
- [ZipNN: Lossless Compression for AI Models](https://mlsanity.com/paper/2411.05239/) (2024)
- [Qinco2: Vector Compression and Search with Improved Implicit Neural Codebooks](https://mlsanity.com/paper/2501.03078/) (2025)
- [PCDVQ: Enhancing Vector Quantization for Large Language Models via Polar Coordinate Decoupling](https://mlsanity.com/paper/2506.05432/) (2025)
- [FCBench: Cross-Domain Benchmarking of Lossless Compression for Floating-Point Data](https://mlsanity.com/paper/2312.10301/) (2023)
- [To Compress or Not? Pushing the Frontier of Lossless GenAI Model Weights Compression with Exponent Concentration](https://mlsanity.com/paper/2510.02676/) (2025)
- [Inline Vector Compression for Computational Physics](https://mlsanity.com/paper/2003.02633/) (2020)

## Abstract (arXiv)

We present an ε-bounded 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 bounded by float32 machine epsilon (1.19 × 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.