Practical and Asymptotically Optimal Quantization of High-Dimensional Vectors in Euclidean Space for Approximate Nearest Neighbor Search

TL;DR

This paper introduces an extended quantization method for high-dimensional vectors in Euclidean space that improves upon RaBitQ by achieving asymptotic optimality, supporting higher accuracy at lower space costs, and demonstrating superior empirical performance.

Contribution

We extend RaBitQ to support higher accuracy with better space-error trade-offs, maintaining theoretical guarantees and improving practical efficiency for ANN search.

Findings

Our method outperforms state-of-the-art baselines in accuracy and efficiency.

It achieves asymptotic optimality in space-error trade-off.

Experimental results confirm superior performance on real-world datasets.

Abstract

Approximate nearest neighbor (ANN) query in high-dimensional Euclidean space is a key operator in database systems. For this query, quantization is a popular family of methods developed for compressing vectors and reducing memory consumption. Recently, a method called RaBitQ achieves the state-of-the-art performance among these methods. It produces better empirical performance in both accuracy and efficiency when using the same compression rate and provides rigorous theoretical guarantees. However, the method is only designed for compressing vectors at high compression rates (32x) and lacks support for achieving higher accuracy by using more space. In this paper, we introduce a new quantization method to address this limitation by extending RaBitQ. The new method inherits the theoretical guarantees of RaBitQ and achieves the asymptotic optimality in terms of the trade-off between space and error bounds as to be proven in this study. Additionally, we present efficient implementations of the method, enabling its application to ANN queries to reduce both space and time consumption. Extensive experiments on real-world datasets confirm that our method consistently outperforms the state-of-the-art baselines in both accuracy and efficiency when using the same amount of memory.