JHQ: Johnson-Lindenstrauss Enhanced Hierarchical Quantization for High-Dimensional Approximate Nearest Neighbor Search
Abstract
High-dimensional approximate nearest neighbor (ANN) search is fundamental to modern AI applications including retrieval-augmented generation and recommendation systems. While vector quantization (VQ) methods excel at compressing vectors for efficient search, existing approaches face critical bottlenecks: prolonged indexing times due to expensive data-dependent training, slow query processing from quadratic distance computations, and poor scalability on large datasets. In this paper, we introduce a novel quantization framework that leverages the orthogonal Johnson-Lindenstrauss (JL) transformation to lay the foundation for resolving these bottlenecks. Our key insight is that the JL induces a predictable near-Gaussian distribution with independent dimensions, enabling quick codebook generation without expensive iterative training. Based on that, we propose two algorithms: JQ (JL-enhanced Quantization) achieves fast indexing through training-free codebook construction while maintaining provable distance error bounds; and JHQ (JL-enhanced Hierarchical Quantization) extends JQ with a two-level architecture that uses primary quantization for rapid candidate filtering and residual quantization for accurate refinement, achieving better query accuracy-speed tradeoff on large scale datasets. Finally, extensive experiments on six benchmark datasets with up to 3,072 dimensions demonstrate that our methods achieve 3–10$\times$ query speedup over state-of-the-art baselines at $\geq$95\% recall, with 10-30$\times$ index construction speedup. Particularly, JHQ excels on massive datasets, maintaining 2–10$\times$ higher queries-per-second at >90\% recall compared to JQ.
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