Routing-Guided Learned Product Quantization for Graph-Based Approximate Nearest Neighbor Search

Given a vector dataset $\mathcal{X}$, a query vector $\vec{x}q$, graph-based Approximate Nearest Neighbor Search (ANNS) aims to build a proximity graph (PG) as an index of $\mathcal{X}$ and approximately return vectors with minimum distances to $\vec{x}q$ by searching over the PG index. It suffers from the large-scale $\mathcal{X}$ because a PG with full vectors is too large to fit into the memory, e.g., a billion-scale $\mathcal{X}$ in 128 dimensions would consume nearly 600 GB memory. To solve this, Product Quantization (PQ) integrated graph-based ANNS is proposed to reduce the memory usage, using smaller compact codes of quantized vectors in memory instead of the large original vectors. Existing PQ methods do not consider the important routing features of PG, resulting in low-quality quantized vectors that affect the ANNS's effectiveness. In this paper, we present an end-to-end Routing-guided learned Product Quantization (RPQ) for graph-based ANNS. It consists of (1) a \textit{differentiable quantizer} used to make the standard discrete PQ differentiable to suit for back-propagation of end-to-end learning, (2) a \textit{sampling-based feature extractor} used to extract neighborhood and routing features of a PG, and (3) a \textit{multi-feature joint training module} with two types of feature-aware losses to continuously optimize the differentiable quantizer. As a result, the inherent features of a PG would be embedded into the learned PQ, generating high-quality quantized vectors. Moreover, we integrate our RPQ with the state-of-the-art DiskANN and existing popular PGs to improve their performance. Comprehensive experiments on real-world large-scale datasets (from 1M to 1B) demonstrate RPQ's superiority, e.g., 1.7$\times$-4.2$\times$ improvement on QPS at the same recall@10 of 95\%.