Approximate Nearest Neighbor Search (ANNS) plays a pivotal role in modern deep learning pipelines. Recently, many ANNS systems have been proposed to either provide broad functionality or reach high performance. However, it is yet difficult to achieve both with minimal programming efforts. We propose ANNLib to address the gap. ANNLib is a library that provides a programming framework for achieving high performance and flexible functionality in ANNS systems, based on popular graph-based ANNS algorithms. We carefully decouple and independently optimize both the algorithm and the data structure components of an ANNS system. In addition, we integrate state-of-the-art algorithms and data structures into ANNLib as modules, along with our new designs. Users can choose combinations of components to implement sophisticated settings with high performance, such as filter search, fully dynamic updates, and historical queries on snapshots. Our experiments show that our new solution provides a simple interface for various applications and achieves comparable or even better performance than previous work, specifically for each application.
Hierarchical Navigable Small World (HNSW) graphs serve as the industry standard due to their logarithmic complexity and strong empirical performance. However, HNSW relies on greedy graph traversal, a heuristic that provides no theoretical guarantees of correctness. In this paper, we propose a novel "Certify-then-Rectify" framework that bridges the gap between the speed of heuristic search and the rigor of exact retrieval. Rather than discarding HNSW, our approach first employs a distribution-free statistical certifier to dynamically evaluate the quality of a standard HNSW search with minimal overhead. If certification indicates that the retrieved neighbors are of low quality, the framework safely escalates to a rigorous exact recovery algorithm. To make this exact recovery computationally feasible, we reinterpret the HNSW graph as a geometric spanner and utilize Extreme Value Theory to stochastically estimate its maximum empirical stretch factor. This allows us to mathematically bound the maximum distance of true nearest neighbors. Extensive evaluations on benchmark datasets demonstrate that our tiered framework delivers the average-case speed of HNSW while ensuring the worst-case correctness of exact search and outperforming other applicable approaches.