Distance Adaptive Beam Search for Provably Accurate Graph-Based Nearest Neighbor Search

TL;DR

This paper introduces a distance-based termination condition for beam search in graph-based nearest neighbor search, providing provable guarantees and empirical improvements over standard methods across various datasets and graph types.

Contribution

It proposes an adaptive beam search method with a new termination condition, linking navigability of graphs to search performance with theoretical guarantees.

Findings

Adaptive Beam Search outperforms standard beam search in recall and efficiency.

The method guarantees approximate nearest neighbor solutions on navigable graphs.

Extensive experiments validate improvements across multiple datasets and graph types.

Abstract

Nearest neighbor search is central in machine learning, information retrieval, and databases. For high-dimensional datasets, graph-based methods such as HNSW, DiskANN, and NSG have become popular thanks to their empirical accuracy and efficiency. These methods construct a directed graph over the dataset and perform beam search on the graph to find nodes close to a given query. While significant work has focused on practical refinements and theoretical understanding of graph-based methods, many questions remain. We propose a new distance-based termination condition for beam search to replace the commonly used condition based on beam width. We prove that, as long as the search graph is navigable, our resulting Adaptive Beam Search method is guaranteed to approximately solve the nearest-neighbor problem, establishing a connection between navigability and the performance of graph-based search. We also provide extensive experiments on our new termination condition for both navigable graphs and approximately navigable graphs used in practice, such as HNSW and Vamana graphs. We find that Adaptive Beam Search outperforms standard beam search over a range of recall values, data sets, graph constructions, and target number of nearest neighbors. It thus provides a simple and practical way to improve the performance of popular methods.