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

2025-05-21

AI Summary

Beam search in graph-based nearest neighbor search (e.g., HNSW, NSG, DiskANN) relies on a fixed beam width, lacks theoretical guarantees on correctness, and suffers from suboptimal query efficiency. Method: This paper proposes a distance-driven adaptive termination condition for beam search. It establishes, for the first time, a theoretical link between graph navigability and search accuracy, proving correctness guarantees for approximate nearest neighbors. The method requires no modification to graph construction—enabling plug-and-play deployment—and integrates dynamic distance pruning with navigability analysis to support diverse graph structures (e.g., HNSW, Vamana). Contribution/Results: Evaluated across multiple datasets and graph configurations, it achieves 15–30% lower average query latency at equal recall rates, while natively supporting arbitrary *k*-nearest neighbor retrieval without additional overhead.

Technology Category

• Search and Optimization: Distributed Search
• Machine Learning: Graph-based Machine Learning
• Constraint Satisfaction and Optimization: Search

Application Category

• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

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.

Problem

• Improving nearest neighbor search accuracy in high-dimensional datasets
• Proposing a distance-based termination condition for beam search
• Ensuring provable accuracy in graph-based nearest neighbor search

Innovation

• Distance-based termination condition for beam search
• Proven accuracy with navigable search graphs
• Outperforms standard beam search in experiments