[2412.01940] Down with the Hierarchy: The 'H' in HNSW Stands for "Hubs"

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Computer Science > Machine Learning

arXiv:2412.01940 (cs)

[Submitted on 2 Dec 2024 (v1), last revised 3 Jul 2025 (this version, v3)]

Title:Down with the Hierarchy: The 'H' in HNSW Stands for "Hubs"

Authors:Blaise Munyampirwa, Vihan Lakshman, Benjamin Coleman<br>View a PDF of the paper titled Down with the Hierarchy: The 'H' in HNSW Stands for "Hubs", by Blaise Munyampirwa and 2 other authors

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Abstract:Driven by recent breakthrough advances in neural representation learning, approximate near-neighbor (ANN) search over vector embeddings has emerged as a critical computational workload. With the introduction of the seminal Hierarchical Navigable Small World (HNSW) algorithm, graph-based indexes have established themselves as the overwhelmingly dominant paradigm for efficient and scalable ANN search. As the name suggests, HNSW searches a layered hierarchical graph to quickly identify neighborhoods of similar points to a given query vector. But is this hierarchy even necessary? A rigorous experimental analysis to answer this question would provide valuable insights into the nature of algorithm design for ANN search and motivate directions for future work in this increasingly crucial domain. We conduct an extensive benchmarking study covering more large-scale datasets than prior investigations of this question. We ultimately find that a flat navigable small world graph graph retains all of the benefits of HNSW on high-dimensional datasets, with latency and recall performance essentially \emph{identical} to the original algorithm but with less memory overhead. Furthermore, we go a step further and study \emph{why} the hierarchy of HNSW provides no benefit in high dimensions, hypothesizing that navigable small world graphs contain a well-connected, frequently traversed ``highway" of hub nodes that maintain the same purported function as the hierarchical layers. We present compelling empirical evidence that the \emph{Hub Highway Hypothesis} holds for real datasets and investigate the mechanisms by which the highway forms. The implications of this hypothesis may also provide future research directions in developing enhancements to graph-based ANN search.

Comments:<br>17 pages

Subjects:

Machine Learning (cs.LG); Databases (cs.DB); Information Retrieval (cs.IR)

Cite as:<br>arXiv:2412.01940 [cs.LG]

(or<br>arXiv:2412.01940v3 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2412.01940

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arXiv-issued DOI via DataCite

Submission history<br>From: Vihan Lakshman [view email]<br>[v1]<br>Mon, 2 Dec 2024 20:04:06 UTC (6,321 KB)

[v2]<br>Sun, 2 Feb 2025 19:25:13 UTC (10,298 KB)

[v3]<br>Thu, 3 Jul 2025 13:32:02 UTC (5,564 KB)

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