[Submitted on 1 Jul 2026]
Title:Scaling Laws for Grid-Based Approximate Nearest Neighbor Search in High Dimensions
View a PDF of the paper titled Scaling Laws for Grid-Based Approximate Nearest Neighbor Search in High Dimensions, by Matthew J Liu and 6 other authors
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Abstract:Grid-based approaches to approximate nearest neighbor (ANN) search have been absent from modern scaling analyses. We present a systematic characterization of a multiprobe grid algorithm with respect to dataset size $N$ and dimensionality $d$. Our experiments reveal a previously unreported $d$-scaling crossover on the GloVe embedding family, in which multiprobe grid search maintains an approximately constant dimensional scaling exponent while other graph-, tree-, and partitioning-based methods exhibit degrading throughput. The advantage comes with near-linear query scaling in $N$, but also with lower indexing cost than competing ANN methods. Our results suggest that grid-based methods such as multiprobe grid may be competitive in rebuild-heavy or high-dimensional settings where indexing cost and dimensional robustness dictate performance. More broadly, recent work has formalized self-attention as an ANN operation. Thus, the $N$- and $d$-scaling properties of ANN algorithms may guide cost analysis of efficient transformer architectures. Code is available at: this https URL.
Subjects:
Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
Cite as: arXiv:2607.01283 [cs.LG]
(or arXiv:2607.01283v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2607.01283
arXiv-issued DOI via DataCite
Submission history
From: Noah Flynn [view email] [v1] Wed, 1 Jul 2026 08:42:38 UTC (449 KB)
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