高维空间中基于网格的近似最近邻搜索的缩放定律

摘要

基于网格的近似最近邻（ANN）搜索方法在现代扩展性分析中鲜有涉及。本文系统刻画了多探针网格算法在数据集规模N和维度d上的性能特征。实验揭示了GloVe嵌入系列中此前未报道的d-缩放交叉现象：当其他基于图、树和分区的算法吞吐量下降时，多探针网格搜索却能维持近似恒定的维度缩放指数。该优势不仅体现在查询复杂度随N接近线性增长，其索引构建成本也低于其他ANN方法。研究结果表明，在索引重建频繁或高维场景中，多探针网格等基于网格的方法可能具有竞争力——此类场景下索引开销和维度鲁棒性决定了性能表现。更广泛而言，近期研究已将自注意力机制形式化为ANN操作，因此ANN算法的N和d缩放特性可为高效Transformer架构的成本分析提供指导。代码开源地址：https://github.com/weiz345/MultiProbeANN。

English

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: https://github.com/weiz345/MultiProbeANN.