高維度中基於網格的近似最近鄰搜索的縮放定律

摘要

基於網格的近似最近鄰（ANN）搜尋方法在當代規模化分析中長期缺席。我們針對多探針網格演算法，系統性地刻畫其在資料集規模N與維度d下的表現。實驗結果揭示出GloVe嵌入家族中一項先前未被報導的維度縮放交叉現象：多探針網格搜尋維持近似恆定的維度縮放指數，而其他基於圖、樹與分割的方法則呈現吞吐量下降。此優勢不僅在N上呈近線性查詢縮放，其索引成本亦低於其他競爭性ANN方法。結果顯示，多探針網格等基於網格的方法，在索引成本與維度穩健性主導效能的密集重建或高維場景中，可能具競爭力。更廣泛而言，近期研究已將自注意力機制形式化為ANN運算。因此，ANN演算法的N與d縮放特性，可引導高效Transformer架構的成本分析。程式碼已開源於：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.