Maximum inner product search (MIPS) over dense and sparse vectors have progressed independently in a bifurcated literature for decades; the latter is better known as top-$k$ retrieval in Information Retrieval. This duality exists because sparse and dense vectors serve different end goals. That is despite the fact that they are manifestations of the same mathematical problem. In this work, we ask if algorithms for dense vectors could be applied effectively to sparse vectors, particularly those that violate the assumptions underlying top-$k$ retrieval methods. We study IVF-based retrieval where vectors are partitioned into clusters and only a fraction of clusters are searched during retrieval. We conduct a comprehensive analysis of dimensionality reduction for sparse vectors, and examine standard and spherical KMeans for partitioning. Our experiments demonstrate that IVF serves as an efficient solution for sparse MIPS. As byproducts, we identify two research opportunities and demonstrate their potential. First, we cast the IVF paradigm as a dynamic pruning technique and turn that insight into a novel organization of the inverted index for approximate MIPS for general sparse vectors. Second, we offer a unified regime for MIPS over vectors that have dense and sparse subspaces, and show its robustness to query distributions.

翻译：针对稠密向量与稀疏向量的最大内积搜索（MIPS）在数十年间沿袭着两条独立的分岔研究路径发展，后者在信息检索领域更广为人知的是 top-$k$ 检索。这种二元结构源于稀疏向量与稠密向量服务于不同的最终目标，尽管它们在数学上属于同一问题。本研究探讨能否将稠密向量算法有效应用于稀疏向量，特别是那些违背 top-$k$ 检索方法隐含假设的稀疏向量。我们系统研究了基于 IVF（倒排文件）的检索方法——向量被划分为若干聚类，检索时仅搜索部分聚类。通过全面分析稀疏向量的降维技术，并对比标准 KMeans 与球形 KMeans 的聚类效果，实验证明 IVF 是解决稀疏 MIPS 的高效方案。作为衍生成果，我们识别出两个研究方向并验证其潜力：其一，将 IVF 范式重构为动态剪枝技术，并基于该视角提出一种面向通用稀疏向量的近似 MIPS 倒排索引新型组织架构；其二，建立针对同时包含稠密与稀疏子空间向量的统一 MIPS 体系，并验证其对查询分布的鲁棒性。