Bridging Dense and Sparse Maximum Inner Product Search

TL;DR

This paper explores applying dense vector algorithms to sparse vectors in maximum inner product search, demonstrating IVF-based retrieval as an efficient solution and proposing a unified approach for mixed dense-sparse vectors.

Contribution

It introduces IVF-based retrieval for sparse MIPS, analyzes dimensionality reduction techniques, and proposes a unified framework for vectors with dense and sparse subspaces.

Findings

IVF is effective for sparse MIPS

Dimensionality reduction improves sparse vector retrieval

Unified approach is robust across query distributions

Abstract

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.