Optimistic Query Routing in Clustering-based Approximate Maximum Inner Product Search

TL;DR

This paper introduces an optimistic routing algorithm for clustering-based maximum inner product search that leverages distribution moments to reduce the number of points probed, improving efficiency without sacrificing accuracy.

Contribution

It formalizes an optimism-based framework for shard routing in maximum inner product search, achieving comparable accuracy with fewer probes and minimal space overhead.

Findings

Probes up to 50% fewer points than state-of-the-art methods.

Uses only first two moments of inner product distribution.

Space-efficient sketch of second moment independent of dataset size.

Abstract

Clustering-based nearest neighbor search is an effective method in which points are partitioned into geometric shards to form an index, with only a few shards searched during query processing to find a set of top-$k$ vectors. Even though the search efficacy is heavily influenced by the algorithm that identifies the shards to probe, it has received little attention in the literature. This work bridges that gap by studying routing in clustering-based maximum inner product search. We unpack existing routers and notice the surprising contribution of optimism. We then take a page from the sequential decision making literature and formalize that insight following the principle of ``optimism in the face of uncertainty.'' In particular, we present a framework that incorporates the moments of the distribution of inner products within each shard to estimate the maximum inner product. We then present an instance of our algorithm that uses only the first two moments to reach the same accuracy as state-of-the-art routers such as ScaNN by probing up to $50\%$ fewer points on benchmark datasets. Our algorithm is also space-efficient: we design a sketch of the second moment whose size is independent of the number of points and requires $\mathcal{O}(1)$ vectors per shard.