On the adversarial robustness of Locality-Sensitive Hashing in Hamming space

TL;DR

This paper investigates the robustness of locality-sensitive hashing in Hamming space against adaptive adversarial queries, showing that an adversary can efficiently find queries that cause the data structure to fail.

Contribution

It introduces an adversarial algorithm that exploits the structure of LSH in Hamming space to find failure queries exponentially faster than random sampling.

Findings

Adversary can find failure queries efficiently in Hamming LSH

Adaptive queries can break the robustness of LSH data structures

Failure queries can be found exponentially faster than random methods

Abstract

Locality-sensitive hashing~[Indyk,Motwani'98] is a classical data structure for approximate nearest neighbor search. It allows, after a close to linear time preprocessing of the input dataset, to find an approximately nearest neighbor of any fixed query in sublinear time in the dataset size. The resulting data structure is randomized and succeeds with high probability for every fixed query. In many modern applications of nearest neighbor search the queries are chosen adaptively. In this paper, we study the robustness of the locality-sensitive hashing to adaptive queries in Hamming space. We present a simple adversary that can, under mild assumptions on the initial point set, provably find a query to the approximate near neighbor search data structure that the data structure fails on. Crucially, our adaptive algorithm finds the hard query exponentially faster than random sampling.