  Space partitions of $\mathbb{R}^d$ underlie a vast and important class of
fast nearest neighbor search (NNS) algorithms. Inspired by recent theoretical
work on NNS for general metric spaces [Andoni, Naor, Nikolov, Razenshteyn,
Waingarten STOC 2018, FOCS 2018], we develop a new framework for building space
partitions reducing the problem to balanced graph partitioning followed by
supervised classification. We instantiate this general approach with the KaHIP
graph partitioner [Sanders, Schulz SEA 2013] and neural networks, respectively,
to obtain a new partitioning procedure called Neural Locality-Sensitive Hashing
(Neural LSH). On several standard benchmarks for NNS, our experiments show that
the partitions obtained by Neural LSH consistently outperform partitions found
by quantization-based and tree-based methods as well as classic, data-oblivious
LSH.
