Learning Space Partitions for Nearest Neighbor Search
Space partitions of 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 et al. 2018b,c), 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 and Schulz 2013) and neural networks, respectively, to obtain a new partitioning procedure called Neural Locality-Sensitive Hashing (Neural LSH). On several standard benchmarks for NNS (Aumuller et al. 2017), 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.
The authors propose a learnable space partitioning nearest-neighbour algorithm where the model learns a hierarchical space partition of the data (using graph partitioning) and learns to predict which buckets a query will reside in (using a learnable model). The paper is an interesting combination of classical optimization and deep learning. The authors make a concerted effort to compare to a range of space-partitioning-based nearest neighbour algorithms, however crucially none of these algorithms are state-of-the-art in comparison to some of the best PQ NNS or hierarchical Navigable Small World Graphs. In terms of writing, the model description requires significant overhaul. I had to re-read it several times and sketch out what exactly you are doing. I would recommend an algorithm box to summarize both the hierarchical graph partitioning *and* the learnable query network. 4.3 *additional experiments* is some of the most interesting parts of the paper, I would recommend promoting these experimental results to the main paper. I would recommend accepting this paper because I think it may lead to state-of-the-art NNS algorithms with theoretical guarantees, especially with a more powerful query network.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Learning Space Partitions for Nearest Neighbor Search
Space partitions of 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 et al. 2018b,c), 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 and Schulz 2013) and neural networks, respectively, to obtain a new partitioning procedure called Neural Locality-Sensitive Hashing (Neural LSH). On several standard benchmarks for NNS (Aumuller et al. 2017), 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.
user
<think>Okay, to do a decent peer review, I should start with summarizing what the work is about. This includes novelty, contributions, clarity, and impact. I might include suggestions to issues that I find critical to the usefulness of the work. Starting with novelty, there are different types of novelty. The first aspect of novelty is scope and scale. Is the work covering a broader perspective than previous works? The second aspect is methodology. Is the proposed methodology novel compared to previous methods? Do they provide any significant advantage over previous methodologies? The third aspect is results. Are the results different compared previous work? Does this lead to any novel theories or an extension of current theories? Next is clarity, I will be reading the work in depth and analyze if any sentences can be potentially ambiguous or misleading. If any sentences are ambiguous, I will state them and give a suggestion on how to rephrase such sentence or how to make more clear to the audience. Lastly, impact is important. I will attempt to predict how such work will impact the scientific community. This might include the applications of such work and how the work might transform the way we study a certain topic. Finally, I will might only mention issues that are critical. This is to keep the review as concise and helpful as possible.</think>



The authors propose a learnable space partitioning nearest-neighbour algorithm where the model learns a hierarchical space partition of the data (using graph partitioning) and learns to predict which buckets a query will reside in (using a learnable model). The paper is an interesting combination of classical optimization and deep learning. The authors make a concerted effort to compare to a range of space-partitioning-based nearest neighbour algorithms, however crucially none of these algorithms are state-of-the-art in comparison to some of the best PQ NNS or hierarchical Navigable Small World Graphs. In terms of writing, the model description requires significant overhaul. I had to re-read it several times and sketch out what exactly you are doing. I would recommend an algorithm box to summarize both the hierarchical graph partitioning *and* the learnable query network. 4.3 *additional experiments* is some of the most interesting parts of the paper, I would recommend promoting these experimental results to the main paper. I would recommend accepting this paper because I think it may lead to state-of-the-art NNS algorithms with theoretical guarantees, especially with a more powerful query network.
assistant
The authors propose a learnable space partitioning nearest-neighbour algorithm where the model learns a hierarchical space partition of the data (using graph partitioning) and learns to predict which buckets a query will reside in (using a learnable model). The paper is an interesting combination of classical optimization and deep learning. The authors make a concerted effort to compare to a range of space-partitioning-based nearest neighbour algorithms, however crucially none of these algorithms are state-of-the-art in comparison to some of the best PQ NNS or hierarchical Navigable Small World Graphs. In terms of writing, the model description requires significant overhaul. I had to re-read it several times and sketch out what exactly you are doing. I would recommend an algorithm box to summarize both the hierarchical graph partitioning *and* the learnable query network. 4.3 *additional experiments* is some of the most interesting parts of the paper, I would recommend promoting these experimental results to the main paper. I would recommend accepting this paper because I think it may lead to state-of-the-art NNS algorithms with theoretical guarantees, especially with a more powerful query network.