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Maximum Inner Product Search (MIPS) for high-dimensional vectors is pivotal across databases, information retrieval, and artificial intelligence. Existing methods either reduce MIPS to Nearest Neighbor Search (NNS) while suffering from…

Databases · Computer Science 2025-07-24 Tingyang Chen , Cong Fu , Kun Wang , Xiangyu Ke , Yunjun Gao , Wenchao Zhou , Yabo Ni , Anxiang Zeng

We focus on Maximum Inner Product Search (MIPS), which is an essential problem in many machine learning communities. Given a query, MIPS finds the most similar items with the maximum inner products. Methods for Nearest Neighbor Search (NNS)…

Information Retrieval · Computer Science 2022-01-25 Chao Feng , Defu Lian , Xiting Wang , Zheng liu , Xing Xie , Enhong Chen

Maximum Inner Product Search (MIPS) is a fundamental challenge in machine learning and information retrieval, particularly in high-dimensional data applications. Existing approaches to MIPS either rely solely on Inner Product (IP)…

Databases · Computer Science 2025-07-24 Tingyang Chen , Cong Fu , Xiangyu Ke , Yunjun Gao , Yabo Ni , Anxiang Zeng

We present a new approach for the approximate K-nearest neighbor search based on navigable small world graphs with controllable hierarchy (Hierarchical NSW, HNSW). The proposed solution is fully graph-based, without any need for additional…

Data Structures and Algorithms · Computer Science 2018-08-16 Yu. A. Malkov , D. A. Yashunin

Neyshabur and Srebro proposed Simple-LSH, which is the state-of-the-art hashing method for maximum inner product search (MIPS) with performance guarantee. We found that the performance of Simple-LSH, in both theory and practice, suffers…

Machine Learning · Computer Science 2018-10-23 Xiao Yan , Jinfeng Li , Xinyan Dai , Hongzhi Chen , James Cheng

Due to the wide applications in recommendation systems, multi-class label prediction and deep learning, the Maximum Inner Product (MIP) search problem has received extensive attention in recent years. Faced with large-scale datasets…

Databases · Computer Science 2021-04-12 Yang Song , Yu Gu , Rui Zhang , Ge Yu

Approximate nearest neighbor search (ANNS) is a fundamental problem in databases and data mining. A scalable ANNS algorithm should be both memory-efficient and fast. Some early graph-based approaches have shown attractive theoretical…

Machine Learning · Computer Science 2025-07-08 Cong Fu , Chao Xiang , Changxu Wang , Deng Cai

We propose shifted inner-product similarity (SIPS), which is a novel yet very simple extension of the ordinary inner-product similarity (IPS) for neural-network based graph embedding (GE). In contrast to IPS, that is limited to…

Machine Learning · Statistics 2019-02-25 Akifumi Okuno , Geewook Kim , Hidetoshi Shimodaira

Maximum Inner Product Search (MIPS) is an important task in many machine learning applications such as the prediction phase of a low-rank matrix factorization model for a recommender system. There have been some works on how to perform MIPS…

Data Structures and Algorithms · Computer Science 2016-10-12 Hsiang-Fu Yu , Cho-Jui Hsieh , Qi Lei , Inderjit S. Dhillon

Near neighbor search (NNS) is a powerful abstraction for data access; however, data indexing is troublesome even for approximate indexes. For intrinsically high-dimensional data, high-quality fast searches demand either indexes with…

Data Structures and Algorithms · Computer Science 2021-06-30 Eric S. Tellez , Guillermo Ruiz , Edgar Chavez , Mario Graff

Efficient Maximum Inner Product Search (MIPS) is an important task that has a wide applicability in recommendation systems and classification with a large number of classes. Solutions based on locality-sensitive hashing (LSH) as well as…

Machine Learning · Computer Science 2015-12-01 Alex Auvolat , Sarath Chandar , Pascal Vincent , Hugo Larochelle , Yoshua Bengio

There has been substantial research on sub-linear time approximate algorithms for Maximum Inner Product Search (MIPS). To achieve fast query time, state-of-the-art techniques require significant preprocessing, which can be a burden when the…

Machine Learning · Computer Science 2018-12-18 Rui Liu , Tianyi Wu , Barzan Mozafari

Maximum Inner Product Search (MIPS) is a ubiquitous task in machine learning applications such as recommendation systems. Given a query vector and $n$ atom vectors in $d$-dimensional space, the goal of MIPS is to find the atom that has the…

Machine Learning · Computer Science 2023-06-28 Mo Tiwari , Ryan Kang , Je-Yong Lee , Donghyun Lee , Chris Piech , Sebastian Thrun , Ilan Shomorony , Martin Jinye Zhang

Nearest Neighbor Search (NNS) has recently drawn a rapid increase of interest due to its core role in managing high-dimensional vector data in data science and AI applications. The interest is fueled by the success of neural embedding,…

Distributed, Parallel, and Cluster Computing · Computer Science 2022-02-01 Zhen Peng , Minjia Zhang , Kai Li , Ruoming Jin , Bin Ren

Recently it was shown that the problem of Maximum Inner Product Search (MIPS) is efficient and it admits provably sub-linear hashing algorithms. Asymmetric transformations before hashing were the key in solving MIPS which was otherwise…

Machine Learning · Statistics 2014-11-14 Anshumali Shrivastava , Ping Li

Mixed-integer linear programs (MILPs) are extensively used to model practical problems such as planning and scheduling. A prominent method for solving MILPs is large neighborhood search (LNS), which iteratively seeks improved solutions…

Optimization and Control · Mathematics 2024-12-12 Wenbo Liu , Akang Wang , Wenguo Yang , Qingjiang Shi

Proximity graphs (PG) have gained increasing popularity as the state-of-the-art solutions to $k$-approximate nearest neighbor ($k$-ANN) search on high-dimensional data, which serves as a fundamental function in various fields, e.g.,…

Databases · Computer Science 2025-02-18 Shuo Yang , Jiadong Xie , Yingfan Liu , Jeffrey Xu Yu , Xiyue Gao , Qianru Wang , Yanguo Peng , Jiangtao Cui

Large Neighborhood Search (LNS) is a combinatorial optimization heuristic that starts with an assignment of values for the variables to be optimized, and iteratively improves it by searching a large neighborhood around the current…

Optimization and Control · Mathematics 2022-05-23 Nicolas Sonnerat , Pengming Wang , Ira Ktena , Sergey Bartunov , Vinod Nair

We propose $\textit{weighted inner product similarity}$ (WIPS) for neural network-based graph embedding. In addition to the parameters of neural networks, we optimize the weights of the inner product by allowing positive and negative…

Machine Learning · Computer Science 2019-06-04 Geewook Kim , Akifumi Okuno , Kazuki Fukui , Hidetoshi Shimodaira

Approximate nearest neighbor search under universal L_p metrics (ANNS-U-L_p) is an important and challenging research problem, as it requires answering queries under all possible p (0<p <= 2) values simultaneously without building an index…

Databases · Computer Science 2026-05-08 Huayi Wang , Jingfan Meng , Jun Xu
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