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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

The inner-product navigable small world graph (ip-NSW) represents the state-of-the-art method for approximate maximum inner product search (MIPS) and it can achieve an order of magnitude speedup over the fastest baseline. However, to date…

Information Retrieval · Computer Science 2019-12-10 Jie Liu , Xiao Yan , Xinyan Dai , Zhirong Li , James Cheng , Ming-Chang Yang

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

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

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

We propose a quantization based approach for fast approximate Maximum Inner Product Search (MIPS). Each database vector is quantized in multiple subspaces via a set of codebooks, learned directly by minimizing the inner product quantization…

Artificial Intelligence · Computer Science 2015-09-07 Ruiqi Guo , Sanjiv Kumar , Krzysztof Choromanski , David Simcha

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

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

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

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

Exact Maximum Inner Product Search (MIPS) is an important task that is widely pertinent to recommender systems and high-dimensional similarity search. The brute-force approach to solving exact MIPS is computationally expensive, thus…

Information Retrieval · Computer Science 2019-03-18 Firas Abuzaid , Geet Sethi , Peter Bailis , Matei Zaharia

The $k$-Maximum Inner Product Search ($k$MIPS) serves as a foundational component in recommender systems and various data mining tasks. However, while most existing $k$MIPS approaches prioritize the efficient retrieval of highly relevant…

Information Retrieval · Computer Science 2024-02-22 Qiang Huang , Yanhao Wang , Yiqun Sun , Anthony K. H. Tung

Maximum inner product search (MIPS) over dense and sparse vectors have progressed independently in a bifurcated literature for decades; the latter is better known as top-$k$ retrieval in Information Retrieval. This duality exists because…

Information Retrieval · Computer Science 2024-05-20 Sebastian Bruch , Franco Maria Nardini , Amir Ingber , Edo Liberty

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

We present the first provably sublinear time algorithm for approximate \emph{Maximum Inner Product Search} (MIPS). Our proposal is also the first hashing algorithm for searching with (un-normalized) inner product as the underlying…

Machine Learning · Statistics 2014-05-23 Anshumali Shrivastava , Ping Li

Maximum inner product search (MIPS) is a crucial subroutine in machine learning, requiring the identification of key vectors that align best with a given query. We propose amortized MIPS: a learning-based approach that trains neural…

Machine Learning · Computer Science 2026-03-10 Theo X. Olausson , João Monteiro , Michal Klein , Marco Cuturi

We propose a novel dimensionality reduction method for maximum inner product search (MIPS), named CEOs, based on the theory of concomitants of extreme order statistics. Utilizing the asymptotic behavior of these concomitants, we show that a…

Data Structures and Algorithms · Computer Science 2021-08-19 Ninh Pham

The MIPS (maximum inner product search), which finds the item with the highest inner product with a given query user, is an essential problem in the recommendation field. It is usual that e-commerce companies face situations where they want…

Databases · Computer Science 2021-10-15 Daichi Amagata , Takahiro Hara

Sparse vector Maximum Inner Product Search (MIPS) is crucial in multi-path retrieval for Retrieval-Augmented Generation (RAG). Recent inverted index-based and graph-based algorithms have achieved high search accuracy with practical…

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
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