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In this paper we show how the complexity of performing nearest neighbor (NNS) search on a metric space is related to the expansion of the metric space. Given a metric space we look at the graph obtained by connecting every pair of points…

Data Structures and Algorithms · Computer Science 2010-05-05 Rina Panigrahy , Kunal Talwar , Udi Wieder

In some game scenarios, due to the uncertainty of the number of enemy units and the priority of various attributes, the evaluation of the threat level of enemy units as well as the screening has been a challenging research topic, and the…

Machine Learning · Computer Science 2025-04-28 Wuzhou Sun , Siyi Li , Qingxiang Zou , Zixing Liao

Recent research works have shown that image retrieval models are vulnerable to adversarial attacks, where slightly modified test inputs could lead to problematic retrieval results. In this paper, we aim to design a provably robust image…

Information Retrieval · Computer Science 2022-06-23 Yihan Wu , Hongyang Zhang , Heng Huang

Approximate $k$-nearest neighbor search (A$k$-NNS) is a core operation in vector databases, underpinning applications such as retrieval-augmented generation (RAG) and image retrieval. In these scenarios, users often prefer diverse result…

Databases · Computer Science 2025-11-03 Jiachen Zhao , Xiao Yan , Eric Lo

Deep neural networks (DNNs) are notorious for their vulnerability to adversarial attacks, which are small perturbations added to their input images to mislead their prediction. Detection of adversarial examples is, therefore, a fundamental…

Machine Learning · Computer Science 2020-03-20 Gilad Cohen , Guillermo Sapiro , Raja Giryes

This study combines two different learning paradigms, k-nearest neighbor (k-NN) rule, as memory-based learning paradigm and relevance vector machines (RVM), as statistical learning paradigm. This combination is performed in kernel space and…

Machine Learning · Computer Science 2021-03-09 Sara Hosseinzadeh Kassani , Farhood Rismanchian , Peyman Hosseinzadeh Kassani

Trustworthiness in model predictions is crucial for safety-critical applications in the real world. However, deep neural networks often suffer from the issues of uncertainty estimation, such as miscalibration. In this study, we propose…

Computation and Language · Computer Science 2025-02-07 Wataru Hashimoto , Hidetaka Kamigaito , Taro Watanabe

In pattern recognition or machine learning, it is a very fundamental task to find nearest neighbors of a given point. All the methods for the task work basically by comparing the given point to all the points in the data set. That is why…

Machine Learning · Computer Science 2019-12-10 Hayoung Um , Heeyoul Choi

High dimensionality, i.e. data having a large number of variables, tends to be a challenge for most machine learning tasks, including classification. A classifier usually builds a model representing how a set of inputs explain the outputs.…

Machine Learning · Computer Science 2018-03-12 Francisco J. Pulgar , Francisco Charte , Antonio J. Rivera , María J. del Jesus

In the past five years, deep learning methods have become state-of-the-art in solving various inverse problems. Before such approaches can find application in safety-critical fields, a verification of their reliability appears mandatory.…

Machine Learning · Computer Science 2023-01-18 Martin Genzel , Jan Macdonald , Maximilian März

Deep Neural networks are efficient and flexible models that perform well for a variety of tasks such as image, speech recognition and natural language understanding. In particular, convolutional neural networks (CNN) generate a keen…

Machine Learning · Computer Science 2018-12-20 Yesmina Jaafra , Jean Luc Laurent , Aline Deruyver , Mohamed Saber Naceur

Nearest neighbor searching of large databases in high-dimensional spaces is inherently difficult due to the curse of dimensionality. A flavor of approximation is, therefore, necessary to practically solve the problem of nearest neighbor…

Databases · Computer Science 2018-04-24 Akhil Arora , Sakshi Sinha , Piyush Kumar , Arnab Bhattacharya

We propose a general framework for end-to-end learning of data structures. Our framework adapts to the underlying data distribution and provides fine-grained control over query and space complexity. Crucially, the data structure is learned…

Machine Learning · Computer Science 2024-11-06 Omar Salemohamed , Laurent Charlin , Shivam Garg , Vatsal Sharan , Gregory Valiant

Being able to reason in an environment with a large number of discrete actions is essential to bringing reinforcement learning to a larger class of problems. Recommender systems, industrial plants and language models are only some of the…

This survey (re)introduces reinforcement learning methods to economists. The curse of dimensionality limits how far exact dynamic programming can be effectively applied, forcing us to rely on suitably "small" problems or our ability to…

General Economics · Economics 2026-03-25 Pranjal Rawat

Reinforcement Learning (RL), bolstered by the expressive capabilities of Deep Neural Networks (DNNs) for function approximation, has demonstrated considerable success in numerous applications. However, its practicality in addressing various…

Machine Learning · Computer Science 2024-04-26 Aditya Mohan , Amy Zhang , Marius Lindauer

Neighbor search is of fundamental important to many engineering and science fields such as physics simulation and computer graphics. This paper proposes to formulate neighbor search as a ray tracing problem and leverage the dedicated ray…

Distributed, Parallel, and Cluster Computing · Computer Science 2022-03-10 Yuhao Zhu

The $k$-d tree is one of the oldest and most widely used data structures for nearest neighbor search. It partitions Euclidean space into axis-aligned rectangular cells. There are two standard ways to find the nearest neighbor to a query in…

Data Structures and Algorithms · Computer Science 2026-05-13 Marco Bazzani , Sanjoy Dasgupta

Representation learning, i.e. the generation of representations useful for downstream applications, is a task of fundamental importance that underlies much of the success of deep neural networks (DNNs). Recently, robustness to adversarial…

Machine Learning · Computer Science 2022-09-16 Christian Cianfarani , Arjun Nitin Bhagoji , Vikash Sehwag , Ben Y. Zhao , Prateek Mittal , Haitao Zheng

Recent studies on neural architecture search have shown that automatically designed neural networks perform as good as expert-crafted architectures. While most existing works aim at finding architectures that optimize the prediction…