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Related papers: Hyperbolic Geometry in Computer Vision: A Survey

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Slot attention has emerged as a powerful framework for unsupervised object-centric learning, decomposing visual scenes into a small set of compact vector representations called \emph{slots}, each capturing a distinct region or object.…

Computer Vision and Pattern Recognition · Computer Science 2026-03-31 Neelu Madan , Àlex Pujol , Andreas Møgelmose , Sergio Escalera , Kamal Nasrollahi , Graham W. Taylor , Thomas B. Moeslund

For image segmentation, the current standard is to perform pixel-level optimization and inference in Euclidean output embedding spaces through linear hyperplanes. In this work, we show that hyperbolic manifolds provide a valuable…

Computer Vision and Pattern Recognition · Computer Science 2022-03-14 Mina GhadimiAtigh , Julian Schoep , Erman Acar , Nanne van Noord , Pascal Mettes

Learning embeddings of entities and relations existing in knowledge bases allows the discovery of hidden patterns in data. In this work, we examine the geometrical space's contribution to the task of knowledge base completion. We focus on…

Computation and Language · Computer Science 2019-08-20 Prodromos Kolyvakis , Alexandros Kalousis , Dimitris Kiritsis

High-dimensional multiplex graphs are characterized by their high number of complementary and divergent dimensions. The existence of multiple hierarchical latent relations between the graph dimensions poses significant challenges to…

Machine Learning · Computer Science 2025-01-30 Kamel Abdous , Nairouz Mrabah , Mohamed Bouguessa

Representing data in hyperbolic space can effectively capture latent hierarchical relationships. With the goal of enabling accurate classification of points in hyperbolic space while respecting their hyperbolic geometry, we introduce…

Machine Learning · Computer Science 2018-06-04 Hyunghoon Cho , Benjamin DeMeo , Jian Peng , Bonnie Berger

Embedding into hyperbolic space is emerging as an effective representation technique for datasets that exhibit hierarchical structure. This development motivates the need for algorithms that are able to effectively extract knowledge and…

Data Structures and Algorithms · Computer Science 2020-09-03 Xian Wu , Moses Charikar

Learning a latent embedding to understand the underlying nature of data distribution is often formulated in Euclidean spaces with zero curvature. However, the success of the geometry constraints, posed in the embedding space, indicates that…

Computer Vision and Pattern Recognition · Computer Science 2022-08-03 Jie Hong , Pengfei Fang , Weihao Li , Junlin Han , Lars Petersson , Mehrtash Harandi

Network data is ubiquitous in various scientific disciplines, including sociology, economics, and neuroscience. Latent space models are often employed in network data analysis, but the geometric effect of latent space curvature remains a…

Methodology · Statistics 2026-02-11 Jinming Li , Gongjun Xu , Ji Zhu

The spectral geometry of negatively curved manifolds has received more attention than its positive curvature counterpart. In this paper we will survey a variety of spectral geometry results that are known to hold in the context of…

Differential Geometry · Mathematics 2024-11-12 Emilio A. Lauret , Benjamin Linowitz

Recent research has shown that alignment between the structure of graph data and the geometry of an embedding space is crucial for learning high-quality representations of the data. The uniform geometry of Euclidean and hyperbolic spaces…

Machine Learning · Computer Science 2023-06-27 Wei Zhao , Federico Lopez , J. Maxwell Riestenberg , Michael Strube , Diaaeldin Taha , Steve Trettel

Learning low-dimensional numerical representations from symbolic data, e.g., embedding the nodes of a graph into a geometric space, is an important concept in machine learning. While embedding into Euclidean space is common, recent…

Machine Learning · Computer Science 2024-10-10 Thomas Bläsius , Jean-Pierre von der Heydt , Maximilian Katzmann , Nikolai Maas

HOLONOMY is a virtual environment based on the mathematical concept of hyperbolic geometry. Unlike other environments, HOLONOMY allows users to seamlessly explore an infinite hyperbolic space by physically walking. They use their body as…

Graphics · Computer Science 2024-09-10 Martin Skrodzki , Scott Jochems , Joris Rijsdijk , Ravi Snellenberg , Rafael Bidarra

Hyperbolic geometry has recently found applications in social networks, machine learning and computational biology. With the increasing popularity, questions about the best representations of hyperbolic spaces arise, as each representation…

Numerical Analysis · Mathematics 2024-04-16 Dorota Celinska-Kopczynska , Eryk Kopczynski

We introduce hyperbolic attention networks to endow neural networks with enough capacity to match the complexity of data with hierarchical and power-law structure. A few recent approaches have successfully demonstrated the benefits of…

Image-text representation learning forms a cornerstone in vision-language models, where pairs of images and textual descriptions are contrastively aligned in a shared embedding space. Since visual and textual concepts are naturally…

Computer Vision and Pattern Recognition · Computer Science 2025-03-04 Avik Pal , Max van Spengler , Guido Maria D'Amely di Melendugno , Alessandro Flaborea , Fabio Galasso , Pascal Mettes

Recent papers in the graph machine learning literature have introduced a number of approaches for hyperbolic representation learning. The asserted benefits are improved performance on a variety of graph tasks, node classification and link…

Machine Learning · Computer Science 2025-02-26 Isay Katsman , Anna Gilbert

Scene graph representations enable structured visual understanding by modeling objects and their relationships, and have been widely used for multiview and 3D scene reasoning. Existing methods such as MSG learn scene graph embeddings in…

Computer Vision and Pattern Recognition · Computer Science 2026-04-21 Liyang Wang , Zeyu Zhang , Hao Tang

We study geometry, topology and deformation spaces of noncompact complex hyperbolic manifolds (geometrically finite, with variable negative curvature), whose properties make them surprisingly different from real hyperbolic manifolds with…

Differential Geometry · Mathematics 2015-06-26 Boris Apanasov

Mapping complex input data into suitable lower dimensional manifolds is a common procedure in machine learning. This step is beneficial mainly for two reasons: (1) it reduces the data dimensionality and (2) it provides a new data…

Machine Learning · Computer Science 2018-11-28 Daniele Zambon , Lorenzo Livi , Cesare Alippi

This survey reviews hyperbolic graph embedding models, and evaluate them on anomaly detection, highlighting their advantages over Euclidean methods in capturing complex structures. Evaluating models like \textit{HGCAE},…