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Related papers: Hyperbolic Manifold Regression

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Multidimensional scaling (MDS) is a widely used approach to representing high-dimensional, dependent data. MDS works by assigning each observation a location on a low-dimensional geometric manifold, with distance on the manifold…

Methodology · Statistics 2023-08-16 Bolun Liu , Shane Lubold , Adrian E. Raftery , Tyler H. McCormick

Multi-step reasoning remains a central challenge for large language models: single-pass generation is efficient but lacks accuracy; tree-search methods explore multiple paths but are computation-heavy. We address this gap by distilling…

Artificial Intelligence · Computer Science 2026-05-29 Yuyu Liu , Haotian Xu , Yanan He , Sarang Rajendra Patil , Mengjia Xu , Tengfei Ma

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

Geometric trees are characterized by their tree-structured layout and spatially constrained nodes and edges, which significantly impacts their topological attributes. This inherent hierarchical structure plays a crucial role in domains such…

Machine Learning · Computer Science 2024-08-19 Zheng Zhang , Allen Zhang , Ruth Nelson , Giorgio Ascoli , Liang Zhao

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

Learning representations for graphs plays a critical role in a wide spectrum of downstream applications. In this paper, we summarize the limitations of the prior works in three folds: representation space, modeling dynamics and modeling…

Machine Learning · Computer Science 2021-04-07 Li Sun , Zhongbao Zhang , Jiawei Zhang , Feiyang Wang , Hao Peng , Sen Su , Philip S. Yu

Learning the manifold structure of remote sensing images is of paramount relevance for modeling and understanding processes, as well as to encapsulate the high dimensionality in a reduced set of informative features for subsequent…

Computer Vision and Pattern Recognition · Computer Science 2022-05-04 Gulsen Taskin , Gustau Camps-Valls

Energy-based predictive world models provide a powerful approach for multi-step visual planning by reasoning over latent energy landscapes rather than generating pixels. However, existing approaches face two major challenges: (i) their…

Computer Vision and Pattern Recognition · Computer Science 2026-05-19 Zeyu Zhang , Danning Li , Ian Reid , Richard Hartley

Most of the existing literature regarding hyperbolic embedding concentrate upon supervised learning, whereas the use of unsupervised hyperbolic embedding is less well explored. In this paper, we analyze how unsupervised tasks can benefit…

Machine Learning · Computer Science 2021-03-31 Jiwoong Park , Junho Cho , Hyung Jin Chang , Jin Young Choi

We present a large scale hyperbolic recommender system. We discuss why hyperbolic geometry is a more suitable underlying geometry for many recommendation systems and cover the fundamental milestones and insights that we have gained from its…

Information Retrieval · Computer Science 2019-02-26 Benjamin Paul Chamberlain , Stephen R. Hardwick , David R. Wardrope , Fabon Dzogang , Fabio Daolio , Saúl Vargas

Recently, there has been an interest in embedding networks in hyperbolic space, since hyperbolic space has been shown to work well in capturing graph/network structure as it can naturally reflect some properties of complex networks.…

Social and Information Networks · Computer Science 2020-11-04 Lili Wang , Ying Lu , Chenghan Huang , Soroush Vosoughi

Adversarial examples in neural networks have been extensively studied in Euclidean geometry, but recent advances in \textit{hyperbolic networks} call for a reevaluation of attack strategies in non-Euclidean geometries. Existing methods such…

Machine Learning · Computer Science 2026-03-24 Minsoo Jo , Dongyoon Yang , Taesup Kim

Hyperbolic machine learning is an emerging field aimed at representing data with a hierarchical structure. However, there is a lack of tools for evaluation and analysis of the resulting hyperbolic data representations. To this end, we…

Hyperbolic space is a geometry that is known to be well-suited for representation learning of data with an underlying hierarchical structure. In this paper, we present a novel hyperbolic distribution called \textit{pseudo-hyperbolic…

Machine Learning · Statistics 2019-05-13 Yoshihiro Nagano , Shoichiro Yamaguchi , Yasuhiro Fujita , Masanori Koyama

Representation of 2D frame less visual space as neural manifold and its modelling in the frame work of information geometry is presented. Origin of hyperbolic nature of the visual space is investigated using evidences from neuroscience.…

Neural and Evolutionary Computing · Computer Science 2020-11-30 Debasis Mazumdar

In large-scale recommender systems, the user-item networks are generally scale-free or expand exponentially. The latent features (also known as embeddings) used to describe the user and item are determined by how well the embedding space…

Information Retrieval · Computer Science 2022-05-31 Menglin Yang , Min Zhou , Jiahong Liu , Defu Lian , Irwin King

In this work, we propose a fashion item recommendation model that incorporates hyperbolic geometry into user and item representations. Using hyperbolic space, our model aims to capture implicit hierarchies among items based on their visual…

Information Retrieval · Computer Science 2024-09-05 Ryotaro Shimizu , Yu Wang , Masanari Kimura , Yuki Hirakawa , Takashi Wada , Yuki Saito , Julian McAuley

Binary Neural Network (BNN) converts full-precision weights and activations into their extreme 1-bit counterparts, making it particularly suitable for deployment on lightweight mobile devices. While binary neural networks are typically…

Machine Learning · Computer Science 2025-01-08 Jun Chen , Jingyang Xiang , Tianxin Huang , Xiangrui Zhao , Yong Liu

Machine learning problems have an intrinsic geometric structure as central objects including a neural network's weight space and the loss function associated with a particular task can be viewed as encoding the intrinsic geometry of a given…

Machine Learning · Computer Science 2021-06-08 Guruprasad Raghavan , Matt Thomson

Representation learning has become an invaluable approach for learning from symbolic data such as text and graphs. However, while complex symbolic datasets often exhibit a latent hierarchical structure, state-of-the-art methods typically…

Artificial Intelligence · Computer Science 2017-05-29 Maximilian Nickel , Douwe Kiela