Results 231 to 240 of about 5,510,773 (262)

Hypformer: Exploring Efficient Transformer Fully in Hyperbolic Space

Knowledge Discovery and Data Mining
Hyperbolic geometry have shown significant potential in modeling complex structured data, particularly those with underlying tree-like and hierarchical structures.
Menglin Yang, Harshit Verma, Delvin Ce Zhang, Jiahong Liu, Irwin King, Rex Ying   +5 more
semanticscholar   +1 more source

Hyperbolic conformality in multidimensional hyperbolic spaces

Mathematical Methods in the Applied Sciences, 2020
In a previous work, the hyperbolic conformality for bicomplex functions was introduced, and it was proved that, with the adequate hypothesis, a bicomplex holomorphic function is hyperbolic conformal. The aim of this paper is to extend this idea to , with the set of hyperbolic numbers.
A. Golberg, M. E. Luna‐Elizarrarás
openaire   +1 more source

Rethinking Generalizable Face Anti-Spoofing via Hierarchical Prototype-Guided Distribution Refinement in Hyperbolic Space

Computer Vision and Pattern Recognition
Generalizable face anti-spoofing (FAS) approaches have drawn growing attention due to their robustness for diverse presentation attacks in unseen scenarios. Most previous methods always utilize domain generalization (DG) frame-works via directly aligning
Chengyang Hu, Ke-Yue Zhang, Taiping Yao, Shouhong Ding, Lizhuang Ma   +4 more
semanticscholar   +1 more source

HyperML: A Boosting Metric Learning Approach in Hyperbolic Space for Recommender Systems

Web Search and Data Mining, 2018
This paper investigates the notion of learning user and item representations in non-Euclidean space. Specifically, we study the connection between metric learning in hyperbolic space and collaborative filtering by exploring Mobius gyrovector spaces where
Lucas Vinh Tran, Yi Tay, Shuai Zhang, G. Cong, Xiaoli Li   +4 more
semanticscholar   +1 more source

Hyperbolically Sasakian and equidistant hyperbolically Kahlerian spaces

Journal of Soviet Mathematics, 1992
See the review in Zbl 0711.53042.
Mikeš, Josef, Starko, G. A.
openaire   +2 more sources

Hyperbolic Spaces

2008
unknown ...
openaire   +3 more sources

Quermassintegral preserving curvature flow in Hyperbolic space

Geometric and Functional Analysis, 2017
We consider the quermassintegral preserving flow of closed h-convex hypersurfaces in hyperbolic space with the speed given by any positive power of a smooth symmetric, strictly increasing, and homogeneous of degree one function f of the principal ...
B. Andrews, Yong Wei
semanticscholar   +1 more source

ON THE UMBILICITY OF HYPERSURFACES IN THE HYPERBOLIC SPACE

Journal of the Australian Mathematical Society, 2016
In this paper, we establish new characterization results concerning totally umbilical hypersurfaces of the hyperbolic space$\mathbb{H}^{n+1}$, under suitable constraints on the behavior of the Lorentzian Gauss map of complete hypersurfaces having some constant higher order mean curvature.
Aquino, C. P., Batista, M., de Lima, H. F.   +2 more
openaire   +1 more source

Busemann Spaces and Hyperbolic Spaces

2014
A Busemann space (also known as a Busemann convex space) is a geodesic metric space X such that for any two geodesics \(\gamma: \left [a,b\right ] \rightarrow X\) and \(\gamma ^{{\prime}}: \left [a^{{\prime}},b^{{\prime}}\right ] \rightarrow X,\) the map \(D_{\gamma,\gamma ^{{\prime}}}: \left [a,b\right ] \times \left [a^{{\prime}},b^{{\prime}}\right ]
William Kirk, Naseer Shahzad
openaire   +1 more source

Hyperbolic Space

1992
Riccardo Benedetti, Carlo Petronio
openaire   +1 more source