Results 21 to 30 of about 1,380,597 (301)
Understanding the Latent Space of Diffusion Models through the Lens of Riemannian Geometry [PDF]
Neural Information Processing Systems, 2023 Despite the success of diffusion models (DMs), we still lack a thorough understanding of their latent space. To understand the latent space $\mathbf{x}_t \in \mathcal{X}$, we analyze them from a geometrical perspective. Our approach involves deriving the
Yong-Hyun Park +4 more
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On the geometry of the tangent bundle with gradient Sasaki metric [PDF]
Arab Journal of Mathematical Sciences, 2023 Purpose – Let (M, g) be a n-dimensional smooth Riemannian manifold. In the present paper, the authors introduce a new class of natural metrics denoted by gf and called gradient Sasaki metric on the tangent bundle TM. The authors calculate its Levi-Civita
Lakehal Belarbi, Hichem Elhendi
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A Riemannian Geometry Theory of Three-Dimensional Binocular Visual Perception. [PDF]
Vision (Basel), 2018 We present a Riemannian geometry theory to examine the systematically warped geometry of perceived visual space attributable to the size⁻distance relationship of retinal images associated with the optics of the human eye.
Neilson PD, Neilson MD, Bye RT.
europepmc +2 more sources
Riemannian geometry and automatic differentiation for optimization problems of quantum physics and quantum technologies [PDF]
New Journal of Physics, 2020 Optimization with constraints is a typical problem in quantum physics and quantum information science that becomes especially challenging for high-dimensional systems and complex architectures like tensor networks.
I. Luchnikov, M. Krechetov, S. Filippov
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Weighted Ricci curvature in Riemann-Finsler geometry [PDF]
AUT Journal of Mathematics and Computing, 2021 Ricci curvature is one of the important geometric quantities in Riemann-Finsler geometry. Together with the $S$-curvature, one can define a weighted Ricci curvature for a pair of Finsler metric and a volume form on a manifold.
Zhongmin Shen
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Generic Riemannian Maps from Nearly Kaehler Manifolds
Computer Sciences & Mathematics Forum, 2023 In order to generalise semi-invariant Riemannian maps, Sahin first introduced the idea of “Generic Riemannian maps”. We extend the idea of generic Riemannian maps to the case in which the total manifold is a nearly Kaehler manifold.
Richa Agarwal, Shahid Ali
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On h-Quasi-Hemi-Slant Riemannian Maps
Axioms, 2022 In the present article, we indroduce and study h-quasi-hemi-slant (in short, h-qhs) Riemannian maps and almost h-qhs Riemannian maps from almost quaternionic Hermitian manifolds to Riemannian manifolds. We investigate some fundamental results mainly on h-
Mohd Bilal +4 more
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Riemannian Geometry of Contact and Symplectic Manifolds
, 2002 David E. Blair
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Dynamic graphs, community detection, and Riemannian geometry. [PDF]
Appl Netw Sci, 2018 A community is a subset of a wider network where the members of that subset are more strongly connected to each other than they are to the rest of the network.
Bakker C +2 more
europepmc +2 more sources