Gradient descent in hyperbolic space

Impossibility of a complete regular surface in euclidean 3-space whose gaussian curvature has a negative upper bound

N. V. Efimov · 1963

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Constant curvature riemannian scaling

Harold Lindman and Terry Caelli · 1978

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Hyperbolic geometry on a hyperboloid

William F. Reynolds · 1993

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Optimization Algorithms on Matrix Manifolds

P.-A. Absil, R. Mahony, and R. Sepulchre · 2008

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On the convergence of gradient descent for finding the riemannian center of mass

Bijan Afsari, Roberto Tron, and René Vidal · 2011

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Stochastic gradient descent on Riemannian manifolds

Original

S. Bonnabel · 2011

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Computing medians and means in hadamard spaces

Miroslav Bacák · 2014

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Spherical and hyperbolic embeddings of data

R. C. Wilson, E. R. Hancock, E. Pekalska, and R. P. W. Duin · 2014

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Multidimensional scaling in the poincaré disk

Andrej Cvetkovski and Mark Crovella · 2016

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MVIRT, a toolbox for manifold-valued image restoration

Ronny Bergmann · 2017

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Neural Embeddings of Graphs in Hyperbolic Space

Original

B. P. Chamberlain, J. Clough, and M. P. Deisenroth · 2017

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Poincaré embeddings for learning hierarchical representations

Maximillian Nickel and Douwe Kiela · 2017

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Representation Tradeoffs for Hyperbolic Embeddings

Original

C. De Sa, A. Gu, C. Ré, and F. Sala · 2018

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Stable geodesic update on hyperbolic space and its application to poincare embeddings

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Yosuke Enokida, Atsushi Suzuki, and Kenji Yamanishi · 2018

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Learning continuous hierarchies in the lorentz model of hyperbolic geometry

Maximilian Nickel and Douwe Kiela · 2018

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Hyperbolic entailment cones for learning hierarchical embeddings

Thomas Hofmann Octavian-Eugen Ganea, Gary Bécigneul · 2018

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