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This paper addresses the growing need to process non-Euclidean data, by introducing a geometric deep learning (GDL) framework for building universal feedforward-type models compatible with differentiable manifold geometries.
Extension of range of functions
E.J McShane · 1934
Earlier work this paper cites.
Differentiable functions defined in closed sets. I
Hassler Whitney · 1934
Earlier work this paper cites.
A logical calculus of the ideas immanent in nervous activity
Warren S. McCulloch and Walter Pitts · 1943
Earlier work this paper cites.
Information and the accuracy attainable in the estimation of statistical parameters
C. Radhakrishna Rao · 1945
Earlier work this paper cites.
Topologies for function spaces
Richard Arens and James Dugundji · 1951
Earlier work this paper cites.
On spaces having the homotopy type of a CW {\rm CW} -complex
John Milnor · 1959
Earlier work this paper cites.
Locally flat imbeddings of topological manifolds
Morton Brown · 1962
Earlier work this paper cites.
Über den Begriff der vollständigen differentialgeometrischen Fläche , pages 64–79
W. Rinow · 1964
Earlier work this paper cites.
Algebraic topology
Edwin H. Spanier · 1966
Earlier work this paper cites.
Algebraic topology
Edwin H. Spanier · 1966
Earlier work this paper cites.
Simple closed geodesics on pinched spheres
Wilhelm Klingenberg · 1968
Earlier work this paper cites.
Visual feature extraction by a multilayered network of analog threshold elements
Kunihiko Fukushima · 1969
Earlier work this paper cites.
Differential topology , volume 33 of Graduate Texts in Mathematics
Morris W. Hirsch · 1976
Earlier work this paper cites.
Concerning locally homotopy negligible sets and characterization of l 2 l_{2} -manifolds
H. Toruńczyk · 1978
Earlier work this paper cites.
Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds
Jeff Cheeger, Mikhail Gromov, and Michael Taylor · 1982
Earlier work this paper cites.
The Fréchet distance between multivariate normal distributions
D. C. Dowson and B. V. Landau · 1982
Earlier work this paper cites.
Shape manifolds, Procrustean metrics, and complex projective spaces
David G. Kendall · 1984
Earlier work this paper cites.
Collapsing Riemannian manifolds while keeping their curvature bounded. I
Jeff Cheeger and Mikhael Gromov · 1986
Earlier work this paper cites.
Filtering with observations on a Riemannian symmetric space
Monique Pontier and Jacques Szpirglas · 1986
Earlier work this paper cites.
Complex cobordism and stable homotopy groups of spheres , volume 121 of Pure and Applied Mathematics
Douglas C. Ravenel · 1986
Earlier work this paper cites.
Statistical analysis of spherical data
N. I. Fisher, T. Lewis, and B. J. J. Embleton · 1987
Earlier work this paper cites.
Topological properties of spaces of continuous functions , volume 1315 of Lecture Notes in Mathematics
Robert A. McCoy and Ibula Ntantu · 1988
Earlier work this paper cites.
Multilayer feedforward networks are universal approximators
K. Hornik, M. Stinchcombe, and H. White · 1989
Earlier work this paper cites.
Probabilistic interpretation of feedforward classification network outputs, with relationships to statistical pattern recognition
John S Bridle · 1990
Earlier work this paper cites.
Collapsing Riemannian manifolds while keeping their curvature bounded. II
Jeff Cheeger and Mikhael Gromov · 1990
Earlier work this paper cites.
Approximation capabilities of multilayer feedforward networks
K. Hornik · 1991
Earlier work this paper cites.
Foundations of portfolio theory
Harry M Markowitz · 1991
Earlier work this paper cites.
Universal approximation bounds for superpositions of a sigmoidal function
Andrew R. Barron · 1993
Earlier work this paper cites.
Constructive Approximation
R.A DeVore and G.G. Lorentz · 1993
Earlier work this paper cites.
The Riemannian structure of Euclidean shape spaces: a novel environment for statistics
Hui Ling Le and David G. Kendall · 1993
Earlier work this paper cites.
Polynomial interpolation in several variables
J. Alexander and A. Hirschowitz · 1995
Earlier work this paper cites.
Propagating covariance in computer vision
Robert M Haralick · 1996
Earlier work this paper cites.
The convenient setting of global analysis , volume 53 of Mathematical Surveys and Monographs
Andreas Kriegl and Peter W. Michor · 1997
Earlier work this paper cites.
H3: Laying out large directed graphs in 3d hyperbolic space
Tamara Munzner · 1997
Earlier work this paper cites.
Projective shape analysis
Colin R Goodall and Kanti V Mardia · 1999
Earlier work this paper cites.
Multivariate normal distributions parametrized as a Riemannian symmetric space
Miroslav Lovrić, Maung Min-Oo, and Ernst A. Ruh · 1999
Earlier work this paper cites.
Approximation theory of the MLP model in neural networks
Allan Pinkus · 1999
Earlier work this paper cites.
A course in approximation theory
W. Cheney and W. Light · 2000
Earlier work this paper cites.
Topology
James R. Munkres · 2000
Earlier work this paper cites.
A course in metric geometry , volume 33 of Graduate Studies in Mathematics
Dmitri Burago, Yuri Burago, and Sergei Ivanov · 2001
Earlier work this paper cites.
The infinite-dimensional topology of function spaces , volume 64 of North-Holland Mathematical Library
Jan van Mill · 2001
Earlier work this paper cites.
Algebraic topology
Allen Hatcher · 2002
Earlier work this paper cites.
Differentiable functions defined in closed sets. A problem of Whitney
Edward Bierstone, Pierre D. Milman, and Wiesł aw Pawł ucki · 2003
Earlier work this paper cites.
Principal geodesic analysis for the study of nonlinear statistics of shape
P.T. Fletcher, Conglin Lu, S.M. Pizer, and Sarang Joshi · 2004
Cited alongside, same era.
Visualization of high-dimensional data with relational perspective map
James Xinzhi Li · 2004
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Approximation theory using positive linear operators
R. Paltanea · 2004
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A sharp form of Whitney’s extension theorem
Charles L. Fefferman · 2005
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Directions and projective shapes
Kanti V. Mardia and Vic Patrangenaru · 2005
Cited alongside, same era.
Affine invariance revisited
Evgeni Begelfor and Michael Werman · 2006
Cited alongside, same era.
Wasserstein generative adversarial networks
Martin Arjovsky, Soumith Chintala, and Léon Bottou · 2017
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Information geometry , volume 64 of Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics]
Nihat Ay, Jürgen Jost, Hông Vân Lê, and Lorenz Schwachhöfer · 2017
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Convex analysis and monotone operator theory in Hilbert spaces
Heinz H. Bauschke and Patrick L. Combettes · 2017
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Geometric deep learning: going beyond euclidean data
Michael M Bronstein, Joan Bruna, Yann LeCun, Arthur Szlam, and Pierre Vandergheynst · 2017
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Improved training of wasserstein gans
Ishaan Gulrajani, Faruk Ahmed, Martin Arjovsky, Vincent Dumoulin, and Aaron C Courville · 2017
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Edward Bierstone, Pierre D. Milman, and Wiesł aw Pawł ucki · 2006
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A riemannian framework for tensor computing
Xavier Pennec, Pierre Fillard, and Nicholas Ayache · 2006
Cited alongside, same era.
Spherical-homoscedastic distributions: The equivalency of spherical and normal distributions in classification
Onur C. Hamsici and Aleix M. Martinez · 2007
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The geometric median on riemannian manifolds with application to robust atlas estimation
P. Thomas Fletcher, Suresh Venkatasubramanian, and Sarang Joshi · 2009
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On the coincidence of set-open and uniform topologies
S. E. Nokhrin and A. V. Osipov · 2009
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Population shape regression from random design data
Brad C Davis, P Thomas Fletcher, Elizabeth Bullitt, and Sarang Joshi · 2010
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Deep learning on lie groups for skeleton-based action recognition
Z. Huang, C. Wan, T. Probst, and L. V. Gool · 2017
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Riemannian geometry and geometric analysis
Jürgen Jost · 2017
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Convolutional neural networks on surfaces via seamless toric covers
Haggai Maron, Meirav Galun, Noam Aigerman, Miri Trope, Nadav Dym, Ersin Yumer, Vladimir G. Kim, and Yaron Lipman · 2017
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Poincaré embeddings for learning hierarchical representations
Maximillian Nickel and Douwe Kiela · 2017
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A Bayesian mixed-effects model to learn trajectories of changes from repeated manifold-valued observations
Jean-Baptiste Schiratti, Stéphanie Allassonnière, Olivier Colliot, and Stanley Durrleman · 2017
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Error bounds for approximations with deep relu networks
Dmitry Yarotsky · 2017
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Linear extension operators between spaces of Lipschitz maps and optimal transport
Luigi Ambrosio and Daniele Puglisi · 2018
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Riemannian adaptive optimization methods
Gary Bécigneul and Octavian-Eugen Ganea · 2018
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Neural ordinary differential equations
Ricky TQ Chen, Yulia Rubanova, Jesse Bettencourt, and David K Duvenaud · 2018
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Hyperbolic neural networks
Octavian Ganea, Gary Becigneul, and Thomas Hofmann · 2018
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Proper homotopy types and 𝒵 \mathcal{Z} -boundaries of spaces admitting geometric group actions
Craig R. Guilbault and Molly A. Moran · 2018
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Wasserstein Riemannian geometry of Gaussian densities
Luigi Malagò, Luigi Montrucchio, and Giovanni Pistone · 2018
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Representation tradeoffs for hyperbolic embeddings
Frederic Sala, Chris De Sa, Albert Gu, and Christopher Re · 2018
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Spatial temporal graph convolutional networks for skeleton-based action recognition
S. Yan, Y. Xiong, and D. Lin · 2018
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Low-rank plus sparse decomposition of covariance matrices using neural network parametrization
Michel Baes, Calypso Herrera, Ariel Neufeld, and Pierre Ruyssen · 2019
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Trivializations for gradient-based optimization on manifolds
Mario Lezcano Casado · 2019
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Adaptivity of deep reLU network for learning in besov and mixed smooth besov spaces: optimal rate and curse of dimensionality
Taiji Suzuki · 2019
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Linear Lipschitz and C 1 C^{1} extension operators through random projection
Elia Bruè, Simone Di Marino, and Federico Stra · 2020
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Sparse Gaussian processes with spherical harmonic features
Vincent Dutordoir, Nicolas Durrande, and James Hensman · 2020
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First order methods for optimization on Riemannian manifolds
Orizon P. Ferreira, Mauricio S. Louzeiro, and Leandro F. Prudente · 2020
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Denise: Deep robust principal component analysis for positive semidefinite matrices
Calypso Herrera, Florian Krach, Anastasis Kratsios, Pierre Ruyssen, and Josef Teichmann · 2020
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Universal Approximation with Deep Narrow Networks
Patrick Kidger and Terry Lyons · 2020
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Non-Euclidean Universal Approximation
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Density estimation and modeling on symmetric spaces
Didong Li, Yulong Lu, Emmanuel Chevallier, and David B. Dunson · 2020
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Geodesic convolutional neural networks on riemannian manifolds
J. Masci, D. Boscaini, M. M. Bronstein, and P. Vandergheynst · 2020
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Geomstats: A python package for riemannian geometry in machine learning
Nina Miolane, Nicolas Guigui, Alice Le Brigant, Johan Mathe, Benjamin Hou, Yann Thanwerdas, Stefan Heyder, Olivier Peltre, Niklas Koep, Hadi Zaatiti, Hatem Hajri, Yann Cabanes, Thomas Gerald, Paul Chauchat, Christian Shewmake, Daniel Brooks, Bernhard Kainz, Claire Donnat, Susan Holmes, and Xavier Pennec · 2020
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Globally injective relu networks
Michael Puthawala, Konik Kothari, Matti Lassas, Ivan Dokmanić, and Maarten de Hoop · 2020
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Approximation rates for neural networks with general activation functions
Jonathan W. Siegel and Jinchao Xu · 2020
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The phase diagram of approximation rates for deep neural networks
Dmitry Yarotsky and Anton Zhevnerchuk · 2020
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Graph neural networks: A review of methods and applications
Jie Zhou, Ganqu Cui, Shengding Hu, Zhengyan Zhang, Cheng Yang, Zhiyuan Liu, Lifeng Wang, Changcheng Li, and Maosong Sun · 2020
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Geometric deep learning: Grids, groups, graphs, geodesics, and gauges
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