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In this paper, we introduce McTorch, a manifold optimization library for deep learning that extends PyTorch.
The geometry of algorithms with orthogonality constraints
A. Edelman, T.A. Arias, and S.T. Smith · 1998
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Optimization Algorithms on Matrix Manifolds
P.-A. Absil, R. Mahony, and R. Sepulchre · 2008
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Positive definite matrices
R. Bhatia · 2009
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Linear regression under fixed-rank constraints: a Riemannian approach
G. Meyer, S. Bonnabel, and R. Sepulchre · 2011
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Stochastic gradient descent on Riemannian manifolds
S. Bonnabel · 2013
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Low-rank tensor completion by Riemannian optimization
D. Kressner, M. Steinlechner, and B. Vandereycken · 2013
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A new, globally convergent Riemannian conjugate gradient method
H. Sato and T. Iwai · 2013
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Low-rank matrix completion by Riemannian optimization
B. Vandereycken · 2013
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Manopt, a Matlab toolbox for optimization on manifolds
N. Boumal, B. Mishra, P.-A. Absil, and R. Sepulchre · 2014
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Fixed-rank matrix factorizations and Riemannian low-rank optimization
B. Mishra, G. Meyer, S. Bonnabel, and R. Sepulchre · 2014
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Symmetry-invariant optimization in deep networks
V. Badrinarayanan, B. Mishra, and R. Cipolla · 2015
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Matrix manifold optimization for gaussian mixtures
R. Hosseini and S. Sra · 2015
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Unitary evolution recurrent neural networks
M. Arjovsky, A. Shah, and Y. Bengio · 2016
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Nonconvex phase synchronization
N. Boumal · 2016
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ROPTLIB: an object-oriented C++ library for optimization on Riemannian manifolds
W. Huang, P.-A. Absil, K. A. Gallivan, and P. Hand · 2016
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Low-rank tensor completion: a riemannian manifold preconditioning approach
H. Kasai and B. Mishra · 2016
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Madmm: a generic algorithm for non-smooth optimization on manifolds
A. Kovnatsky, K. Glashoff, and M. M. Bronstein · 2016
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Pymanopt: A Python toolbox for optimization on manifolds using automatic differentiation
J. Townsend, N. Koep, and S. Weichwald · 2016
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The space of essential matrices as a Riemannian quotient manifold
R. Tron and K. Daniilidis · 2017
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Global rates of convergence for nonconvex optimization on manifolds
N. Boumal, P.-A. Absil, and C. Cartis · 2018
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Building deep networks on Grassmann manifolds
Z. Huang, J. Wu, and L. Van Gool · 2018
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Learning multilingual word embeddings in latent metric space: a geometric approach
P. Jawanpuria, A. Balgovind, A. Kunchukuttan, and B. Mishra · 2018
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A unified framework for structured low-rank matrix learning
P. Jawanpuria and B. Mishra · 2018
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Riemannian stochastic recursive gradient algorithm
H. Kasai, H. Sato, and B. Mishra · 2018
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Geometric mean metric learning
P. Zadeh, R. Hosseini, and S. Sra · 2016
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Riemannian svrg: Fast stochastic optimization on Riemannian manifolds
H. Zhang, S. J. Reddi, and S. Sra · 2016
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Orthogonal weight normalization: Solution to optimization over multiple dependent Stiefel manifolds in deep neural networks
L. Huang, X. Liu, B. Lang, A. W. Yu, Y. Wang, and B. Li · 2017
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Automatic differentiation in PyTorch
A. Paszke, S. Gross, S. Chintala, G. Chanan, E. Yang, Z. DeVito, Z. Lin, A. Desmaison, L. Antiga, and A. Lerer · 2017
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Riemannian stochastic variance reduced gradient
H. Sato, H. Kasai, and B. Mishra · 2017
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Learning continuous hierarchies in the Lorentz model of hyperbolic geometry
M. Nickel and D. Kiela · 2018
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A dual framework for low-rank tensor completion
M. Nimishakavi, P. Jawanpuria, and B. Mishra · 2018
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Training CNNs with normalized kernels
M. Ozay and T. Okatani · 2018
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Geometry aware constrained optimization techniques for deep learning
S. K. Roy, Z. Mhammedi, and M. Harandi · 2018
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Near-optimal bounds for phase synchronization
Y. Zhong and N. Boumal · 2018
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