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Explicit, momentum-based dynamics for optimizing functions defined on Lie groups was recently constructed, based on techniques such as variational optimization and left trivialization.
The representation of lie algebras by matrices
ID Ado · 1947
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Non-existence of continuous convex functions on certain riemannian manifolds
Shing-Tung Yau · 1974
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Curvatures of left invariant metrics on lie groups, 1976
John Milnor · 1976
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Foundations of mechanics
Ralph Abraham and Jerrold E Marsden · 1978
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Calculation of the coefficients in the campbell–hausdorff formula
EB Dynkin · 2000
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Stochastic analysis on manifolds
Elton P Hsu · 2002
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Representations of compact Lie groups , volume 98
Theodor Bröcker and Tammo Tom Dieck · 2013
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Introductory lectures on convex optimization: A basic course , volume 87
Yurii Nesterov · 2013
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Reflection couplings and contraction rates for diffusions
Andreas Eberle · 2016
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First-order methods for geodesically convex optimization
Hongyi Zhang and Suvrit Sra · 2016
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Parseval networks: Improving robustness to adversarial examples
Moustapha Cisse, Piotr Bojanowski, Edouard Grave, Yann Dauphin, and Nicolas Usunier · 2017
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Theoretical guarantees for approximate sampling from smooth and log-concave densities
Arnak S Dalalyan · 2017
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Convergence of langevin mcmc in kl-divergence
Xiang Cheng and Peter Bartlett · 2018
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Underdamped langevin mcmc: A non-asymptotic analysis
Xiang Cheng, Niladri S Chatterji, Peter L Bartlett, and Michael I Jordan · 2018
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Irreversible langevin mcmc on lie groups
Alexis Arnaudon, Alessandro Barp, and So Takao · 2019
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Analysis of langevin monte carlo via convex optimization
Alain Durmus, Szymon Majewski, and Błażej Miasojedow · 2019
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Couplings and quantitative contraction rates for langevin dynamics
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Cheap orthogonal constraints in neural networks: A simple parametrization of the orthogonal and unitary group
Mario Lezcano-Casado and David Martınez-Rubio · 2019
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A reduced parallel transport equation on lie groups with a left-invariant metric
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Sqrt(d) dimension dependence of langevin monte carlo
Ruilin Li, Hongyuan Zha, and Molei Tao · 2021
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Is there an analog of nesterov acceleration for gradient-based mcmc?
Yi-An Ma, Niladri S Chatterji, Xiang Cheng, Nicolas Flammarion, Peter L Bartlett, and Michael I Jordan · 2021
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Efficient sampling on riemannian manifolds via langevin mcmc
Xiang Cheng, Jingzhao Zhang, and Suvrit Sra · 2022
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Convergence of langevin monte carlo in chi-squared and rényi divergence
Murat A Erdogdu, Rasa Hosseinzadeh, and Shunshi Zhang · 2022
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Santosh Vempala and Andre Wibisono · 2019
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From nesterov’s estimate sequence to riemannian acceleration
Kwangjun Ahn and Suvrit Sra · 2020
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On sampling from a log-concave density using kinetic langevin diffusions
Arnak S Dalalyan and Lionel Riou-Durand · 2020
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Variational optimization on lie groups, with examples of leading (generalized) eigenvalue problems
Molei Tao and Tomoki Ohsawa · 2020
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Khashayar Gatmiry and Santosh S Vempala · 2022
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Faster high-accuracy log-concave sampling via algorithmic warm starts
Jason M Altschuler and Sinho Chewi · 2023
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Momentum stiefel optimizer, with applications to suitably-orthogonal attention, and optimal transport
Lingkai Kong, Yuqing Wang, and Molei Tao · 2023
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Markov chain monte carlo for gaussian: A linear control perspective
Bo Yuan, Jiaojiao Fan, Yuqing Wang, Molei Tao, and Yongxin Chen · 2023
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Improved discretization analysis for underdamped langevin monte carlo
Shunshi Zhang, Sinho Chewi, Mufan Li, Krishna Balasubramanian, and Murat A Erdogdu · 2023
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Log-concave sampling
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Quantitative convergences of lie group momentum optimizers
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