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We propose automatic optimisation methods considering the geometry of matrix manifold for the normalised parameters of neural networks.
Fast Exact Multiplication by the Hessian
Barak A. Pearlmutter · 1994
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Optimization Algorithms on Matrix Manifolds
Pierre-Antoine Absil, Robert Mahony, and Rodolphe Sepulchre · 2008
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Deep Learning via Hessian-Free Optimization
James Martens · 2010
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MM Optimization Algorithms
Kenneth Lange · 2016
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Spectrally-Normalized Margin Bounds for Neural Networks
Peter L. Bartlett, Dylan J. Foster, and Matus J. Telgarsky · 2017
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Spectral Normalization for Generative Adversarial Networks
Takeru Miyato, Toshiki Kataoka, Masanori Koyama, and Yuichi Yoshida · 2018
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Sorting Out Lipschitz Function Approximation
Cem Anil, James Lucas, and Roger Grosse · 2019
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Neural Lander: Stable Drone Landing Control Using Learned Dynamics
Guanya Shi, Xichen Shi, Michael O’Connell, Rose Yu, Kamyar Azizzadenesheli, Animashree Anandkumar, Yisong Yue, and Soon-Jo Chung · 2019
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On the Distance Between Two Neural Networks and the Stability of Learning
Jeremy Bernstein, Arash Vahdat, Yisong Yue, and Ming-Yu Liu · 2020
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Robust Regression for Safe Exploration in Control
Anqi Liu, Guanya Shi, Soon-Jo Chung, Anima Anandkumar, and Yisong Yue · 2020
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Why Spectral Normalization Stabilizes GANs: Analysis and Improvements
Zinan Lin, Vyas Sekar, and Giulia Fanti · 2021
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Learning by Turning: Neural Architecture Aware Optimisation
Yang Liu, Jeremy Bernstein, Markus Meister, and Yisong Yue · 2021
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Neural-Swarm2: Planning and Control of Heterogeneous Multirotor Swarms Using Learned Interactions
Guanya Shi, Wolfgang Hönig, Xichen Shi, Yisong Yue, and Soon-Jo Chung · 2021
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Spherical Motion Dynamics: Learning Dynamics of Normalized Neural Network using SGD and Weight Decay
Ruosi Wan, Zhanxing Zhu, Xiangyu Zhang, and Jian Sun · 2021
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Bridging the Model-Reality Gap With Lipschitz Network Adaptation
Automatic Gradient Descent: Deep Learning without Hyperparameters, 2023
Jeremy Bernstein, Chris Mingard, Kevin Huang, Navid Azizan, and Yisong Yue · 2023
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Optimisation & Generalisation in Networks of Neurons
Jeremy David Bernstein · 2023
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An Introduction to Optimization on Smooth Manifolds
Nicolas Boumal · 2023
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MM Optimization: Proximal Distance Algorithms, Path Following, and Trust Regions
Alfonso Landeros, Jason Xu, and Kenneth Lange · 2023
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Reliable Learning and Control in Dynamic Environments: Towards Unified Theory and Learned Robotic Agility
Guanya Shi · 2023
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Universal Majorization-Minimization Algorithms, 2023
Matthew Streeter · 2023
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Spherical Perspective on Learning with Normalization Layers
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