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We study implicit regularization when optimizing an underdetermined quadratic objective over a matrix $X$ with gradient descent on a factorization of $X$.
SciPy: Open source scientific tools for Python, 2001
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A nonlinear programming algorithm for solving semidefinite programs via low-rank factorization
Samuel Burer and Renato DC Monteiro · 2003
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Generalization error bounds for collaborative prediction with low-rank matrices
Nathan Srebro, Noga Alon, and Tommi S Jaakkola · 2005
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In search of the real inductive bias: On the role of implicit regularization in deep learning
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Global optimality of local search for low rank matrix recovery
Srinadh Bhojanapalli, Behnam Neyshabur, and Nathan Srebro · 2016
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Matrix completion has no spurious local minimum
Rong Ge, Jason D Lee, and Tengyu Ma · 2016
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Gradient descent only converges to minimizers
Jason D. Lee, Max Simchowitz, Michael I. Jordan, and Benjamin Recht · 2016
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On large-batch training for deep learning: Generalization gap and sharp minima
Nitish Shirish Keskar, Dheevatsa Mudigere, Jorge Nocedal, Mikhail Smelyanskiy, and Ping Tak Peter Tang · 2017
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Geometry of optimization and implicit regularization in deep learning
Behnam Neyshabur, Ryota Tomioka, Ruslan Salakhutdinov, and Nathan Srebro · 2017
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Understanding deep learning requires rethinking generalization
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Chiyuan Zhang, Samy Bengio, Moritz Hardt, Benjamin Recht, and Oriol Vinyals · 2017
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