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Despite the widespread use of gradient-based algorithms for optimizing high-dimensional non-convex functions, understanding their ability of finding good minima instead of being trapped in spurious ones remains to a large extent an open problem.
The question of phase retrieval in optics
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Rémi Monasson · 1995
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Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices
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Silvio Franz, Giorgio Parisi, Maxime Sevelev, Pierfrancesco Urbani, and Francesco Zamponi · 2017
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A geometric analysis of phase retrieval
Ju Sun, Qing Qu, and John Wright · 2018
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Bad global minima exist and sgd can reach them
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Passed & spurious: analysing descent algorithms and local minima in spiked matrix-tensor model
Stefano Sarao Mannelli, Florent Krzakala, Pierfrancesco Urbani, and Lenka Zdeborova · 2019
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Who is afraid of big bad minima? analysis of gradient-flow in spiked matrix-tensor models
Stefano Sarao Mannelli, Giulio Biroli, Chiara Cammarota, Florent Krzakala, and Lenka Zdeborová · 2019
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Rong Ge, Jason D Lee, and Tengyu Ma · 2016
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Jason D Lee, Max Simchowitz, Michael I Jordan, and Benjamin Recht · 2016
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Glassy nature of the hard phase in inference problems
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Gradient descent with random initialization: Fast global convergence for nonconvex phase retrieval
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Optimal errors and phase transitions in high-dimensional generalized linear models
Jean Barbier, Florent Krzakala, Nicolas Macris, Léo Miolane, and Lenka Zdeborová · 2019
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Marco Mondelli and Andrea Montanari · 2019
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Phase transitions of spectral initialization for high-dimensional non-convex estimation
Yue M Lu and Gen Li · 2019
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Marvels and pitfalls of the langevin algorithm in noisy high-dimensional inference
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