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We propose a new algorithm to learn a one-hidden-layer convolutional neural network where both the convolutional weights and the outputs weights are parameters to be learned.
A polynomial time algorithm that learns two hidden unit nets
Eric B Baum · 1990
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Gershgorin circle theorem
Eric W Weisstein · 2003
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Spectral properties of banded Toeplitz matrices , volume 96
Albrecht Boeóttcher and Sergei M Grudsky · 2005
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Provable methods for training neural networks with sparse connectivity
Hanie Sedghi and Anima Anandkumar · 2014
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The loss surfaces of multilayer networks
Anna Choromanska, Mikael Henaff, Michael Mathieu, Gérard Ben Arous, and Yann LeCun · 2015
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Escaping from saddle points − - online stochastic gradient for tensor decomposition
Rong Ge, Furong Huang, Chi Jin, and Yang Yuan · 2015
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Global optimality in tensor factorization, deep learning, and beyond
Benjamin D Haeffele and René Vidal · 2015
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Batch normalization: Accelerating deep network training by reducing internal covariate shift
Sergey Ioffe and Christian Szegedy · 2015
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Beating the perils of non-convexity: Guaranteed training of neural networks using tensor methods
Majid Janzamin, Hanie Sedghi, and Anima Anandkumar · 2015
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Learning halfspaces and neural networks with random initialization
Yuchen Zhang, Jason D Lee, Martin J Wainwright, and Michael I Jordan · 2015
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Global optimality of local search for low rank matrix recovery
Srinadh Bhojanapalli, Behnam Neyshabur, and Nati Srebro · 2016
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Topology and geometry of half-rectified network optimization
C Daniel Freeman and Joan Bruna · 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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Reliably learning the ReLU in polynomial time
Surbhi Goel, Varun Kanade, Adam Klivans, and Justin Thaler · 2016
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Identity matters in deep learning
Moritz Hardt and Tengyu Ma · 2016
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Deep residual learning for image recognition
Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun · 2016
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How to escape saddle points efficiently
Chi Jin, Rong Ge, Praneeth Netrapalli, Sham M. Kakade, and Michael I. Jordan · 2017
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Convergence analysis of two-layer neural networks with ReLU activation
Yuanzhi Li and Yang Yuan · 2017
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Non-square matrix sensing without spurious local minima via the Burer-Monteiro approach
Dohyung Park, Anastasios Kyrillidis, Constantine Carmanis, and Sujay Sanghavi · 2017
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Spurious local minima are common in two-layer relu neural networks
Itay Safran and Ohad Shamir · 2017
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Learning ReLUs via gradient descent
Mahdi Soltanolkotabi · 2017
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Kenji Kawaguchi · 2016
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Symmetry, saddle points, and global geometry of nonconvex matrix factorization
Xingguo Li, Zhaoran Wang, Junwei Lu, Raman Arora, Jarvis Haupt, Han Liu, and Tuo Zhao · 2016
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The landscape of empirical risk for non-convex losses
Song Mei, Yu Bai, and Andrea Montanari · 2016
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On the quality of the initial basin in overspecified neural networks
Itay Safran and Ohad Shamir · 2016
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Globally optimal gradient descent for a convnet with gaussian inputs
Alon Brutzkus and Amir Globerson · 2017
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When is a convolutional filter easy to learn?
Simon S Du, Jason D Lee, and Yuandong Tian
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Gradient descent learns one-hidden-layer cnn: Don’t be afraid of spurious local minima
Simon S Du, Jason D Lee, Yuandong Tian, Barnabas Poczos, and Aarti Singh
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Complete dictionary recovery over the sphere I: Overview and the geometric picture
Ju Sun, Qing Qu, and John Wright · 2017
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Yuandong Tian · 2017
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The landscape of deep learning algorithms
Pan Zhou and Jiashi Feng · 2017
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On the power of over-parametrization in neural networks with quadratic activation
Simon S Du and Jason D Lee · 2018
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Learning one convolutional layer with overlapping patches
Surbhi Goel, Adam Klivans, and Raghu Meka · 2018
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