Recovery Guarantees for One-hidden-layer Neural Networks
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Inderjit S. Dhillon | Prateek Jain | Peter L. Bartlett | Zhao Song | Kai Zhong | P. Bartlett | Prateek Jain | I. Dhillon | Kai Zhong | Zhao Song
[1] Varun Kanade,et al. Reliably Learning the ReLU in Polynomial Time , 2016, COLT.
[2] Anima Anandkumar,et al. Tensor decompositions for learning latent variable models , 2012, J. Mach. Learn. Res..
[3] Peter L. Bartlett,et al. The Sample Complexity of Pattern Classification with Neural Networks: The Size of the Weights is More Important than the Size of the Network , 1998, IEEE Trans. Inf. Theory.
[4] Kenji Kawaguchi,et al. Deep Learning without Poor Local Minima , 2016, NIPS.
[5] Kurt Hornik,et al. Approximation capabilities of multilayer feedforward networks , 1991, Neural Networks.
[6] Surya Ganguli,et al. Exponential expressivity in deep neural networks through transient chaos , 2016, NIPS.
[7] Nadav Cohen,et al. On the Expressive Power of Deep Learning: A Tensor Analysis , 2015, COLT 2016.
[8] David P. Woodruff,et al. Low Rank Approximation with Entrywise $\ell_1$-Norm Error , 2016, 1611.00898.
[9] Zhi-Quan Luo,et al. Guaranteed Matrix Completion via Non-Convex Factorization , 2014, IEEE Transactions on Information Theory.
[10] David P. Woodruff,et al. Sublinear Time Orthogonal Tensor Decomposition , 2016, NIPS.
[11] Sanjeev Arora,et al. Learning Topic Models -- Going beyond SVD , 2012, 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science.
[12] Matus Telgarsky,et al. Benefits of Depth in Neural Networks , 2016, COLT.
[13] Martin J. Wainwright,et al. Convexified Convolutional Neural Networks , 2016, ICML.
[14] Yoram Singer,et al. Train faster, generalize better: Stability of stochastic gradient descent , 2015, ICML.
[15] Amnon Shashua,et al. Convolutional Rectifier Networks as Generalized Tensor Decompositions , 2016, ICML.
[16] Razvan Pascanu,et al. On the Number of Linear Regions of Deep Neural Networks , 2014, NIPS.
[17] Anima Anandkumar,et al. Beating the Perils of Non-Convexity: Guaranteed Training of Neural Networks using Tensor Methods , 2017 .
[18] Prateek Jain,et al. Low-rank matrix completion using alternating minimization , 2012, STOC '13.
[19] Daniel M. Roy,et al. Complexity of Inference in Latent Dirichlet Allocation , 2011, NIPS.
[20] Amir Globerson,et al. Globally Optimal Gradient Descent for a ConvNet with Gaussian Inputs , 2017, ICML.
[21] Yuchen Zhang,et al. L1-regularized Neural Networks are Improperly Learnable in Polynomial Time , 2015, ICML.
[22] David Balduzzi,et al. Deep Online Convex Optimization with Gated Games , 2016, ArXiv.
[23] David P. Woodruff,et al. Relative Error Tensor Low Rank Approximation , 2017, Electron. Colloquium Comput. Complex..
[24] Yann LeCun,et al. The Loss Surfaces of Multilayer Networks , 2014, AISTATS.
[25] Sanjeev Arora,et al. Computing a nonnegative matrix factorization -- provably , 2011, STOC '12.
[26] Joan Bruna,et al. Topology and Geometry of Half-Rectified Network Optimization , 2016, ICLR.
[27] Sham M. Kakade,et al. A tail inequality for quadratic forms of subgaussian random vectors , 2011, ArXiv.
[28] Surya Ganguli,et al. On the Expressive Power of Deep Neural Networks , 2016, ICML.
[29] David P. Woodruff,et al. Optimal Sample Complexity for Matrix Completion and Related Problems via 𝓁s2-Regularization , 2017, ArXiv.
[30] Anima Anandkumar,et al. Provable Methods for Training Neural Networks with Sparse Connectivity , 2014, ICLR.
[31] Tengyu Ma,et al. Identity Matters in Deep Learning , 2016, ICLR.
[32] Roi Livni,et al. On the Computational Efficiency of Training Neural Networks , 2014, NIPS.
[33] Shie Mannor,et al. Ensemble Robustness of Deep Learning Algorithms , 2016, ArXiv.
[34] Martin J. Wainwright,et al. On the Learnability of Fully-Connected Neural Networks , 2017, AISTATS.
[35] David P. Woodruff,et al. Low rank approximation with entrywise l1-norm error , 2017, STOC.
[36] Ehsan Elhamifar,et al. Sparse subspace clustering , 2009, 2009 IEEE Conference on Computer Vision and Pattern Recognition.
[37] Yoram Singer,et al. Toward Deeper Understanding of Neural Networks: The Power of Initialization and a Dual View on Expressivity , 2016, NIPS.
[38] Percy Liang,et al. Tensor Factorization via Matrix Factorization , 2015, AISTATS.
[39] Inderjit S. Dhillon,et al. Mixed Linear Regression with Multiple Components , 2016, NIPS.
[40] Aditya Bhaskara,et al. Provable Bounds for Learning Some Deep Representations , 2013, ICML.
[41] Johan Håstad,et al. Tensor Rank is NP-Complete , 1989, ICALP.
[42] Nicolas Le Roux,et al. Convex Neural Networks , 2005, NIPS.
[43] Yuandong Tian,et al. Symmetry-Breaking Convergence Analysis of Certain Two-layered Neural Networks with ReLU nonlinearity , 2017, ICLR.
[44] Nicolas Gillis,et al. On the Complexity of Robust PCA and ℓ1-norm Low-Rank Matrix Approximation , 2015, Math. Oper. Res..
[45] Sham M. Kakade,et al. Learning mixtures of spherical gaussians: moment methods and spectral decompositions , 2012, ITCS '13.
[46] Ohad Shamir,et al. On the Quality of the Initial Basin in Overspecified Neural Networks , 2015, ICML.
[47] Yann LeCun,et al. Singularity of the Hessian in Deep Learning , 2016, ArXiv.
[48] Joel A. Tropp,et al. User-Friendly Tail Bounds for Sums of Random Matrices , 2010, Found. Comput. Math..
[49] David Balduzzi,et al. Neural Taylor Approximations: Convergence and Exploration in Rectifier Networks , 2016, ICML.
[50] Sanjeev Arora,et al. Provable learning of noisy-OR networks , 2016, STOC.
[51] Xinhua Zhang,et al. Convex Deep Learning via Normalized Kernels , 2014, NIPS.
[52] Nicolas Gillis,et al. Low-Rank Matrix Approximation with Weights or Missing Data Is NP-Hard , 2010, SIAM J. Matrix Anal. Appl..
[53] Le Song,et al. Diversity Leads to Generalization in Neural Networks , 2016, ArXiv.
[54] Moritz Hardt,et al. Understanding Alternating Minimization for Matrix Completion , 2013, 2014 IEEE 55th Annual Symposium on Foundations of Computer Science.
[55] Surya Ganguli,et al. Identifying and attacking the saddle point problem in high-dimensional non-convex optimization , 2014, NIPS.
[56] Alexander J. Smola,et al. Fast and Guaranteed Tensor Decomposition via Sketching , 2015, NIPS.
[57] David P. Woodruff,et al. Weighted low rank approximations with provable guarantees , 2016, STOC.
[58] René Vidal,et al. Global Optimality in Tensor Factorization, Deep Learning, and Beyond , 2015, ArXiv.
[59] Alexandr Andoni,et al. Learning Polynomials with Neural Networks , 2014, ICML.
[60] Anima Anandkumar,et al. Online and Differentially-Private Tensor Decomposition , 2016, NIPS.
[61] Samy Bengio,et al. Understanding deep learning requires rethinking generalization , 2016, ICLR.
[62] Christopher J. Hillar,et al. Most Tensor Problems Are NP-Hard , 2009, JACM.
[63] Ronald L. Rivest,et al. Training a 3-node neural network is NP-complete , 1988, COLT '88.
[64] Ohad Shamir,et al. Distribution-Specific Hardness of Learning Neural Networks , 2016, J. Mach. Learn. Res..
[65] Daniel Soudry,et al. No bad local minima: Data independent training error guarantees for multilayer neural networks , 2016, ArXiv.
[66] Andreas Krause,et al. Advances in Neural Information Processing Systems (NIPS) , 2014 .
[67] Razvan Pascanu,et al. Local minima in training of deep networks , 2017, ArXiv.
[68] Francis R. Bach,et al. Breaking the Curse of Dimensionality with Convex Neural Networks , 2014, J. Mach. Learn. Res..
[69] A. Appendix. Alternating Minimization for Mixed Linear Regression , 2014 .
[70] Ankur Moitra,et al. Algorithms and Hardness for Robust Subspace Recovery , 2012, COLT.