On the Expressive Power of Deep Polynomial Neural Networks
暂无分享,去创建一个
[1] T. Willmore. Algebraic Geometry , 1973, Nature.
[2] J. Landsberg. Tensors: Geometry and Applications , 2011 .
[3] Francis Bach,et al. On the Global Convergence of Gradient Descent for Over-parameterized Models using Optimal Transport , 2018, NeurIPS.
[4] Wei Hu,et al. A Convergence Analysis of Gradient Descent for Deep Linear Neural Networks , 2018, ICLR.
[5] George Cybenko,et al. Approximation by superpositions of a sigmoidal function , 1989, Math. Control. Signals Syst..
[6] Lisa Nicklasson,et al. On the Hilbert series of ideals generated by generic forms , 2015, 1502.06762.
[7] Adel Javanmard,et al. Theoretical Insights Into the Optimization Landscape of Over-Parameterized Shallow Neural Networks , 2017, IEEE Transactions on Information Theory.
[8] Yoshua Bengio,et al. Shallow vs. Deep Sum-Product Networks , 2011, NIPS.
[9] James Martens,et al. On the Expressive Efficiency of Sum Product Networks , 2014, ArXiv.
[10] Amnon Shashua,et al. Convolutional Rectifier Networks as Generalized Tensor Decompositions , 2016, ICML.
[11] Luke Oeding,et al. Learning Algebraic Models of Quantum Entanglement , 2019, Quantum Inf. Process..
[12] Allan Pinkus,et al. Multilayer Feedforward Networks with a Non-Polynomial Activation Function Can Approximate Any Function , 1991, Neural Networks.
[13] C. D. Boor,et al. Polynomial interpolation in several variables , 1994 .
[14] Joe W. Harris,et al. Algebraic Geometry: A First Course , 1995 .
[15] Kurt Hornik,et al. Multilayer feedforward networks are universal approximators , 1989, Neural Networks.
[16] Kenji Kawaguchi,et al. Deep Learning without Poor Local Minima , 2016, NIPS.
[17] Nadav Cohen,et al. On the Expressive Power of Deep Learning: A Tensor Analysis , 2015, COLT 2016.
[18] Tomas Sauer,et al. Polynomial interpolation in several variables , 2000, Adv. Comput. Math..
[19] Edgar E. Enochs,et al. On Cohen-Macaulay rings , 1994 .
[20] Joan Bruna,et al. Spurious Valleys in Two-layer Neural Network Optimization Landscapes , 2018, 1802.06384.
[21] D. Eisenbud. Commutative Algebra: with a View Toward Algebraic Geometry , 1995 .
[22] Jason D. Lee,et al. On the Power of Over-parametrization in Neural Networks with Quadratic Activation , 2018, ICML.
[23] Joan Bruna,et al. Pure and Spurious Critical Points: a Geometric Study of Linear Networks , 2020, ICLR.
[24] Joan Bruna,et al. Neural Networks with Finite Intrinsic Dimension have no Spurious Valleys , 2018, ArXiv.
[25] Tingting Tang,et al. The Loss Surface of Deep Linear Networks Viewed Through the Algebraic Geometry Lens , 2018, IEEE Transactions on Pattern Analysis and Machine Intelligence.
[26] Giorgio Ottaviani,et al. On the Waring problem for polynomial rings , 2011, Proceedings of the National Academy of Sciences.
[27] Sanjeev Arora,et al. On the Optimization of Deep Networks: Implicit Acceleration by Overparameterization , 2018, ICML.
[28] Rekha R. Thomas,et al. The Euclidean Distance Degree of an Algebraic Variety , 2013, Foundations of Computational Mathematics.
[29] Samuel Lundqvist,et al. On generic and maximal k-ranks of binary forms , 2017, Journal of Pure and Applied Algebra.
[30] Pedro M. Domingos,et al. Sum-product networks: A new deep architecture , 2011, 2011 IEEE International Conference on Computer Vision Workshops (ICCV Workshops).
[31] Andrea Montanari,et al. A mean field view of the landscape of two-layer neural networks , 2018, Proceedings of the National Academy of Sciences.
[32] Zach Teitler,et al. On maximum, typical and generic ranks , 2014, ArXiv.