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We study deep neural networks with polynomial activations, particularly their expressive power.
Approximation by superpositions of a sigmoidal function
George Cybenko · 1989
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Kurt Hornik, Maxwell Stinchcombe, and Halbert White · 1989
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Cohen-Macaulay rings
Winfried Bruns and Jürgen Herzog · 1993
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Multilayer feedforward networks with a nonpolynomial activation function can approximate any function
Moshe Leshno, Vladimir Ya. Lin, Allan Pinkus, and Shimon Schocken · 1993
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Polynomial interpolation in several variables
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Ralf Fröberg, Giorgio Ottaviani, and Boris Shapiro · 2012
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Grigoriy Blekherman and Zach Teitler · 2015
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On the expressive power of deep learning: a tensor analysis
Nadav Cohen, Or Sharir, and Amnon Shashua · 2016
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Nadav Cohen and Amnon Shashua · 2016
On the Hilbert series of ideals generated by generic forms
Lisa Nicklasson · 2017
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On the optimization of deep networks: implicit acceleration by overparameterization
Sanjeev Arora, Nadav Cohen, and Elad Hazan · 2018
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On the global convergence of gradient descent for over-parameterized models using optimal transport
Lenaic Chizat and Francis Bach · 2018
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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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A mean field view of the landscape of two-layer neural networks
Song Mei, Andrea Montanari, and Phan-Minh Nguyen · 2018
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Spurious valleys in two-layers neural network optimization landscapes
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A convergence analysis of gradient descent for deep linear neural networks
Sanjeev Arora, Nadav Cohen, Noah Golowich, and Wei Hu · 2019
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On generic and maximal k k -ranks of binary forms
Samuel Lundqvist, Alessandro Oneto, Bruce Reznick, and Boris Shapiro · 2019
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Theoretical insights into the optimization landscape of over-parameterized shallow neural networks
Mahdi Soltanolkotabi, Adel Javanmard, and Jason D. Lee · 2019
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