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In this effort we propose a novel approach for reconstructing multivariate functions from training data, by identifying both a suitable network architecture and an initialization using polynomial-based approximations.
Testing multidimensional integration routines
A. Genz · 1984
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Approximation by superpositions of a sigmoidal function
George Cybenko · 1989
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Constructive approximation , volume 303 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]
Ronald A. DeVore and George G. Lorentz · 1993
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Neural network initialization
Georg Thimm and Emile Fiesler · 1995
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ImageNet: A Large-Scale Hierarchical Image Database
J. Deng, W. Dong, R. Socher, L.-J. Li, K. Li, and L. Fei-Fei · 2009
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Understanding the difficulty of training deep feedforward neural networks
Xavier Glorot and Yoshua Bengio · 2010
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Large-scale machine learning with stochastic gradient descent
Léon Bottou · 2010
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Error bounds for approximations with deep relu networks
Dmitry Yarotsky · 2017
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Why deep neural networks for function approximation?
Shiyu Liang and R Srikant · 2017
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How to start training: The effect of initialization and architecture
Boris Hanin and David Rolnick · 2018
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New error bounds for deep relu networks using sparse grids
Hadren Montanelli and Qiang Du · 2019
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Deep learning in high dimension: Neural network expression rates for generalized polynomials chaos expansions in uq
Charles Schwab and Jokob Zech · 2019
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