Shallow neural network representation of polynomials
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Abstract (arXiv)
We show that d-variate polynomials of degree R can be represented on [0,1]d as shallow neural networks of width 2(R+d)d. Also, by SNN representation of localized Taylor polynomials of univariate Cβ-smooth functions, we derive for shallow networks the minimax optimal rate of convergence, up to a logarithmic factor, to unknown univariate regression function.
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References · 7
- 2016Error bounds for approximations with deep ReLU networkscited by 574
- 2017Nonparametric regression using deep neural networks with ReLU activation functioncited by 433
- 2014Breaking the Curse of Dimensionality with Convex Neural Networkscited by 331
- 2021On the approximation of functions by tanh neural networkscited by 81
- 2016Risk Bounds for High-dimensional Ridge Function Combinations Including Neural Networkscited by 26
- 2016Deep nets for local manifold learningcited by 26
- 2021Analytic function approximation by path norm regularized deep networkscited by 3
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