Shallow neural network representation of polynomials

Abstract

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 C^-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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Reproductions