Analysis of Deep Neural Networks with Quasi-optimal polynomial approximation rates

12/04/2019

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by   Joseph Daws, et al.

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We show the existence of a deep neural network capable of approximating a wide class of high-dimensional approximations. The construction of the proposed neural network is based on a quasi-optimal polynomial approximation. We show that this network achieves an error rate that is sub-exponential in the number of polynomial functions, M, used in the polynomial approximation. The complexity of the network which achieves this sub-exponential rate is shown to be algebraic in M.