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

Joseph Daws; Clayton Webster

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arXiv · 1912.02302

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

Joseph Daws·Clayton Webster

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Abstract

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 $M$.

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Joseph Daws, Clayton Webster. 2019-12-04. Analysis of Deep Neural Networks with Quasi-optimal polynomial approximation rates. https://arxiv.org/abs/1912.02302

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