Error bounds for deep ReLU networks using the Kolmogorov--Arnold superposition theorem

06/27/2019

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by   Hadrien Montanelli, et al.

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We prove a theorem concerning the approximation of multivariate continuous functions by deep ReLU networks, for which the curse of the dimensionality is lessened. Our theorem is based on the Kolmogorov--Arnold superposition theorem, and on the approximation of the inner and outer functions that appear in the superposition by very deep ReLU networks.