ON COMPUTATION COMPLEXITY OF HIGH-DIMENSIONAL APPROXIMATION BY DEEP RELU NEURAL NETWORKS - D˜ung, D.; Nguyen, V.K.; Thao, M.X. (Bulletin of L.N. Gumilyov Eurasian National University. Mathematics, computer science, mechanics series, 2020)
We investigate computation complexity of deep ReLU neural networks for approximating functions in H"older-Nikol’skii spaces of mixed smoothness on the unit cube :=[0,1]^d. For any function f, we explicitly construct nonadaptive and adaptive deep ReLU neural networks having an output that approximates f with a prescribed accuracy ε, and prove dimension-dependent bounds for the computation complexity of this approximation, characterized by the size and depth of this deep ReLU neural network, explicitly in d and ε. Our results show the advantage of the adaptive method of approximation by deep ReLU neural networks over nonadaptive one.