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math.FA2021
Quantitative approximation results for complex-valued neural networks
A. Caragea, D. G. Lee, J. Maly +2
Until recently, applications of neural networks in machine learning have almost exclusively relied on real-valued networks. It was recently observed, however, that complex-valued n…
math.FA2017
Optimal approximation of piecewise smooth functions using deep ReLU neural networks
Philipp Petersen, Felix Voigtlaender
We study the necessary and sufficient complexity of ReLU neural networks---in terms of depth and number of weights---which is required for approximating classifier functions in $L^…