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It is proved that ResNets overcome the curse of dimensionality in the numerical approximation of solutions of semilinear heat equations with globally Lipschitz continuous, gradient-independent nonlinearities.
This paper shows that the infimum of the loss is always zero and achievable with at least $d$ active and visible hidden neurons -- that is, hidden neurons with non-zero inner and outer weights -- with pairwise distinct pivots, and provides for arbitrary activation degree $d$ a sharp existence/non-existence criterion fo...
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