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Have you actually tested this before or are you just considering this problem theoretically? We can use some very simple code to show that this is an impractical statement. Here is a simple ReLU MLP trained with gradient descent implemented in numpy, and I've used this to generate the results I'm talking about here. Here's a GIF showing that it is capable of correctly minimizing the error of an approximation.
Code for https://arxiv.org/abs/1502.01852 found: https://github.com/zonetrooper32/VDCNN
Code for https://arxiv.org/abs/1607.06450 found: https://github.com/Waino/hnmt