Dense ReLU networks under natural weight and dimension constraints fail to approximate certain Lipschitz functions, unlike unrestricted networks.
Then, we use these two results to show that for a large enough input dimension, no ReLU architecture can approximate all functions with a small𝜖 error
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Neural Networks With Dense Weights Are Not Universal Approximators
Dense ReLU networks under natural weight and dimension constraints fail to approximate certain Lipschitz functions, unlike unrestricted networks.