Dense ReLU networks under natural weight and dimension constraints fail to approximate certain Lipschitz functions, unlike unrestricted networks.
Then, for any input x∈R 𝑑0 and output channel𝑖∈ [𝑑 𝐿], we have Θ(W,b) (x)𝑖 = Φ 𝐵,𝐿 𝐾 (W,b) , 𝑓 x 𝑣 , whenever𝑣is in the𝑖th interval ofC out 𝑑𝐿
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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.