Neural network integral representations with the ReLU activation function

10/07/2019

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by   Anton Dereventsov, et al.

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We derive a formula for neural network integral representations on the sphere with the ReLU activation function under the finite L_1 norm (with respect to Lebesgue measure on the sphere) assumption on the outer weights. In one dimensional case, we further solve via a closed-form formula all possible such representations. Additionally, in this case our formula allows one to explicitly solve the least L_1 norm neural network representation for a given function.