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arXiv · 1910.02743

Neural network integral representations with the ReLU activation function

Armenak Petrosyan·Anton Dereventsov·Clayton Webster
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Abstract

In this effort, we derive a formula for the integral representation of a shallow neural network with the ReLU activation function. We assume that the outer weighs admit a finite $L_1$-norm with respect to Lebesgue measure on the sphere. For univariate target functions we further provide a closed-form formula for all possible representations. Additionally, in this case our formula allows one to explicitly solve the least $L_1$-norm neural network representation for a given function.

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Armenak Petrosyan, Anton Dereventsov, Clayton Webster. 2019-10-07. Neural network integral representations with the ReLU activation function. https://arxiv.org/abs/1910.02743

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