For finite single-hidden-layer networks with symmetric weight initialization, the output distribution is a Gaussian with an O(1/N) fourth-Hermite correction, an instance of the classical Edgeworth expansion.
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Finite size corrections for neural network Gaussian processes
For finite single-hidden-layer networks with symmetric weight initialization, the output distribution is a Gaussian with an O(1/N) fourth-Hermite correction, an instance of the classical Edgeworth expansion.