For sufficiently wide random MLPs, cumulant and Hermite approximations of layer-wise activation distributions yield expected outputs at lower computational cost than Monte Carlo sampling, with good performance on rare-event probabilities.
(Error bars hidden because they would be too small to be readable.) In most cases, our algorithms underperform sampling
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Estimating the expected output of wide random MLPs more efficiently than sampling
For sufficiently wide random MLPs, cumulant and Hermite approximations of layer-wise activation distributions yield expected outputs at lower computational cost than Monte Carlo sampling, with good performance on rare-event probabilities.