AI RESEARCH
Optimal Non-Asymptotic Edgeworth Expansions for Multivariate Neural Network Outputs
arXiv CS.LG
•
ArXi:2605.24072v1 Announce Type: cross Finite-width fully connected neural networks with Gaussian-initialized weights deviate from their infinite-width Gaussian limit, exhibiting non-vanishing higher-order cumulants. We approximate these deviations, for a neural network evaluated in a finite number of inputs, using multidimensional Edgeworth expansions of arbitrary order $4m-1$, with $m\in\mathbb{N