I’m not exactly sure about “what you want”. It is not the case that you can exactly reconstruct most probability distributions you’ll encounter in real life from their moments/ cumulants (hence the expansion is perturbative, not exact).
But in the interpretability/ field-theoretic model of wide NN’s point of view, this is what you want (specifically, the fourth-order correction)
I’m not exactly sure about “what you want”. It is not the case that you can exactly reconstruct most probability distributions you’ll encounter in real life from their moments/ cumulants (hence the expansion is perturbative, not exact).
But in the interpretability/ field-theoretic model of wide NN’s point of view, this is what you want (specifically, the fourth-order correction)