Diffuse Gaussian Truncation For Deterministic Approximate Counting

What the math gives to ML

The paper's transferable asset is a deterministic truncation principle for weak, dense interactions: exact quadratic resummation removes all second-order effects, leaving a remainder whose first nonzero terms have degree at least three. The resulting tail is bounded by a rapidly decaying term, $(CR/n)^{R/2}$, plus an exponentially small large-support term, while the number of retained subsets is controlled by $R\log(en/R)$. This suggests a weak-interaction neural layer in which a dense Gaussian or energy-based interaction is analytically resummed and only low-order residual interaction subsets are explicitly evaluated.