Asymptotic contractivity of the Bohnenblust--Hille inequality for polynomials with few interacting variables

What the math gives to ML

The paper proves a support-sensitive Bohnenblust–Hille inequality: for degree-m polynomials whose monomials involve at most M variables, the coefficient ℓ_p norm with p=2m/(m+1) is controlled by the supremum norm with a constant tending to 1 as m grows. The transferable asset is a concrete stability certificate linking sparse high-order interaction coefficients to the worst-case response of an interaction module. This can become a regularizer or constraint for polynomial, factorization-machine, or Volterra neural layers, using random unit-modulus probes to estimate the supremum norm and penalizing violations of the bound. The approach is most relevant when a model explicitly represents high-order interactions with bounded support size M.