Support-Sensitive Bohnenblust-Hille Inequalities and Local Invariants on Hamming Schemes
arXiv:2607.05594
2026
Architecture
1 ideas extracted · analyzed Aug 30, 2026
What the math gives to ML
The paper identifies interaction support, rather than nominal polynomial degree, as the quantity controlling Bohnenblust–Hille complexity on finite Hamming schemes. This suggests neural modules for categorical or binary inputs that explicitly decompose functions by the number of coordinates involved and allocate capacity according to interaction order. The most practical transfer is a support-truncated Fourier/polynomial layer equipped with a support-sensitive coefficient budget or regularizer, giving a controllable alternative to a dense MLP for high-dimensional discrete features.
Ideas from this paper
Unverified
2026
Replace the first dense layer on q-ary categorical features by a Fourier interaction layer containing only monomials whose coordinate support is at most s. Use a Bohnenblust–Hille-inspired quasi-norm on coefficients, separately for each interaction order, to prevent a small number of high-order interactions from dominating the output. The resulting model has an explicit interaction-order knob and can be tested against a dense MLP at matched parameter count.
Useful6/10
Difficulty5/10
Novelty7/10