Normalized skew Schur polynomials are Lorentzian

What the math gives to ML

The paper supplies a coefficient-level structural principle: after dividing each monomial coefficient by its multi-index factorial, skew Schur polynomials satisfy Lorentzian curvature constraints and have M-convex supports. This suggests regularizing neural modules whose outputs are nonnegative coefficient tables, such as mixture-count models, routing distributions, or polynomial feature maps, toward Lorentzian coefficient geometry rather than merely imposing entropy penalties. The practical transfer is a sampled Hessian-signature regularizer combined with an M-convex support penalty, encouraging stable redistribution of mass across neighboring expert or feature counts.