Richardson volume models for skew Schur and skew Schur $P/Q$-functions

What the math gives to ML

The paper supplies a constructive source of nonnegative Lorentzian polynomials: normalized skew Schur and skew Schur P/Q coefficient arrays arise as realizable volume polynomials of Richardson varieties. The transferable asset is not the particular tableau character, but the resulting Hodge–Riemann/Lorentzian structure, which imposes strong, checkable curvature and log-concavity constraints on a positive coefficient tensor. A practical neural-network adaptation is to treat a small positive polynomial as a structured router or attention interaction and regularize its derivative Hessians toward the Lorentzian signature guaranteed by the geometric construction. Skew-Schur coefficient tensors can additionally provide valid initialization or priors for such modules.