Skew Hives, Skew Skeps, Skew Schur Log-Concavity

What the math gives to ML

The paper supplies a discrete concavity calculus on triangular arrays: hive values satisfy three local rhombus inequalities, while the octahedron recurrence converts between alternative boundary representations using max-plus updates. This is transferable as a structured neural module because its local constraints are cheap, translation-invariant, and enforce global consistency from boundary data rather than requiring a dense learned tensor. The strongest initial test is to use the recurrence as a differentiable dynamic-programming layer for grid or sequence representations, and separately test hive inequalities as a regularizer for latent attention-score grids. The combinatorial counting and bijections themselves are not directly useful for ordinary neural networks, so the proposed transfers focus on the recurrence and discrete concavity rather than Littlewood–Richardson coefficients.