Mutually orthogonal anti-Latin squares

What the math gives to ML

The paper gives deterministic families of categorical grids with three useful properties: every channel is globally balanced, every row and column contains a repeated symbol, and every pair of channels uniquely identifies a grid cell. This structure can replace random or independently learned hash assignments in MoE routing or two-dimensional positional coding. The most practical transfer is a fixed multi-channel routing scheme that guarantees exact marginal bucket balance and pairwise diversity without a learned routing table or an auxiliary load-balancing objective.