Value distributions for read-once polynomials on finite fields

What the math gives to ML

The paper identifies a nonstandard feasible body for categorical distributions that is preserved when independent random variables are combined by group or quasigroup convolution. The transferable asset is a compositional guarantee: distributions satisfying a lower-tail constraint remain non-collapsed after repeated algebraic composition. This suggests a regularizer for categorical latent variables or MoE routing distributions, especially when several independently predicted categorical states are combined through a finite-group operation. The strongest first test is a differentiable barrier on categorical probabilities, followed by repeated group-convolution composition and measurement of collapse, calibration, and task accuracy.