Central-Hermite Sensing and Collision for Frame-Robust Order-Resolved Relaxation on D3Q125

What the math gives to ML

The paper gives a constructive way to prevent uniform translations from mixing different polynomial orders: compute moments after subtracting the local weighted mean, then apply order-specific collision or relaxation independently in that centered basis. The transferable asset is not the D3Q125 lattice itself, but the explicit separation between raw moments, central moments, and order-resolved updates, together with the demonstrated reduction of boost-dependent cross-order contamination. A neural implementation can use centered token or patch features to construct second-, third-, and fourth-order feature channels, process each order with separate residual gates, and map them back to the original feature space. This should be tested as a translation-invariant higher-order feature mixer while monitoring whether removing absolute feature-offset information harms task accuracy.