Finite element discretization of Yang--Mills connections

What the math gives to ML

The paper gives a constructive way to represent differential fields on a manifold with one local field per chart, connected by explicit transition laws rather than forcing a single globally valid coordinate representation. Its transferable asset is the affine gluing constraint between neighboring local outputs, together with weak enforcement through facet or overlap multipliers. This suggests bundle-aware neural fields and geometric networks whose outputs remain globally consistent even when the underlying feature bundle is nontrivial. The most practical first test is to replace ordinary coordinate outputs on a manifold with overlapping local neural outputs and train them using an augmented jump-consistency loss.