An operator-splitting algorithm for the hypergraph $p$-Laplacian with applications to missing data recovery

What the math gives to ML

The transferable object is a hyperedge regularizer that controls the worst pairwise oscillation inside each group, rather than averaging all pairwise discrepancies. This gives a robust notion of groupwise Lipschitzness: one badly inconsistent pair dominates the penalty, which may help enforce invariance among tokens, augmentations, views, or samples sharing a latent entity. The hyperedge decomposition also permits blockwise computation, although the supplied extraction does not include enough proximal-ADMM equations to reproduce the paper's solver exactly. A practical first transfer is therefore a structured representation regularizer evaluated on groups already present in the training data.