Renormalization group connection of the multigrid object layer

Investigate whether the coarse-graining performed by the multigrid object layer in Metriplector corresponds to the full renormalization group structure, extending beyond its observed resemblance to block-spin methods.

Background

The multigrid object layer performs learned soft assignment and coarse-level Poisson solves, functionally similar to classical multigrid V-cycles and conceptually akin to block-spin coarse-graining. Clarifying whether this similarity extends to a full renormalization group structure would connect the learned hierarchy to established physics formalisms, potentially yielding principled guarantees or new design constraints.