Ensemble-level loopy message passing with generalized-edge closure for percolation

What the math gives to ML

The paper provides a constructive way to repair tree-like message passing when short loops make incoming messages statistically dependent. Its transferable mechanism is to replace ordinary edges by generalized edges defined as intersections of node-centered subgraphs, then refine predictions by increasing neighborhood order. The generalized-edge closure coefficient (GECC) is especially useful for neural networks because it is an a priori, local-statistics diagnostic of whether an independence-based message-passing approximation should be trusted. A practical transfer is a loop-aware GNN whose aggregation is corrected or gated by generalized-edge overlap features, with GECC predicting when the correction should matter.