Consensus-Corrected Topology-Invariant GNN

1. Integration point: insert this block into every message-passing layer in a PyTorch Geometric or DGL model. Use the active graph for each sample, including node and edge masks; removed edges must not be treated as ordinary edges. Compute the graph mean with a segment reduction, preserving linear complexity in the number of active nodes. 2. Pseudocode: compute edge messages and aggregate them into $m$; compute $g=\operatorname{sigmoid}(a([h,m]))$; compute $\bar h$ over active nodes; update $h\leftarrow\operatorname{LayerNorm}(h+g\odot W_m m+\alpha W_c(\bar h-h))$; apply the task head. Initialize $\alpha=0.05$ and parameterize it with softplus, while clipping it to $0.9/\widehat{\lambda}_{\max}(L)$. 3. Quantities computed directly are the active adjacency, graph mean, and Laplacian estimate. Estimate $\widehat{\lambda}_{\max}(L)$ with five power iterations per batch or cache it from topology statistics. The consensus mechanism comes from the paper; the contraction inequality is the stability monitor. Estimate the local message Jacobian with one additional power iteration if necessary. 4. First cheap experiment: train a six-layer GNN on 14-bus or 118-bus power-flow regression with random edge outages, comparing a standard GNN, residual GNN, and consensus-corrected GNN. Record representation disagreement $D^{(\ell)}$, prediction error, and outage degradation. The predicted signature is geometric disagreement decay with slope approximately $(1-\alpha\lambda_2(L))^2$ when local-message gain is small. Sweep $\alpha$ at $0.5$, $0.9$, $1.1$, and $1.5$ times $2/\widehat{\lambda}_{\max}(L)$; embedding instability should begin near the predicted boundary within 20 percent.