Spectral-safe edge dropout

(1) Integration point: apply this rule to the binary edge mask immediately before message aggregation in a GNN, or immediately before constructing a sparse attention matrix over tokens, patches, or retrieved items. Let A be the fixed candidate adjacency or the binary graph induced by top-k attention connections. Do not modify the dense value projection; only mask communication edges. Always preserve diagonal self-loops. (2) Pseudocode: initialize a positive random vector q with unit norm; for t from 1 to T, compute z = A q and q = z divided by its Euclidean norm; after the final iteration compute lambda_hat = norm(A q); choose epsilon from {0.1, 0.25, 0.5}; set p = min(1, (1 + epsilon) divided by max(lambda_hat, 1e-6)); sample an independent Bernoulli mask M for non-diagonal candidate edges; set M_ii = 1; form A_p = A elementwise-multiplied by M; then use A_p in graph aggregation or add a large negative logit to dropped sparse-attention entries. (3) Computed from the paper's mathematics: the spectral-radius estimate, the threshold p lambda_hat(A) greater than 1, and the safety margin. Estimated empirically: the actual largest connected-component fraction, isolated-node rate, realized spectral radius, validation accuracy, and loss variance across masks. (4) First cheap experiment: train a 3-layer GCN on Cora or CiteSeer. Compare fixed dropout, average-degree calibration p = (1 + epsilon) divided by d(G), and spectral calibration p = (1 + epsilon) divided by lambda_hat(A), matching expected retained edges where possible. Sweep epsilon from 0 to 0.5 and report accuracy, loss variance, largest-component fraction, isolated-node fraction, and wall-clock time. The prediction is that spectral calibration reduces disconnected-mask failures and accuracy variance at high sparsity, especially on graphs whose degree distribution makes average degree a poor proxy for spectral radius.