arXiv:2608.19145 2026 Regularization 1 ideas extracted · analyzed Sep 1, 2026
The paper identifies the spectral radius of a graph, rather than only its average degree, as the critical scale for Bernoulli edge percolation: the effective transition occurs near p lambda(G) = 1. This gives a principled way to choose random sparsification or edge-dropout rates in graph neural networks and sparse attention without accidentally fragmenting the communication graph. The most direct transfer is a spectral-radius-calibrated mask generator that enforces a safety margin above the percolation threshold and compares connectivity, accuracy, and compute against degree-based dropout.
Calibrate random edge dropout in a GNN or sparse-attention layer using the spectral radius of the underlying communication graph. Retain edges with probability p chosen so that p lambda(A) is at least 1 plus a safety margin, preventing the random computation graph from entering a subcritical fragmented regime while retaining high sparsity.