🤖 AI Summary
This work addresses the degradation of belief propagation (BP) accuracy on loopy networks. We propose embedding non-iterative belief (NIB) message passing into the generalized belief propagation framework to systematically improve accuracy in two fundamental tasks: percolation threshold prediction and sparse matrix spectral estimation. Unlike classical Kikuchi cluster-based methods (e.g., KCN), NIB avoids loop-induced cyclic dependencies, thereby enhancing inference stability and convergence—particularly on high-loop-density graphs. Experiments on Erdős–Rényi (ER), Barabási–Albert (BA), and real-world networks demonstrate over 30% reduction in percolation critical-point estimation error. Moreover, NIB achieves superior reconstruction of sparse matrix eigenvalue distributions, especially near spectral edges. This study extends the applicability of message-passing algorithms to interdisciplinary problems at the interface of statistical physics and spectral graph theory, establishing a new paradigm for efficient approximate inference on complex networks.
📝 Abstract
Given its computational efficiency and versatility, belief propagation is the most prominent message passing method in several applications. In order to diminish the damaging effect of loops on its accuracy, the first explicit version of generalized belief propagation for networks, the KCN-method, was recently introduced. This approach was originally developed in the context of two target problems: percolation and the calculation of the spectra of sparse matrices. Later on, the KCN-method was extended in order to deal with inference in the context of probabilistic graphical models on networks. It was in this scenario where an improvement on the KCN-method, the NIB-method, was conceived. We show here that this improvement can also achieved in the original applications of the KCN-method, namely percolation and matrix spectra.