Belief propagation for finite networks using a symmetry-breaking source node

TL;DR

This paper demonstrates that fixing a well-connected node in finite networks enhances belief propagation accuracy, especially in sparse, tree-like networks, by breaking symmetry and capturing finite-size effects without extra computational cost.

Contribution

Introducing a symmetry-breaking source node in belief propagation significantly improves inference accuracy in finite networks, particularly in sparse, tree-like structures.

Findings

Fixing a source node improves BP estimates in finite networks.

The method captures finite-size effects effectively.

No additional computational cost is required.

Abstract

Belief Propagation (BP) is an efficient message-passing algorithm widely used for inference in graphical models and for solving various problems in statistical physics. However, BP often yields inaccurate estimates of order parameters and their susceptibilities in finite systems, particularly in sparse networks with few loops. Here, we show for both percolation and Ising models that fixing the state of a single well-connected "source" node to break global symmetry substantially improves inference accuracy and captures finite-size effects across a broad range of networks, especially tree-like ones, at no additional computational cost.