Hierarchy-GBP: Accelerating Factor Graph Inference via Abstraction and Recovery

2026-10-03

AI Summary

This study addresses the slow global error convergence of Gaussian Belief Propagation (GBP) on large-scale graphs by proposing the H-GBP framework. Grounded in spectral radius analysis and matrix operator derivations, this method introduces a novel two-level acceleration mechanism based on iterative graph abstraction and recovery. Furthermore, the convergence of the proposed algorithm toward the optimal solution is rigorously proven. Experimental results demonstrate that H-GBP achieves substantial speedups on linear sparse graphs and attains state-of-the-art computational efficiency in pose graph optimization and bundle adjustment tasks.

Abstract

Gaussian Belief Propagation (GBP) is a distributed inference algorithm that passes messages in graphical models, making it attractive for scalable spatial intelligence. However, we find GBP most effective locally: it rapidly smooths message errors that vary sharply between neighbor variables, but corrects global errors across distant graph regions incrementally through long-range message propagations. We propose Hierarchy-GBP (H-GBP), an iterative, two-stage framework that accelerates GBP by first solving these global errors with a coarse graph approximation (abstraction) and projecting the results back to the original graph (recovery), then refining the remaining local errors with GBP. We prove H-GBP convergence to the optimum by deriving the combined matrix operator of our abstraction and recovery steps and analyzing its spectral radius. Experiments on linear sparse graphs show that H-GBP converges fundamentally faster than standard GBP. Moreover, we validate H-GBP on two important spatial problems: Pose Graph Optimization (PGO) and Bundle Adjustment (BA). H-GBP markedly accelerates large-scale PGO and achieves state-of-the-art runtime across all tested BA scales.

Problem

• Gaussian Belief Propagation
• Factor Graph Inference
• Convergence Acceleration
• Pose Graph Optimization
• Bundle Adjustment

Innovation

• Gaussian Belief Propagation
• Hierarchical Inference
• Factor Graph
• Pose Graph Optimization
• Bundle Adjustment