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

Researchers posted arXiv:2610.06978v1, introducing Hierarchy-GBP (H-GBP), a two-stage framework that accelerates Gaussian Belief Propagation (GBP) by solving global message errors with a coarse graph approximation and projecting results back to the original graph before refining local errors with GBP. The authors prove H-GBP converges to the optimum by deriving the combined matrix operator of the abstraction and recovery steps and analyzing its spectral radius, and report that H-GBP converges fundamentally faster than standard GBP on linear sparse graphs. Validated on 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.

arXiv:2610.06978v1 Announce Type: new 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.