# Circular Belief Propagation for Approximate Probabilistic Inference

arXiv: https://arxiv.org/abs/2403.12106 · HTML: https://mlsanity.com/paper/2403.12106/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 77 references that are in the map.
- First posted on arXiv 17 Mar 2024.

## Builds on (most cited first, 10 of 10)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Expectation Propagation for approximate Bayesian inference](https://mlsanity.com/paper/1301.2294/) (2013)
- [Loopy Belief Propagation for Approximate Inference: An Empirical Study](https://mlsanity.com/paper/1301.6725/) (2013)
- [Neural Enhanced Belief Propagation on Factor Graphs](https://mlsanity.com/paper/2003.01998/) (2020)
- [Inference in Probabilistic Graphical Models by Graph Neural Networks](https://mlsanity.com/paper/1803.07710/) (2018)
- [Belief Propagation Neural Networks](https://mlsanity.com/paper/2007.00295/) (2020)
- [Perturb-and-max-product: Sampling and learning in discrete energy-based models](https://mlsanity.com/paper/2111.02458/) (2021)
- [Concavity of reweighted Kikuchi approximation](https://mlsanity.com/paper/1410.7098/) (2014)
- [α Belief Propagation as Fully Factorized Approximation](https://mlsanity.com/paper/1908.08906/) (2019)

## Abstract (arXiv)

Belief Propagation (BP) is a simple probabilistic inference algorithm, consisting of passing messages between nodes of a graph representing a probability distribution. Its analogy with a neural network suggests that it could have far-ranging applications for neuroscience and artificial intelligence. Unfortunately, it is only exact when applied to cycle-free graphs, which restricts the potential of the algorithm. In this paper, we propose Circular Belief Propagation (CBP), an extension of BP which limits the detrimental effects of message reverberation caused by cycles by learning to detect and cancel spurious correlations and belief amplifications. We show in numerical experiments involving binary probabilistic graphs that CBP far outperforms BP and reaches good performance compared to that of previously proposed algorithms.