# Neural Enhanced Belief Propagation on Factor Graphs

arXiv: https://arxiv.org/abs/2003.01998 · HTML: https://mlsanity.com/paper/2003.01998/

## Key facts

- Cited by 57 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Mar 2020.

## Built on by (most cited first, 30 of 57)

- [Graph Neural Networks for Wireless Communications: From Theory to Practice](https://mlsanity.com/paper/2203.10800/) (2022)
- [Multi-Agent MDP Homomorphic Networks](https://mlsanity.com/paper/2110.04495/) (2021)
- [Differentiable Spatial Planning using Transformers](https://mlsanity.com/paper/2112.01010/) (2021)
- [Understanding Non-linearity in Graph Neural Networks from the Bayesian-Inference Perspective](https://mlsanity.com/paper/2207.11311/) (2022)
- [NSNet: A General Neural Probabilistic Framework for Satisfiability Problems](https://mlsanity.com/paper/2211.03880/) (2022)
- [Autoregressive Belief Propagation for Decoding Block Codes](https://mlsanity.com/paper/2103.11780/) (2021)
- [Factor Graph Neural Networks](https://mlsanity.com/paper/2308.00887/) (2023)
- [A visual introduction to Gaussian Belief Propagation](https://mlsanity.com/paper/2107.02308/) (2021)
- [Neural Structured Prediction for Inductive Node Classification](https://mlsanity.com/paper/2204.07524/) (2022)
- [Deep learning via message passing algorithms based on belief propagation](https://mlsanity.com/paper/2110.14583/) (2021)
- [Neural Enhanced Belief Propagation for Multiobject Tracking](https://mlsanity.com/paper/2212.08340/) (2022)
- [Joint Entity and Relation Extraction with Span Pruning and Hypergraph Neural Networks](https://mlsanity.com/paper/2310.17238/) (2023)
- [Neural Enhanced Belief Propagation for Data Association in Multiobject Tracking](https://mlsanity.com/paper/2203.09948/) (2022)
- [Graph Neural Networks for Channel Decoding](https://mlsanity.com/paper/2207.14742/) (2022)
- [Low-complexity Near-optimum Symbol Detection Based on Neural Enhancement of Factor Graphs](https://mlsanity.com/paper/2203.16417/) (2022)
- [Message Passing Meets Graph Neural Networks: A New Paradigm for Massive MIMO Systems](https://mlsanity.com/paper/2302.06896/) (2023)
- [Offline Tracking with Object Permanence](https://mlsanity.com/paper/2310.01288/) (2023)
- [Constrained Layout Generation with Factor Graphs](https://mlsanity.com/paper/2404.00385/) (2024)
- [Neural Belief Propagation for Scene Graph Generation](https://mlsanity.com/paper/2112.05727/) (2021)
- [Graph Neural Networks Intersect Probabilistic Graphical Models: A Survey](https://mlsanity.com/paper/2206.06089/) (2022)
- [Deep Graph Unfolding for Beamforming in MU-MIMO Interference Networks](https://mlsanity.com/paper/2304.00446/) (2023)
- [The END: An Equivariant Neural Decoder for Quantum Error Correction](https://mlsanity.com/paper/2304.07362/) (2023)
- [Neural Enhanced Belief Propagation for Cooperative Localization](https://mlsanity.com/paper/2105.12903/) (2021)
- [Decoding Quantum LDPC Codes Using Graph Neural Networks](https://mlsanity.com/paper/2408.05170/) (2024)
- [Relational Reasoning Networks](https://mlsanity.com/paper/2106.00393/) (2021)
- [Towards Better Generalization with Flexible Representation of Multi-Module Graph Neural Networks](https://mlsanity.com/paper/2209.06589/) (2022)
- [Generalization Bounds for Neural Belief Propagation Decoders](https://mlsanity.com/paper/2305.10540/) (2023)
- [Neural Enhancement of Factor Graph-based Symbol Detection](https://mlsanity.com/paper/2203.03333/) (2022)
- [Learning to Solve the Constrained Most Probable Explanation Task in Probabilistic Graphical Models](https://mlsanity.com/paper/2404.11606/) (2024)
- [Bayesian Multiobject Tracking With Neural-Enhanced Motion and Measurement Models](https://mlsanity.com/paper/2506.18124/) (2025)

## Abstract (arXiv)

A graphical model is a structured representation of locally dependent random variables. A traditional method to reason over these random variables is to perform inference using belief propagation. When provided with the true data generating process, belief propagation can infer the optimal posterior probability estimates in tree structured factor graphs. However, in many cases we may only have access to a poor approximation of the data generating process, or we may face loops in the factor graph, leading to suboptimal estimates. In this work we first extend graph neural networks to factor graphs (FG-GNN). We then propose a new hybrid model that runs conjointly a FG-GNN with belief propagation. The FG-GNN receives as input messages from belief propagation at every inference iteration and outputs a corrected version of them. As a result, we obtain a more accurate algorithm that combines the benefits of both belief propagation and graph neural networks. We apply our ideas to error correction decoding tasks, and we show that our algorithm can outperform belief propagation for LDPC codes on bursty channels.