Neural Enhanced Belief Propagation on Factor Graphs
This work addresses the challenge of accurate inference in graphical models for applications like error correction decoding, representing an incremental improvement by integrating neural networks with traditional methods.
The paper tackles the problem of suboptimal posterior probability estimates in factor graphs due to poor approximations of the data generating process or loops, by proposing a hybrid model that combines belief propagation with a factor graph graph neural network (FG-GNN) to correct messages, resulting in improved accuracy for error correction decoding tasks, such as outperforming belief propagation for LDPC codes on bursty channels.
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.