  Probabilistic graphical models provide a powerful tool to describe complex
statistical structure, with many real-world applications in science and
engineering from controlling robotic arms to understanding neuronal
computations. A major challenge for these graphical models is that inferences
such as marginalization are intractable for general graphs. These inferences
are often approximated by a distributed message-passing algorithm such as
Belief Propagation, which does not always perform well on graphs with cycles,
nor can it always be easily specified for complex continuous probability
distributions. Such difficulties arise frequently in expressive graphical
models that include intractable higher-order interactions. In this paper we
define the Recurrent Factor Graph Neural Network (RF-GNN) to achieve fast
approximate inference on graphical models that involve many-variable
interactions. Experimental results on several families of graphical models
demonstrate the out-of-distribution generalization capability of our method to
different sized graphs, and indicate the domain in which our method outperforms
Belief Propagation (BP). Moreover, we test the RF-GNN on a real-world
Low-Density Parity-Check dataset as a benchmark along with other baseline
models including BP variants and other GNN methods. Overall we find that
RF-GNNs outperform other methods under high noise levels.
