In recent years, we have witnessed a surge of Graph Neural Networks (GNNs), most of which can learn powerful representations in an end-to-end fashion with great success in many real-world applications. They have resemblance to Probabilistic Graphical Models (PGMs), but break free from some limitations of PGMs. By aiming to provide expressive methods for representation learning instead of computing marginals or most likely configurations, GNNs provide flexibility in the choice of information flowing rules while maintaining good performance. Despite their success and inspirations, they lack efficient ways to represent and learn higher-order relations among variables/nodes. More expressive higher-order GNNs which operate on k-tuples of nodes need increased computational resources in order to process higher-order tensors. We propose Factor Graph Neural Networks (FGNNs) to effectively capture higher-order relations for inference and learning. To do so, we first derive an efficient approximate Sum-Product loopy belief propagation inference algorithm for discrete higher-order PGMs. We then neuralize the novel message passing scheme into a Factor Graph Neural Network (FGNN) module by allowing richer representations of the message update rules; this facilitates both efficient inference and powerful end-to-end learning. We further show that with a suitable choice of message aggregation operators, our FGNN is also able to represent Max-Product belief propagation, providing a single family of architecture that can represent both Max and Sum-Product loopy belief propagation. Our extensive experimental evaluation on synthetic as well as real datasets demonstrates the potential of the proposed model.

翻译：近年来，我们见证了图神经网络（GNN）的蓬勃发展，此类模型大多能以端到端方式学习强大表示，并在众多实际应用中获得巨大成功。它们与概率图模型（PGM）存在相似性，但突破了PGM的某些限制。GNN旨在为表示学习提供富有表现力的方法，而非计算边缘概率或最可能配置，这使得它们在保持良好性能的同时，能在信息传递规则选择上具备灵活性。尽管取得显著成功并带来启示，但现有GNN在表示和学习变量/节点间高阶关系方面缺乏高效途径。作用于节点k元组的更高阶GNN需要增加计算资源以处理高阶张量。我们提出因子图神经网络（FGNN）以有效捕获高阶关系用于推理与学习。为此，我们首先推导了离散高阶PGM的高效近似和积环置信传播推理算法，随后通过允许消息更新规则具有更丰富表示，将新型消息传递方案神经化为因子图神经网络（FGNN）模块——这同时促进了高效推理与强大端到端学习。进一步研究表明，通过适当选择消息聚合算子，我们的FGNN也能表示最大积置信传播，从而提供能同时表示最大积与和积环置信传播的统一架构。在合成数据集与真实数据集上的广泛实验评估证明了所提模型的潜力。