将图神经网络与概率推理结合,实现更智能的图数据建模。
A Neuro-Symbolic Approach for Probabilistic Reasoning on Graph Data
- 用符号模型融合图神经网络,兼顾学习与推理能力。
- 在节点分类任务中提升准确率,尤其在同质/异质模式下表现更优。
- 适合需要可解释推理的复杂决策场景,如环境规划优化。
图神经网络(GNN)在图结构数据上表现优异,但难以融入符号领域知识和进行泛化推理。关系贝叶斯网络(RBN)则支持对图状结构的完全生成式概率建模,并具备丰富的符号知识表达与概率推断能力。本文提出一种神经符号框架,将GNN无缝集成至RBN中,融合了GNN的学习优势与RBN的灵活推理能力。我们设计了两种实现方式:一种将GNN直接编译为原生RBN语言,另一种保持GNN作为外部组件。两种方法均保留GNN的语义与计算特性,且完全符合RBN建模范式。我们还提出最大后验(MAP)推理方法。为验证框架通用性,应用于两个不同问题:一是将节点分类GNN转化为显式建模同质与异质标签模式的集体分类模型,在合成与真实数据集上显著提升准确率;二是提出环境规划中的多目标网络优化问题,利用MAP推理与连续数值松弛实现复杂决策。两项应用均包含新的公开基准数据集。本工作构建了一个强大而一致的神经符号图数据处理方法,推动学习与推理的融合,赋能新应用场景并提升多任务性能。
原文摘要 · Abstract (English)
Graph neural networks (GNNs) excel at predictive tasks on graph-structured data but often lack the ability to incorporate symbolic domain knowledge and perform general reasoning. Relational Bayesian Networks (RBNs), in contrast, enable fully generative probabilistic modeling over graph-like structures and support rich symbolic knowledge and probabilistic inference. This paper presents a neuro-symbolic framework that seamlessly integrates GNNs into RBNs, combining the learning strength of GNNs with the flexible reasoning capabilities of RBNs. We develop two implementations of this integration: one compiles GNNs directly into the native RBN language, while the other maintains the GNN as an external component. Both approaches preserve the semantics and computational properties of GNNs while fully aligning with the RBN modeling paradigm. We also propose a maximum a posteriori (MAP) inference method for these neuro-symbolic models. To demonstrate the framework's versatility, we apply it to two distinct problems. First, we transform a GNN for node classification into a collective classification model that explicitly models homo- and heterophilic label patterns, substantially improving accuracy on both synthetic and real-world datasets. Second, we introduce a multi-objective network optimization problem in environmental planning, where MAP inference and continuous numeric relaxation support a complex decision-making task. Both applications include new publicly available benchmark datasets. This work introduces a powerful and coherent neuro-symbolic approach to graph data, bridging learning and reasoning in ways that enable novel applications and improved performance across diverse tasks.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品;中文卡片由大模型生成,请以原文为准。