A Neuro-Symbolic Approach for Probabilistic Reasoning on Graph Data

2025-07-29

AI Summary

This paper addresses the challenge of jointly achieving strong representation learning and symbolic reasoning on graph-structured data. To this end, we propose a neuro-symbolic fusion framework that seamlessly integrates the representation learning capability of Graph Neural Networks (GNNs) with the probabilistic modeling and logical reasoning capacity of Relational Bayesian Networks (RBNs). Our key contributions are: (1) two novel GNN–RBN co-fusion mechanisms enabling bidirectional knowledge exchange; and (2) a unified, end-to-end Maximum A Posteriori (MAP) inference paradigm that supports both symbolic knowledge injection and collective reasoning over relational structures. Empirically, the framework significantly improves node classification accuracy while enhancing model interpretability and cross-domain generalization. We release two new benchmark datasets to facilitate evaluation of neuro-symbolic graph learning, and demonstrate the framework’s effectiveness in a real-world multi-objective environmental network optimization decision-making task.

Technology Category

• Machine Learning: Neuro-Symbolic Learning
• Reasoning under Uncertainty: Relational Probabilistic Models
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

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. Second, we introduce a multi-objective network optimization problem in environmental planning, where MAP inference supports complex decision-making. 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.

Problem

• Integrate GNNs with RBNs for probabilistic reasoning on graphs
• Combine learning strength of GNNs with reasoning of RBNs
• Apply neuro-symbolic framework to improve accuracy and decision-making

Innovation

• Integrates GNNs into Relational Bayesian Networks
• Combines learning strength with reasoning capabilities
• Proposes MAP inference for neuro-symbolic models