Over the past decade, deep learning has gained significant attention in processing and analyzing graph data. The complexity and challenges of generating and analyzing graph data have created a need for advanced methods to model and produce accurate, high-quality graphs. In this research, the latest advancements in logical systems and neural networks have been utilized to present an innovative method for improving deep generative models using domain knowledge. This method leverages first-order logic to provide precise, interpretable insights into relational structures, ultimately improving the quality and accuracy of generated graphs. This research builds on concepts from Statistical Relational Learning (SRL), which integrates statistical learning with the modeling of structural relationships between entities. In this approach, relational data is utilized to identify patterns and make predictions, particularly when the data is represented as graphs or networks. In this field, combining logic with statistical models enables the application of logical rules in graph analysis. A key concept in this area is Rule Moment Matching, where the model aims to replicate patterns of relationships between entities, mirroring those found in real data. The aim of this method is for the model to accurately grasp how entities relate to one another, as observed in real data. In this research, the proposed concept is implemented so that the expected count of each rule aligns with its observed count in the data. Variational Graph Autoencoders (VGAEs) are used in this study as a type of probabilistic generative model that leverages Graph Neural Networks (GNNs) to learn node representations within a graph. Initially, a logical system extracts the rules from the graph data, and rule counting is then performed automatically using a differentiable algorithm based on matrix multiplication. This algorithm can autonomously count the rules after receiving the necessary information. Beyond eva‎luating the quality of the generated graphs, this research also includes assessments based on edge prediction and node classification metrics, showing that the model has made significant advances in node classification. Additionally, a learning curve eva‎luation was conducted to demonstrate the effect of rule moment matching under different conditions by varying the amount of data. Experimental eva‎luations on five benchmark datasets reveal a significant improvement in the quality of generated graphs, attributed to greater accuracy in rule matching and reduced modeling errors. Ultimately, this research demonstrates that integrating logical knowledge with machine learning techniques can support the development of generative graph models. These advancements have potential applications in diverse fields, including social networks, bioinformatics, and traffic analysis.

عبدالرضا ميرزايي

عليرضا بصيري