Deep Learning and Graph Neural Networks for Mathematical Pattern Recognition: Techniques, Challenges, and Advances

Complex systems are often modelled using graphs, and one of the key tasks in complex system analysis is identifying anomalies in a graph. A graph anomaly is a pattern that does not follow the typical patterns predicted by the graph's structures and/or properties. The present article provides a comprehensive review of the techniques, challenges, and advancements in the field of Deep Learning and Graph Neural Networks for Mathematical Pattern Recognition. This review highlights the effectiveness of Deep Learning (DL) and Graph Neural Networks (GNNs) in mathematical pattern recognition. Graph-based models, particularly GraphMR built on Graph2Seq, demonstrate superior performance in model accuracy and efficiency over traditional Seq2Seq methods. GNNs effectively handle structured data like ASTs and DAGs, preserving semantic and syntactic information. The integration of encoder–decoder architectures and graph-based reasoning shows significant advancements in recognizing mathematical structures. The evolution from structural methods to DL and GNN approaches underscores the progress in recognition accuracy. As ML adoption grows, the need for large, high-quality datasets becomes critical for training next-generation models.