Towards A Generalizable and Expressive Graph Neural Network for Graph-Level Tasks with Theoretical Guarantees

Abstract Graph Neural Networks (GNNs) have become essential for solving graph-level tasks, such as classification and regression, across diverse domains including social networks and biology. However, existing GNNs struggle with the expressivity that captures complex structural patterns, and the generalization that ensures robust performance on diverse and noisy datasets. To address these challenges, we propose a novel GNN model that integrates a k -path rooted subgraph encoder, an adaptive graph contrastive learning approach, and a consistency-aware loss. The k -path rooted subgraph encoder enhances expressivity by capturing and distinguishing intricate substructures, with theoretical guarantees for counting paths and cycles. The adaptive graph contrastive learning framework improves generalization by generating domain-aware graph augmentations based on edge importance, while the consistency-aware loss ensures task-relevant properties are preserved across augmented views. Extensive experiments on 26 datasets spanning graph classification, regression, and realistic scenarios such as noise, class imbalance, and few-shot learning show that our model achieves superior performance against 18 state-of-the-art GNN models in both effectiveness and efficiency. The code is released in https://anonymous.4open.science/r/GEGNN .