Robust OOD Graph Learning via Mean Constraints and Noise Reduction

Abstract: Graph Out-of-Distribution (OOD) classification often suffers from sharp performance drops, particularly under category imbalance and structural noise. This work tackles two pressing challenges in this context: (1) the underperformance of minority classes due to skewed label distributions, and (2) their heightened sensitivity to structural noise in graph data. To address these problems, we propose two complementary solutions. First, Constrained Mean Optimization (CMO) improves minority class robustness by encouraging similarity-based instance aggregation under worst-case conditions. Second, the Neighbor-Aware Noise Reweighting (NNR) mechanism assigns dynamic weights to training samples based on local structural consistency, mitigating noise influence. We provide theoretical justification for our methods, and validate their effectiveness with extensive experiments on both synthetic and real-world datasets, showing significant improvements in Graph OOD generalization and classification accuracy. The code for our method is available at: https://anonymous.4open.science/r/CMO-NNR-2F30.