From Phase Transition to Systemic Failure: A Decoupled Analytics Framework for GNN Robustness

Graph neural networks (GNNs) are increasingly deployed in real-world applications where distribution shift is un-avoidable. However, how such shifts affect model calibration, defined as the agreement between predictive confidence and actual accuracy, remains poorly understood, and existing graph calibration methods typically rely on labeled validation data from the deployment distribution. In this work, I present the first closed-form theoretical characterization of GNN calibration under distribution shift. I show that calibration is governed by a single scalar quantity that explicitly depends on structural changes between the source and target graphs, as well as feature quality. This characterization precisely identifies when a model becomes over-confident, under-confident, or remains calibrated, and directly yields the optimal temperature scaling strategy. I further extend the analysis to graph convolutional networks with symmetric normalization, multi-class classification, and covariate shift, and derive a theoretical upper bound on the expected calibration error. My analysis also reveals that, under homogeneous distribution shift, a single global temperature is theoretically optimal, providing a principled explanation for why more complex node-wise recalibration methods offer no additional benefit. Building on these theoretical insights, I propose STAC, a source-free, label-free calibration method. Experiments on synthetic benchmarks demonstrate substantial calibration improvements, while evaluations on five real-world graph datasets show that reliable calibration without target labels remains challenging despite the strong predictive power of the theory.

Graph Convolutional Networks (GCNs) are highly sensitive to label noise, since corrupted supervision can propagate through the graph and degrade learned node representations. This work proposes PCC+GCN, a hybrid framework that uses Particle Competition and Cooperation (PCC) as a graph-based label-refinement stage before GCN training. PCC identifies suspicious labeled nodes through particle domination dynamics and determines whether their labels should be preserved, removed, or reassigned before GCN training. The framework also allows the graph used by PCC to be augmented with feature-based $k$-nearest-neighbor edges, while the GCN itself is trained on the original graph structure and node features. The proposed method was evaluated on ten graph datasets from the NoisyGL benchmark under conventional Uniform, Pair, and Random label noise, as well as under instance-dependent label noise. A detailed hyperparameter analysis was also conducted on Cora, CiteSeer, and PubMed. Under conventional noise, PCC+GCN achieved the highest overall average accuracy and the best average rank among the evaluated methods, with an average gain of $1.67$ percentage points over the baseline GCN across the clean setting and all noisy scenarios. Under instance-dependent noise, PCC+GCN remained competitive with the best-performing robust methods while requiring substantially lower execution time, being the fastest robust method on eight of the ten datasets. The results indicate that PCC-based label refinement provides an effective and computationally efficient preprocessing strategy for improving GCN robustness under noisy supervision.

Graph Convolutional Networks (GCNs) have demonstrated exceptional performance on graph-structured data. However, their success heavily relies on the availability of clean labels, an assumption that often fails in real-world scenarios. The learnability of GCNs is intrinsically linked to the neighborhood structure of nodes, making it critical to understand how this structure changes in the presence of label noise. In this work, we investigate how the neighborhood label distribution of a node changes under label noise. We mathematically derive that label noise smooths this distribution, which inherently increases its entropy and severely decreases interclass distinguishability. To address this challenge, we propose Leave-one-out Entropy Node Screening (LENS), an end-to-end framework that identifies noisy nodes by measuring the reduction in neighborhood entropy when a specific node is removed. LENS further incorporates a relabeling mechanism to recover and preserve valuable feature information instead of entirely discarding the identified noisy nodes. Crucially, the end-to-end computational overhead of LENS is remarkably low. Extensive evaluations demonstrate that our algorithm achieves state-of-the-art node classification accuracy while executing an order of magnitude faster than existing noise-robust approaches.