SETTA: Parameter-Free Test-Time Adaptation for Graph Neural Networks via Spectral-Energy-Guided Semantic Refinement

Node classification is a central graph data mining task, yet repeated message passing can over-smooth representations and degrade frozen graph neural network (GNN) predictions after deployment. We present SETTA (Spectral-Energy Test-Time Adaptation), a prediction-level graph test-time adaptation framework that refines frozen outputs without test labels, gradients, parameter updates, or learnable adaptation parameters. SETTA denoises features for semantic-neighbor construction, adds complementary semantic routes while preserving observed edges, monitors a smoothness-energy proxy during diffusion, and accepts refinements through entropy-based gating. Configurations are fixed by a dataset-level protocol or selected using validation data only. Across six mostly homophilic benchmarks with 2708–19,717 nodes, SETTA improved a frozen two-layer GCN on every dataset and achieved the highest mean accuracy among the evaluated methods on five, with gains of 4.61, 3.08, and 2.01 percentage points on Cora, CiteSeer, and PubMed, respectively. Positive mean gains were also observed across all 30 dataset–backbone settings. Ablations and transition analyses indicate that semantic injection is most beneficial on sparse citation graphs and that selective refinement limits harmful changes. The current dense implementation supports benchmark-scale, amortized refinement; scalability and robustness on heterophilic graphs remain open.