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Understanding and Mitigating Under-Confidence in GNNs from the Final Layer

NeurIPS 2026 · Graph learning › GNN architectures · approach: Robustness, privacy, and fairness of GNNs · 0 citations (OpenAlex)

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Proposes SCAR, a training-free post-hoc graph calibration method that reduces final-layer weight decay (class-centroid calibration) and pulls test nodes toward their predicted class prototypes (node-level calibration) to fix GNN under-confidence.

Problem

GNNs are often under-confident, and existing graph calibration methods rely on extra calibration networks trained on validation sets rather than explaining how the model itself produces confidence.

Approach

Theoretically links final-layer weight decay to a softmax temperature greater than 1 (causing under-confidence) and shows the logits decompose into prototype similarities; reducing final-layer weight decay enlarges class-prototype separation, and a training-free node-level shift toward the predicted class prototype further sharpens confidence.

Key results

• On GCN with 20 labels per class, SCAR reduces ECE on Cora to 3.35% from 4.88% for TS (best prior GETS 3.83%).
• On GAT with 20 labels per class, SCAR achieves ECE 4.37% on Citeseer versus 5.85% for GETS.
• The paper reports SCAR improves ECE on average by 16.9% over GETS across datasets and label rates.

Surprising findings

• Adjusting global weight decay substantially hurts accuracy, whereas reducing only final-layer weight decay preserves it.
• Accuracy also improves slightly with SCAR, despite the calibration procedure changing final-layer parameters.

Limitations

• Node-level calibration depends on the bias of GNN message passing; the paper introduces a heuristic two-level refinement with extra hyperparameters alpha and beta.
• Theoretical results rely on simplifying assumptions such as fixed representations and a linearized GNN.

Experimental setup

Datasets: Cora Citeseer Pubmed CoraFull Chameleon Squirrel

Benchmarks: Cora Citeseer Pubmed CoraFull Chameleon Squirrel

Metrics: ECE (20 bins) accuracy

Baselines: TS MS AU-LS CaGCN GATS DCGC GETS

Builds on: temperature scaling CaGCN GATS GETS

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