The Final Layer Holds the Key: A Unified and Efficient GNN Calibration Framework

2025-05-16

AI Summary

Graph Neural Networks (GNNs) commonly suffer from underconfident predictions, undermining decision reliability; existing calibration methods rely on auxiliary modules, lack theoretical grounding, and incur additional computational overhead. Method: We propose Terminal-layer Unified Calibration (TUC), a parameter- and architecture-free framework. We first reveal that terminal-layer confidence is jointly governed by class-center-level and node-level calibration. Theoretically, we show that reducing terminal-layer weight decay mitigates underconfidence, while a node-level distance constraint pulls test nodes closer to their predicted class centers. TUC models class centers directly from terminal-layer representations and jointly optimizes weight decay and node-to-center distances. Results: On multiple benchmark datasets, TUC significantly reduces Expected Calibration Error (ECE), achieving an average improvement of 28.6% over prior state-of-the-art methods—while introducing zero additional parameters and incurring negligible computational overhead.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Graphical Models
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Graph Neural Networks (GNNs) have demonstrated remarkable effectiveness on graph-based tasks. However, their predictive confidence is often miscalibrated, typically exhibiting under-confidence, which harms the reliability of their decisions. Existing calibration methods for GNNs normally introduce additional calibration components, which fail to capture the intrinsic relationship between the model and the prediction confidence, resulting in limited theoretical guarantees and increased computational overhead. To address this issue, we propose a simple yet efficient graph calibration method. We establish a unified theoretical framework revealing that model confidence is jointly governed by class-centroid-level and node-level calibration at the final layer. Based on this insight, we theoretically show that reducing the weight decay of the final-layer parameters alleviates GNN under-confidence by acting on the class-centroid level, while node-level calibration acts as a finer-grained complement to class-centroid level calibration, which encourages each test node to be closer to its predicted class centroid at the final-layer representations. Extensive experiments validate the superiority of our method.

Problem

• GNNs exhibit miscalibrated predictive confidence harming reliability
• Existing methods lack theoretical guarantees and increase overhead
• Proposes unified framework linking final-layer parameters to calibration

Innovation

• Unified GNN calibration via final-layer analysis
• Reduce final-layer weight decay for under-confidence
• Node-level complements class-centroid calibration