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MaxEnt Loss: Calibrating Graph Neural Networks under Out-of-Distribution Shift (Student Abstract)
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Proposes MaxEnt loss, a focal loss augmented with a maximum-entropy mean constraint, to calibrate GNNs on a novel graph version of CelebA under in-distribution and resolution-shift OOD settings.
Problem
Miscalibration of graph neural networks, both in-distribution and under out-of-distribution (resolution) shift, where predicted probabilities do not reflect correctness.
Approach
Adds a maximum-entropy-derived mean constraint term (with a Lagrange multiplier computed via Newton-Raphson) to the focal loss so that the predicted probabilities match the class-prior mean, improving calibration of GNNs.
Key results
- MaxEnt loss gives roughly 5% additional calibration improvement over focal loss, which itself improves on cross-entropy by roughly 10%.
- All loss functions reach similar mean average precision, while CE loss yields the worst calibration.
- Under OOD resolution shift, all methods lose performance but MaxEnt loss remains the best calibrated.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| replace CE loss with Focal loss | GCN · CelebA graph ID | calibration performance: roughly 10% | Helped |
| replace Focal loss with MaxEnt loss | GCN · CelebA graph ID | calibration performance: 5% | Helped |
| replace CE loss or Focal loss with MaxEnt loss | GCN · CelebA graph OOD | calibration performance | Helped |
| evaluate on OOD rather than ID inputs | CE loss, Focal loss, and MaxEnt loss · CelebA graph ID and OOD | MAP | Hurt |
| evaluate on OOD rather than ID inputs | CE loss, Focal loss, and MaxEnt loss · CelebA graph ID and OOD | ECE | Hurt |
| train with CE loss rather than Focal or MaxEnt loss | GCN · CelebA graph ID | calibration performance | Hurt |
Surprising findings
- CE-trained GNNs tend to be underconfident, agreeing with Hsu et al. 2022.
Limitations
- Evaluation limited to a single GCN architecture and a single constructed dataset.
- Preliminary student abstract; results reported only as learning curves with approximate percentages.
- Calibration baselines limited to CE and focal loss.
Experimental setup
Datasets: CelebA
Benchmarks: CelebA graph (ID) CelebA graph (OOD resolution shift)
Metrics: ECE mean average precision
Baselines: cross-entropy loss focal loss
Builds on: focal loss maximum entropy principle GCNConv
Closest papers by meaning
- Understanding and Mitigating Under-Confidence in GNNs from the Final Layer (NeurIPS 2026 · similarity 0.90)
- Improving GNN Calibration with Discriminative Ability: Insights and Strategies (AAAI 2024 · similarity 0.89)
- SimCalib: Graph Neural Network Calibration Based on Similarity between Nodes (AAAI 2024 · similarity 0.88)
- MaxEnt Loss: Constrained Maximum Entropy for Calibration under Out-of-Distribution Shift (AAAI 2024 · similarity 0.88)
- GETS: Ensemble Temperature Scaling for Calibration in Graph Neural Networks (ICLR 2025 · similarity 0.86)
- Moderate Message Passing Improves Calibration: A Universal Way to Mitigate Confidence Bias in Graph Neural Networks (AAAI 2024 · similarity 0.86)
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