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A Data-Driven Measure of Relative Uncertainty for Misclassification Detection
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Proposes Rel-U, a learnable relative uncertainty measure over softmax outputs (closed-form distance matrix trained on positive vs. negative instances) for misclassification detection, outperforming MSP, ODIN, and Doctor on CIFAR-10/100 and under mismatch.
Problem
Misclassification detection: conventional uncertainty measures such as Shannon entropy and Gini fail to identify unreliable predictions, since overconfident wrong predictions get low uncertainty.
Approach
Defines a relative uncertainty s_d(x)=p D p^T with a distance matrix D learned from correctly vs. incorrectly classified validation samples; a closed-form solution gives D* as a ReLU of contrastive expected outer-product differences, so no network retraining is needed.
Key results
- On CIFAR-10 with DenseNet-121 trained with cross-entropy, Rel-U achieves 18.3% FPR at 95% TPR vs. 32.7% for MSP and 21.5% for Doctor.
- Rel-U performs best in 11 of 20 matched-data configurations, and is second-best in four of the remaining nine.
- Calibration helps Doctor substantially on ImageNet (76.0 to 55.4 FPR) while Rel-U is largely invariant (51.7 to 53.0).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use Rel-U instead of Doctor | DenseNet-121 · CIFAR-10, matched; CrossEntropy | FPR at 95% TPR: 21.5 (0.2) -> 18.3 (0.2) | Helped |
| Use Rel-U instead of Doctor | DenseNet-121 · CIFAR-100, matched; CrossEntropy | FPR at 95% TPR: 41.5 (0.2) -> 41.5 (0.2) | No clear effect |
| Use Rel-U instead of Doctor | ResNet-34 · CIFAR-10, matched; CrossEntropy | FPR at 95% TPR: 14.3 (0.2) -> 14.1 (0.1) | Helped |
| Use Rel-U instead of Doctor | ResNet-34 · CIFAR-100, matched; CrossEntropy | FPR at 95% TPR: 34.9 (0.5) -> 32.7 (0.3) | Helped |
| Apply temperature calibration | Rel-U on ResNet-50 · ImageNet | FPR at 95% TPR: 51.7 (0.0) -> 53.0 (0.3) | Hurt |
| Apply temperature calibration | Rel-U on DenseNet-121 · CIFAR-10 | FPR at 95% TPR: 32.7 (1.7) -> 27.7 (2.1) | Helped |
| Apply temperature calibration | Rel-U on DenseNet-121 · CIFAR-100 | FPR at 95% TPR: 45.7 (0.9) -> 46.6 (0.6) | Hurt |
| Apply temperature calibration | Rel-U on ResNet-34 · CIFAR-10 | FPR at 95% TPR: 26.2 (0.0) -> 24.2 (0.1) | Helped |
| Apply temperature calibration | Rel-U on ResNet-34 · CIFAR-100 | FPR at 95% TPR: 40.6 (0.7) -> 38.9 (0.9) | Helped |
| Increase the tuning-split size (ablation) | Rel-U · CIFAR-10 and CIFAR-100 | FPR at 95% TPR | Helped |
| Use lambda above 0.5 (ablation) | Rel-U · Matched misclassification detection | FPR at 95% TPR | Helped |
| Use a low temperature (ablation) | Rel-U · Matched misclassification detection | FPR at 95% TPR | Helped |
Surprising findings
- Misclassified soft-predictions can carry high Rel-U uncertainty even when their Shannon entropy is low.
- Setting the input perturbation epsilon to zero is close to optimal in most ablations, so the method relies only on softmax outputs.
Limitations
- Requires a held-out set of positive and negative samples to learn the measure, so performance depends on the validation size.
- Results on LogitNorm-trained models are negative, and gains are not uniform across training losses and architectures.
- As with any detector, it may be vulnerable to targeted attacks.
Experimental setup
Datasets: CIFAR-10 CIFAR-100 ImageNet CIFAR-10C
Benchmarks: CIFAR-10 CIFAR-100 ImageNet CIFAR-10C
Metrics: FPR at 95% TPR AUC AUROC AURC
Baselines: MSP ODIN Doctor MCDropout Deep Ensembles MLP LogitNorm MixUp RegMixUp OpenMix
Builds on: ODIN Doctor Gini coefficient LogitNorm
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