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How Does Unlabeled Data Provably Help Out-of-Distribution Detection?
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Proposes SAL, which filters candidate outliers from unlabeled in-the-wild data via a top-singular-vector gradient score and then trains a binary ID-vs-outlier classifier, with separability and learnability error bounds.
Problem
Understanding theoretically how unlabeled in-the-wild data (a mixture of ID and OOD) can help OOD detection without a clean OOD set.
Approach
Score each wild sample by the squared projection of its gradient (relative to a reference ID gradient) onto the top singular vector of the wild gradient matrix, keep high-score samples as candidate outliers, and train an OOD classifier on ID data versus these candidates; provides error bounds for filtering and generalization.
Key results
- On CIFAR-100, SAL achieves average FPR95 of 1.88% and AUROC 99.51%, versus 7.80% FPR95 for WOODS.
- On CIFAR-100, SAL reduces FPR95 by 64.77% on Places365 compared with KNN+.
- Replacing SAL's filtering score with GradNorm raises average FPR95 to 23.84% on CIFAR-100 (vs 1.88%).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use SAL rather than WOODS | OOD detection with wild data · CIFAR-100 OOD average | FPR95: 7.80 -> 1.88 | Helped |
| use SAL rather than KNN+ (ID data only) | OOD detection · CIFAR-100 OOD average | FPR95: 46.40 -> 1.88 | Helped |
| use SAL rather than WOODS | OOD detection with wild data · CIFAR-100 OOD average | AUROC: 97.43 -> 99.51 | Helped |
| replace the SAL filtering score with GradNorm (ablation) | SAL · CIFAR-100 OOD average | FPR95: 1.88 -> 23.84 | Hurt |
| replace the SAL filtering score with GradNorm (ablation) | SAL · CIFAR-100 OOD average | AUROC: 99.51 -> 93.12 | Hurt |
| use in-the-wild data in addition to ID data | OOD detection · CIFAR-100 OOD: Places365 | FPR95: +64.77% reduction | Helped |
Surprising findings
- SAL's ID accuracy (73.71%) is slightly below baselines, attributed to using only 25,000 labeled ID samples versus 50,000 for baselines.
Limitations
- Theory relies on assumptions such as beta-smoothness, bounded parameter spaces, and the discrepancy condition, which are only mildly justified for neural networks.
- Filtering error on OOD samples (ERR_out=0.30 on CIFAR-100 with Textures) is substantially higher in harder classification settings.
Experimental setup
Datasets: CIFAR-10 CIFAR-100 SVHN Places365 LSUN-Resize LSUN-C Textures
Benchmarks: CIFAR-100 OOD detection (SVHN, Places365, LSUN-C, LSUN-Resize, Textures)
Metrics: FPR95 AUROC ID accuracy
Baselines: MSP ODIN Mahalanobis Energy ReAct DICE KNN ASH CSI KNN+ OE Energy (w/ OE)
Builds on: WOODS Outlier Exposure GradNorm KNN+
Closest papers by meaning
- When and How Does In-Distribution Label Help Out-of-Distribution Detection? (ICML 2024 · similarity 0.90)
- Can We Ignore Labels in Out of Distribution Detection? (ICLR 2025 · similarity 0.90)
- A Noisy Elephant in the Room: Is Your Out-of-Distribution Detector Robust to Label Noise? (CVPR 2024 · similarity 0.90)
- Out-Of-Distribution Detection with Diversification (Provably) (NeurIPS 2024 · similarity 0.89)
- EAT: Towards Long-Tailed Out-of-Distribution Detection (AAAI 2024 · similarity 0.89)
- Long-Tailed Out-of-Distribution Detection: Prioritizing Attention to Tail (AAAI 2025 · similarity 0.89)
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