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When and How Does In-Distribution Label Help Out-of-Distribution Detection?
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Theoretical graph-spectral analysis of whether in-distribution labels help OOD detection, giving an error bound on linear-probing OOD separability with vs. without ID labels, validated on CIFAR-10/100 experiments.
Problem
Understanding when and how in-distribution (ID) labels help OOD detection compared with label-free anomaly detection, which has been empirically observed but not formally analyzed.
Approach
Models ID data as an augmentation graph and shows that supervised (labeled) contrastive learning equals spectral decomposition of a label-augmented adjacency matrix; derives closed-form ID and OOD representations via OOD-ID connectivity and bounds the linear-probing error gap between labeled and unlabeled cases.
Key results
- On CIFAR-100 with near-OOD CIFAR-10, ID labels improve AUROC by about 3 points (85.93 to 89.01) when linear probing and test OOD match, and by 12.3 points in the mismatched-OOD setting per the text.
- On far-OOD SVHN the ID-label benefit is negligible (AUROC 99.96 to 99.97 when matched), supporting the near-OOD prediction.
- Empirical gap G between unlabeled and labeled linear-probing error grows from 0.01 to 0.09 as the ID adjacency Frobenius norm decreases over training epochs.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use labeled rather than unlabeled ID data | ResNet-18 OOD detection · SVHN OOD, P_ood^test = P_ood^LP (CIFAR100 ID) | AUROC: 99.96$^{\pm 0.01}$ -> 99.97$^{\pm 0.03}$ | Helped |
| Use labeled rather than unlabeled ID data | ResNet-18 OOD detection · SVHN OOD, P_ood^test != P_ood^LP (CIFAR100 ID) | AUROC: 77.09$^{\pm 2.17}$ -> 82.97$^{\pm 1.87}$ | Helped |
| Use labeled rather than unlabeled ID data | ResNet-18 OOD detection · Textures OOD, P_ood^test = P_ood^LP (CIFAR100 ID) | AUROC: 99.80$^{\pm 0.15}$ -> 99.86$^{\pm 0.11}$ | Helped |
| Use labeled rather than unlabeled ID data | ResNet-18 OOD detection · Textures OOD, P_ood^test != P_ood^LP (CIFAR100 ID) | AUROC: 70.94$^{\pm 3.77}$ -> 75.15$^{\pm 3.36}$ | Helped |
| Use labeled rather than unlabeled ID data | ResNet-18 OOD detection · Places365 OOD, P_ood^test = P_ood^LP (CIFAR100 ID) | AUROC: 99.98$^{\pm 0.00}$ -> 99.99$^{\pm 0.01}$ | Helped |
| Use labeled rather than unlabeled ID data | ResNet-18 OOD detection · Places365 OOD, P_ood^test != P_ood^LP (CIFAR100 ID) | AUROC: 79.85$^{\pm 1.85}$ -> 85.03$^{\pm 3.19}$ | Helped |
| Use labeled rather than unlabeled ID data | ResNet-18 OOD detection · LSUN-Resize OOD, P_ood^test = P_ood^LP (CIFAR100 ID) | AUROC: 99.95$^{\pm 0.03}$ -> 99.91$^{\pm 0.07}$ | Hurt |
| Use labeled rather than unlabeled ID data | ResNet-18 OOD detection · LSUN-Resize OOD, P_ood^test != P_ood^LP (CIFAR100 ID) | AUROC: 77.57$^{\pm 5.21}$ -> 82.71$^{\pm 1.64}$ | Helped |
| Use labeled rather than unlabeled ID data | ResNet-18 OOD detection · LSUN-C OOD, P_ood^test = P_ood^LP (CIFAR100 ID) | AUROC: 99.20$^{\pm 0.17}$ -> 99.35$^{\pm 0.08}$ | Helped |
| Use labeled rather than unlabeled ID data | ResNet-18 OOD detection · LSUN-C OOD, P_ood^test != P_ood^LP (CIFAR100 ID) | AUROC: 83.43$^{\pm 3.48}$ -> 89.49$^{\pm 1.91}$ | Helped |
| Use labeled rather than unlabeled ID data | ResNet-18 OOD detection · CIFAR10 OOD, P_ood^test = P_ood^LP (CIFAR100 ID) | AUROC: 85.93$^{\pm 1.72}$ -> 89.01$^{\pm 0.98}$ | Helped |
| Use labeled rather than unlabeled ID data | ResNet-18 OOD detection · CIFAR10 OOD, P_ood^test != P_ood^LP (CIFAR100 ID) | AUROC: 55.42$^{\pm 1.64}$ -> 67.72$^{\pm 0.97}$ | Helped |
Surprising findings
- The text reports a 12.3% AUROC gain on CIFAR-10 in the mismatched-OOD setting, while the table shows a larger difference than the 3.08% quoted for matched OOD; the reported numbers are internally inconsistent.
Limitations
- Analysis relies on simplifying assumptions (spectral gap condition, linear span assumption on semantic connection vectors, large N and M).
- Error bound is an upper bound on linear probing error and is only loosely tied to actual OOD detection scores.
- Experiments are limited to CIFAR-scale image benchmarks with ResNet-18.
Experimental setup
Datasets: CIFAR-10 CIFAR-100 SVHN Textures Places365 LSUN-Resize LSUN-C 300K Random Images
Benchmarks: CIFAR-100 far-OOD (SVHN, Textures, Places365, LSUN) CIFAR-100 near-OOD (CIFAR-10) CIFAR-10 as ID
Metrics: FPR95 AUROC linear probing error
Baselines: unlabeled (self-supervised) ID training labeled ID training
Builds on: spectral contrastive learning HaoChen et al. augmentation graph theory Eckart-Young-Mirsky theorem
Closest papers by meaning
- A Noisy Elephant in the Room: Is Your Out-of-Distribution Detector Robust to Label Noise? (CVPR 2024 · similarity 0.91)
- Can We Ignore Labels in Out of Distribution Detection? (ICLR 2025 · similarity 0.90)
- How Does Unlabeled Data Provably Help Out-of-Distribution Detection? (ICLR 2024 · similarity 0.90)
- Mining In-distribution Attributes in Outliers for Out-of-distribution Detection (AAAI 2025 · similarity 0.90)
- Learning to Shape In-distribution Feature Space for Out-of-distribution Detection (NeurIPS 2024 · similarity 0.89)
- EAT: Towards Long-Tailed Out-of-Distribution Detection (AAAI 2024 · similarity 0.88)
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