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CASE: Exploiting Intra-class Compactness and Inter-class Separability of Feature Embeddings for Out-of-Distribution Detection
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Proposes CASE, a dual-loss training objective (compactness loss on scaled squared-Euclidean distance logits plus inter-class separability loss) with learnable class centers, to improve OOD detection with ODIN-style scoring.
Problem
Softmax cross-entropy training yields embeddings that are not optimized for OOD detection because they do not explicitly enforce intra-class compactness and inter-class separability, leading to overconfident predictions on OOD inputs.
Approach
Trains a distance-based classifier where logits are scaled squared Euclidean distances to learnable, gradient-updated class centers, combining a CE-style compactness loss with an exponential inter-center separability loss, and uses ODIN temperature scaling and perturbation at inference.
Key results
- On CIFAR-10 (ResNet-18), CASE with ODIN score reaches 20.18% FPR95 and 96.12% AUROC versus 70.65% FPR95 and 86.57% AUROC for the MSP baseline.
- On CIFAR-100 (ResNet-34), CASE reduces average FPR95 to 47.34% from 84.45% for MSP and 77.18% for ODIN.
- Compared with CE loss, CASE reduces average FPR95 by 50.47% and improves AUROC by 9.55% on CIFAR-10 with softmax score.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Train with CASE instead of CE | ResNet-18 · CIFAR-10, average over nine OOD datasets | FPR95: 52.53 -> 20.18 | Helped |
| Train with CASE instead of CE | ResNet-18 · CIFAR-10, average over nine OOD datasets | AUROC: 88.41 -> 96.12 | Helped |
| Train with CASE instead of CE | ResNet-34 · CIFAR-100, average over nine OOD datasets | FPR95: 77.18 -> 47.34 | Helped |
| Train with CASE instead of CE | ResNet-34 · CIFAR-100, average over nine OOD datasets | AUROC: 78.14 -> 88.70 | Helped |
| Add the separability loss to the compactness loss (ablation) | CASE · CIFAR-100, average over nine OOD datasets | FPR95: 52.58 -> 47.34 | Helped |
| Add the separability loss to the compactness loss (ablation) | CASE · CIFAR-100, average over nine OOD datasets | AUROC: 87.65 -> 88.70 | Helped |
| Add the separability loss to the compactness loss (ablation) | CASE · CIFAR-100 | ID test error: 26.22 -> 25.44 | Helped |
| Add the compactness loss to the separability loss (ablation) | CASE · CIFAR-100, average over nine OOD datasets | FPR95: 94.35 -> 47.34 | Helped |
| Add the compactness loss to the separability loss (ablation) | CASE · CIFAR-100, average over nine OOD datasets | AUROC: 48.51 -> 88.70 | Helped |
| Add the compactness loss to the separability loss (ablation) | CASE · CIFAR-100 | ID test error: 99.06 -> 25.44 | Helped |
Surprising findings
- Learning class centers as free parameters updated by gradient descent outperforms predefined or batch-estimated centers (CESED, batch-estimated methods) on OOD detection.
Limitations
- Auxiliary OOD data is not used, so performance relies solely on ID training; no evaluation on large-scale ImageNet-scale benchmarks beyond ImageNet-10.
- Hyperparameters (temperature, perturbation, loss weight lambda_c) require tuning.
Experimental setup
Datasets: CIFAR-10 CIFAR-100 ImageNet-10
Benchmarks: CIFAR-10 CIFAR-100 ImageNet-10
Metrics: FPR95 AUROC AUPR IDTE
Baselines: MSP ODIN Mahalanobis Energy ReAct G-ODIN IsoMax+ LogitNorm CESED
Builds on: ODIN CESED Generalized ODIN IsoMax+ Mahalanobis
Closest papers by meaning
- Pursuing Feature Separation based on Neural Collapse for Out-of-Distribution Detection (ICLR 2025 · similarity 0.90)
- CADRef: Robust Out-of-Distribution Detection via Class-Aware Decoupled Relative Feature Leveraging (CVPR 2025 · similarity 0.89)
- Provable Discriminative Hyperspherical Embedding for Out-of-Distribution Detection (AAAI 2025 · similarity 0.89)
- Learning to Shape In-distribution Feature Space for Out-of-distribution Detection (NeurIPS 2024 · similarity 0.88)
- Learning with Mixture of Prototypes for Out-of-Distribution Detection (ICLR 2024 · similarity 0.88)
- ProHOC: Probabilistic Hierarchical Out-of-Distribution Classification via Multi-Depth Networks (CVPR 2025 · similarity 0.88)
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