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Hyperbolic Anomaly Detection
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Proposes HypAD, which maps PDN features into Poincaré ball hyperbolic space and trains with a hyperbolic distance between augmented views for one-class industrial anomaly detection, reporting state-of-the-art pixel AUPRO on MVTec AD and VisA.
Problem
Industrial vision anomaly detection typically measures feature embeddings in Euclidean space, which may not capture the non-Euclidean/hierarchical structure of image data, limiting pixel-level localization performance.
Approach
Extends the EfficientAD-style teacher-student self-supervised pipeline into hyperbolic space: features from a PDN-based encoder are exponentially mapped to the Poincaré ball and the two augmented views are pulled together using hyperbolic distance instead of Euclidean distance.
Key results
- Achieves 97.6% mean pixel-level AUPRO on MVTec AD (+3.6 over prior best listed) and 95.4% on VisA (+2.2).
- Image-level AUROC 99.2% on MVTec AD and 98.3% on VisA, with only slight gains since performance is near saturation.
- Curvature c=0.01 performs best on VisA; c=0 (Euclidean) gives 93.4% AUPRO, showing hyperbolic gain.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Map image embeddings to hyperbolic space and optimize with hyperbolic distance | HypAD · MVTec AD | AUPRO (%): +3.6% | Helped |
| Map image embeddings to hyperbolic space and optimize with hyperbolic distance | HypAD · VisA | AUPRO (%): +2.2% | Helped |
| Use hyperbolic embeddings instead of Euclidean embeddings (c=0) (ablation) | HypAD · VisA | AUPRO (%): 93.4 -> 95.4 | Helped |
| Increase curvature from c=0.01 to c=0.05 (ablation) | HypAD · VisA | AUPRO (%): 95.4 -> 95.2 | Hurt |
| Increase curvature from c=0.01 to c=0.1 (ablation) | HypAD · VisA | AUPRO (%): 95.4 -> 95.2 | Hurt |
| Increase curvature from c=0.01 to c=0.3 (ablation) | HypAD · VisA | AUPRO (%): 95.4 -> 95.3 | Hurt |
| Increase curvature from c=0.01 to c=0.5 (ablation) | HypAD · VisA | AUPRO (%): 95.4 -> 95.3 | Hurt |
| Use hyperbolic embeddings and the proposed method | HypAD · MVTec AD | pixel-level AUPR: 60.8 -> 62.5 | Helped |
| Use hyperbolic embeddings and the proposed method | HypAD · VisA | pixel-level AUROC | Helped |
Surprising findings
- Image-level metrics on MVTec AD and VisA show only slight improvement over prior methods, which the authors attribute to saturation.
- Pixel-level AUROC is similar across methods while AUPR differs more, suggesting AUROC exaggerates localization performance.
Limitations
- Only the Poincaré ball model and one-class setting are explored.
- Hyperbolic gains at image level are marginal due to saturation.
- Evaluation on other ADBench CV datasets left to future work.
Experimental setup
Datasets: MVTec AD VisA ImageNet MNIST-C (ADBench)
Benchmarks: MVTec AD VisA MNIST-C (ADBench)
Metrics: AUPRO AUROC AUPR
Baselines: S-T FastFlow PatchCore EfficientAD DiffusionAD FAIR SimpleNet RDAD SPD DevNet
Builds on: EfficientAD Hyperbolic image embeddings (Khrulkov et al.) Hyperbolic vision transformers (Ermolov et al.) PDN Teacher-student anomaly detection
Closest papers by meaning
- MambaAD: Exploring State Space Models for Multi-class Unsupervised Anomaly Detection (NeurIPS 2024 · similarity 0.86)
- Deep Orthogonal Hypersphere Compression for Anomaly Detection (ICLR 2024 · similarity 0.86)
- ResAD: A Simple Framework for Class Generalizable Anomaly Detection (NeurIPS 2024 · similarity 0.85)
- A Diffusion-Based Framework for Multi-Class Anomaly Detection (AAAI 2024 · similarity 0.84)
- A Unified Latent Schrodinger Bridge Diffusion Model for Unsupervised Anomaly Detection and Localization (CVPR 2025 · similarity 0.83)
- AnomalyGPT: Detecting Industrial Anomalies Using Large Vision-Language Models (AAAI 2024 · similarity 0.83)
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