# Is Hyperbolic Space All You Need for Medical Anomaly Detection?

arXiv: https://arxiv.org/abs/2505.21228 · HTML: https://mlsanity.com/paper/2505.21228/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 36 references that are in the map.
- First posted on arXiv 27 May 2025.

## Builds on (most cited first, 27 of 27)

- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [ChestX-ray8: Hospital-scale Chest X-ray Database and Benchmarks on Weakly-Supervised Classification and Localization of Common Thorax Diseases](https://mlsanity.com/paper/1705.02315/) (2017)
- [Towards Total Recall in Industrial Anomaly Detection](https://mlsanity.com/paper/2106.08265/) (2021)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [PaDiM: a Patch Distribution Modeling Framework for Anomaly Detection and Localization](https://mlsanity.com/paper/2011.08785/) (2020)
- [CutPaste: Self-Supervised Learning for Anomaly Detection and Localization](https://mlsanity.com/paper/2104.04015/) (2021)
- [The RSNA-ASNR-MICCAI BraTS 2021 Benchmark on Brain Tumor Segmentation and Radiogenomic Classification](https://mlsanity.com/paper/2107.02314/) (2021)
- [The Liver Tumor Segmentation Benchmark (LiTS)](https://mlsanity.com/paper/1901.04056/) (2019)
- [Anomaly Detection via Reverse Distillation from One-Class Embedding](https://mlsanity.com/paper/2201.10703/) (2022)
- [Matryoshka Representation Learning](https://mlsanity.com/paper/2205.13147/) (2022)
- [Representation Tradeoffs for Hyperbolic Embeddings](https://mlsanity.com/paper/1804.03329/) (2018)
- [Hyperbolic Entailment Cones for Learning Hierarchical Embeddings](https://mlsanity.com/paper/1804.01882/) (2018)
- [Hyperbolic Image-Text Representations](https://mlsanity.com/paper/2304.09172/) (2023)
- [CFA: Coupled-hypersphere-based Feature Adaptation for Target-Oriented Anomaly Localization](https://mlsanity.com/paper/2206.04325/) (2022)
- [Natural Synthetic Anomalies for Self-Supervised Anomaly Detection and Localization](https://mlsanity.com/paper/2109.15222/) (2021)
- [Fully Hyperbolic Neural Networks](https://mlsanity.com/paper/2105.14686/) (2021)
- [Hyperbolic Image Segmentation](https://mlsanity.com/paper/2203.05898/) (2022)
- [BMAD: Benchmarks for Medical Anomaly Detection](https://mlsanity.com/paper/2306.11876/) (2023)
- [On Diffusion Modeling for Anomaly Detection](https://mlsanity.com/paper/2305.18593/) (2023)
- [Fully Hyperbolic Convolutional Neural Networks for Computer Vision](https://mlsanity.com/paper/2303.15919/) (2023)
- [The Numerical Stability of Hyperbolic Representation Learning](https://mlsanity.com/paper/2211.00181/) (2022)
- [Anomaly Detection in Medical Imaging -- A Mini Review](https://mlsanity.com/paper/2108.11986/) (2021)
- [MediCLIP: Adapting CLIP for Few-shot Medical Image Anomaly Detection](https://mlsanity.com/paper/2405.11315/) (2024)
- [Reconstruction Student with Attention for Student-Teacher Pyramid Matching](https://mlsanity.com/paper/2111.15376/) (2021)
- [A Survey on Diffusion Models for Anomaly Detection](https://mlsanity.com/paper/2501.11430/) (2025)
- [Many tasks make light work: Learning to localise medical anomalies from multiple synthetic tasks](https://mlsanity.com/paper/2307.00899/) (2023)
- [Hyperbolic Metric Learning for Visual Outlier Detection](https://mlsanity.com/paper/2403.15260/) (2024)

## Built on by (most cited first, 5 of 5)

- [Foundation Models as Class-Incremental Learners for Dermatological Image Classification](https://mlsanity.com/paper/2507.14050/) (2025)
- [HypCBC: Domain-Invariant Hyperbolic Cross-Branch Consistency for Generalizable Medical Image Analysis](https://mlsanity.com/paper/2602.03264/) (2026)
- [ARGENT: Adaptive Hierarchical Image-Text Representations](https://mlsanity.com/paper/2603.23311/) (2026)
- [Hierarchical Co-Embedding of Font Shapes and Impression Tags](https://mlsanity.com/paper/2604.04158/) (2026)
- [HypOProto: Hyperbolic Ordinal Prototypes for Left Ventricular Filling Pressure Classification](https://mlsanity.com/paper/2606.19804/) (2026)

## Abstract (arXiv)

Medical anomaly detection has emerged as a promising solution to challenges in data availability and labeling constraints. Traditional methods extract features from different layers of pre-trained networks in Euclidean space; however, Euclidean representations fail to effectively capture the hierarchical relationships within these features, leading to suboptimal anomaly detection performance. We propose a novel yet simple approach that projects feature representations into hyperbolic space, aggregates them based on confidence levels, and classifies samples as healthy or anomalous. Our experiments demonstrate that hyperbolic space consistently outperforms Euclidean-based frameworks, achieving higher AUROC scores at both image and pixel levels across multiple medical benchmark datasets. Additionally, we show that hyperbolic space exhibits resilience to parameter variations and excels in few-shot scenarios, where healthy images are scarce. These findings underscore the potential of hyperbolic space as a powerful alternative for medical anomaly detection. The project website can be found at https://hyperbolic-anomalies.github.io