# Curved Geometric Networks for Visual Anomaly Recognition

arXiv: https://arxiv.org/abs/2208.01188 · HTML: https://mlsanity.com/paper/2208.01188/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 60 of its 83 references that are in the map.
- First posted on arXiv 2 Aug 2022.

## Builds on (most cited first, 30 of 60)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Prototypical Networks for Few-shot Learning](https://mlsanity.com/paper/1703.05175/) (2017)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [Unsupervised Representation Learning by Predicting Image Rotations](https://mlsanity.com/paper/1803.07728/) (2018)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loop](https://mlsanity.com/paper/1506.03365/) (2015)
- [Enhancing The Reliability of Out-of-distribution Image Detection in Neural Networks](https://mlsanity.com/paper/1706.02690/) (2017)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [SphereFace: Deep Hypersphere Embedding for Face Recognition](https://mlsanity.com/paper/1704.08063/) (2017)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Unsupervised Anomaly Detection with Generative Adversarial Networks to Guide Marker Discovery](https://mlsanity.com/paper/1703.05921/) (2017)
- [Memorizing Normality to Detect Anomaly: Memory-augmented Deep Autoencoder for Unsupervised Anomaly Detection](https://mlsanity.com/paper/1904.02639/) (2019)
- [CutPaste: Self-Supervised Learning for Anomaly Detection and Localization](https://mlsanity.com/paper/2104.04015/) (2021)
- [Using Self-Supervised Learning Can Improve Model Robustness and Uncertainty](https://mlsanity.com/paper/1906.12340/) (2019)
- [Scaling Out-of-Distribution Detection for Real-World Settings](https://mlsanity.com/paper/1911.11132/) (2019)
- [Likelihood Ratios for Out-of-Distribution Detection](https://mlsanity.com/paper/1906.02845/) (2019)
- [CSI: Novelty Detection via Contrastive Learning on Distributionally Shifted Instances](https://mlsanity.com/paper/2007.08176/) (2020)
- [Generalized ODIN: Detecting Out-of-distribution Image without Learning from Out-of-distribution Data](https://mlsanity.com/paper/2002.11297/) (2020)
- [Training Confidence-calibrated Classifiers for Detecting Out-of-Distribution Samples](https://mlsanity.com/paper/1711.09325/) (2017)
- [Uninformed Students: Student-Teacher Anomaly Detection with Discriminative Latent Embeddings](https://mlsanity.com/paper/1911.02357/) (2019)
- [Multiresolution Knowledge Distillation for Anomaly Detection](https://mlsanity.com/paper/2011.11108/) (2020)
- [Deep Anomaly Detection Using Geometric Transformations](https://mlsanity.com/paper/1805.10917/) (2018)
- [A Unified Model for Multi-class Anomaly Detection](https://mlsanity.com/paper/2206.03687/) (2022)
- [Improving Unsupervised Defect Segmentation by Applying Structural Similarity to Autoencoders](https://mlsanity.com/paper/1807.02011/) (2018)
- [Learning Confidence for Out-of-Distribution Detection in Neural Networks](https://mlsanity.com/paper/1802.04865/) (2018)
- [Hyperbolic Image Embeddings](https://mlsanity.com/paper/1904.02239/) (2019)
- [Patch SVDD: Patch-level SVDD for Anomaly Detection and Segmentation](https://mlsanity.com/paper/2006.16067/) (2020)

## Built on by (most cited first, 15 of 15)

- [Hyperbolic Deep Learning in Computer Vision: A Survey](https://mlsanity.com/paper/2305.06611/) (2023)
- [Hyperbolic Audio-visual Zero-shot Learning](https://mlsanity.com/paper/2308.12558/) (2023)
- [PointCaM: Cut-and-Mix for Open-Set Point Cloud Learning](https://mlsanity.com/paper/2212.02011/) (2022)
- [SHMamba: Structured Hyperbolic State Space Model for Audio-Visual Question Answering](https://mlsanity.com/paper/2406.09833/) (2024)
- [Curvature Learning for Generalization of Hyperbolic Neural Networks](https://mlsanity.com/paper/2508.17232/) (2025)
- [Modality Alignment across Trees on Heterogeneous Hyperbolic Manifolds](https://mlsanity.com/paper/2510.27391/) (2025)
- [Hyperbolic Dual Feature Augmentation for Open-Environment](https://mlsanity.com/paper/2506.08906/) (2025)
- [Geometry-aware Distance Measure for Diverse Hierarchical Structures in Hyperbolic Spaces](https://mlsanity.com/paper/2506.18533/) (2025)
- [Balanced Hyperbolic Embeddings Are Natural Out-of-Distribution Detectors](https://mlsanity.com/paper/2506.10146/) (2025)
- [HyPCV-Former: Hyperbolic Spatio-Temporal Transformer for 3D Point Cloud Video Anomaly Detection](https://mlsanity.com/paper/2508.00473/) (2025)
- [Minimizing Hyperbolic Embedding Distortion with LLM-Guided Hierarchy Restructuring](https://mlsanity.com/paper/2511.20679/) (2025)
- [PiercingEye: Dual-Space Video Violence Detection with Hyperbolic Vision-Language Guidance](https://mlsanity.com/paper/2504.18866/) (2025)
- [Hyperbolic Distillation: Geometry-Guided Cross-Modal Transfer for Robust 3D Object Detection](https://mlsanity.com/paper/2605.09899/) (2026)
- [Learning Taxonomic Trees with Hierarchical Representation Regularization for Large Multimodal Models](https://mlsanity.com/paper/2607.02909/) (2026)
- [Hyperbolic Geometry for Open-World Object Detection in Remote Sensing Imagery](https://mlsanity.com/paper/2609.09626/) (2026)

## Abstract (arXiv)

Learning a latent embedding to understand the underlying nature of data distribution is often formulated in Euclidean spaces with zero curvature. However, the success of the geometry constraints, posed in the embedding space, indicates that curved spaces might encode more structural information, leading to better discriminative power and hence richer representations. In this work, we investigate benefits of the curved space for analyzing anomalies or out-of-distribution objects in data. This is achieved by considering embeddings via three geometry constraints, namely, spherical geometry (with positive curvature), hyperbolic geometry (with negative curvature) or mixed geometry (with both positive and negative curvatures). Three geometric constraints can be chosen interchangeably in a unified design given the task at hand. Tailored for the embeddings in the curved space, we also formulate functions to compute the anomaly score. Two types of geometric modules (i.e., Geometric-in-One and Geometric-in-Two models) are proposed to plug in the original Euclidean classifier, and anomaly scores are computed from the curved embeddings. We evaluate the resulting designs under a diverse set of visual recognition scenarios, including image detection (multi-class OOD detection and one-class anomaly detection) and segmentation (multi-class anomaly segmentation and one-class anomaly segmentation). The empirical results show the effectiveness of our proposal through the consistent improvement over various scenarios.