# Learning Multi-Manifold Embedding for Out-Of-Distribution Detection

arXiv: https://arxiv.org/abs/2409.12479 · HTML: https://mlsanity.com/paper/2409.12479/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 38 references that are in the map.
- First posted on arXiv 19 Sep 2024.

## Builds on (most cited first, 28 of 28)

- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Billion-scale similarity search with GPUs](https://mlsanity.com/paper/1702.08734/) (2017)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [Describing Textures in the Wild](https://mlsanity.com/paper/1311.3618/) (2013)
- [A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks](https://mlsanity.com/paper/1807.03888/) (2018)
- [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)
- [Energy-based Out-of-distribution Detection](https://mlsanity.com/paper/2010.03759/) (2020)
- [Generalized Out-of-Distribution Detection: A Survey](https://mlsanity.com/paper/2110.11334/) (2021)
- [Out-of-Distribution Detection with Deep Nearest Neighbors](https://mlsanity.com/paper/2204.06507/) (2022)
- [Scaling Out-of-Distribution Detection for Real-World Settings](https://mlsanity.com/paper/1911.11132/) (2019)
- [Towards Out-Of-Distribution Generalization: A Survey](https://mlsanity.com/paper/2108.13624/) (2021)
- [Generalized ODIN: Detecting Out-of-distribution Image without Learning from Out-of-distribution Data](https://mlsanity.com/paper/2002.11297/) (2020)
- [ViM: Out-Of-Distribution with Virtual-logit Matching](https://mlsanity.com/paper/2203.10807/) (2022)
- [SSD: A Unified Framework for Self-Supervised Outlier Detection](https://mlsanity.com/paper/2103.12051/) (2021)
- [Mitigating Neural Network Overconfidence with Logit Normalization](https://mlsanity.com/paper/2205.09310/) (2022)
- [Hyperbolic Image Embeddings](https://mlsanity.com/paper/1904.02239/) (2019)
- [Extremely Simple Activation Shaping for Out-of-Distribution Detection](https://mlsanity.com/paper/2209.09858/) (2022)
- [DICE: Leveraging Sparsification for Out-of-Distribution Detection](https://mlsanity.com/paper/2111.09805/) (2021)
- [TurkerGaze: Crowdsourcing Saliency with Webcam based Eye Tracking](https://mlsanity.com/paper/1504.06755/) (2015)
- [Entropy Maximization and Meta Classification for Out-Of-Distribution Detection in Semantic Segmentation](https://mlsanity.com/paper/2012.06575/) (2020)
- [How to Exploit Hyperspherical Embeddings for Out-of-Distribution Detection?](https://mlsanity.com/paper/2203.04450/) (2022)
- [Hyperbolic Vision Transformers: Combining Improvements in Metric Learning](https://mlsanity.com/paper/2203.10833/) (2022)
- [Boosting Adversarial Training with Hypersphere Embedding](https://mlsanity.com/paper/2002.08619/) (2020)
- [SphereFace2: Binary Classification is All You Need for Deep Face Recognition](https://mlsanity.com/paper/2108.01513/) (2021)
- [Hyperbolic Busemann Learning with Ideal Prototypes](https://mlsanity.com/paper/2106.14472/) (2021)
- [SphereReID: Deep Hypersphere Manifold Embedding for Person Re-Identification](https://mlsanity.com/paper/1807.00537/) (2018)
- [SphereFace Revived: Unifying Hyperspherical Face Recognition](https://mlsanity.com/paper/2109.05565/) (2021)

## Built on by (most cited first, 3 of 3)

- [Entropy-Lens: Uncovering Decision Strategies in LLMs](https://mlsanity.com/paper/2502.16570/) (2025)
- [Sharpness-Aware Geometric Defense for Robust Out-Of-Distribution Detection](https://mlsanity.com/paper/2508.17174/) (2025)
- [ArcAD: Anomaly-Rectified Calibration for Cold-Start Supervised Anomaly Detection](https://mlsanity.com/paper/2607.02252/) (2026)

## Abstract (arXiv)

Detecting out-of-distribution (OOD) samples is crucial for trustworthy AI in real-world applications. Leveraging recent advances in representation learning and latent embeddings, Various scoring algorithms estimate distributions beyond the training data. However, a single embedding space falls short in characterizing in-distribution data and defending against diverse OOD conditions. This paper introduces a novel Multi-Manifold Embedding Learning (MMEL) framework, optimizing hypersphere and hyperbolic spaces jointly for enhanced OOD detection. MMEL generates representative embeddings and employs a prototype-aware scoring function to differentiate OOD samples. It operates with very few OOD samples and requires no model retraining. Experiments on six open datasets demonstrate MMEL's significant reduction in FPR while maintaining a high AUC compared to state-of-the-art distance-based OOD detection methods. We analyze the effects of learning multiple manifolds and visualize OOD score distributions across datasets. Notably, enrolling ten OOD samples without retraining achieves comparable FPR and AUC to modern outlier exposure methods using 80 million outlier samples for model training.