# Learning with Mixture of Prototypes for Out-of-Distribution Detection

arXiv: https://arxiv.org/abs/2402.02653 · HTML: https://mlsanity.com/paper/2402.02653/

## Key facts

- Cited by 43 papers in the map (data through 14 Oct 2026).
- Builds on 53 of its 68 references that are in the map.
- First posted on arXiv 5 Feb 2024.

## Builds on (most cited first, 30 of 53)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Prototypical Networks for Few-shot Learning](https://mlsanity.com/paper/1703.05175/) (2017)
- [Unsupervised Learning of Visual Features by Contrasting Cluster Assignments](https://mlsanity.com/paper/2006.09882/) (2020)
- [Supervised Contrastive Learning](https://mlsanity.com/paper/2004.11362/) (2020)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Describing Textures in the Wild](https://mlsanity.com/paper/1311.3618/) (2013)
- [Unsupervised Feature Learning via Non-Parametric Instance-level Discrimination](https://mlsanity.com/paper/1805.01978/) (2018)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks](https://mlsanity.com/paper/1807.03888/) (2018)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [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)
- [Contrastive Multiview Coding](https://mlsanity.com/paper/1906.05849/) (2019)
- [Energy-based Out-of-distribution Detection](https://mlsanity.com/paper/2010.03759/) (2020)
- [Deep Clustering for Unsupervised Learning of Visual Features](https://mlsanity.com/paper/1807.05520/) (2018)
- [Self-Supervised Learning of Pretext-Invariant Representations](https://mlsanity.com/paper/1912.01991/) (2019)
- [Generalized Out-of-Distribution Detection: A Survey](https://mlsanity.com/paper/2110.11334/) (2021)
- [Deep Neural Networks are Easily Fooled: High Confidence Predictions for Unrecognizable Images](https://mlsanity.com/paper/1412.1897/) (2014)
- [Prototypical Contrastive Learning of Unsupervised Representations](https://mlsanity.com/paper/2005.04966/) (2020)
- [Contrastive Learning with Hard Negative Samples](https://mlsanity.com/paper/2010.04592/) (2020)
- [Out-of-Distribution Detection with Deep Nearest Neighbors](https://mlsanity.com/paper/2204.06507/) (2022)
- [Memorizing Normality to Detect Anomaly: Memory-augmented Deep Autoencoder for Unsupervised Anomaly Detection](https://mlsanity.com/paper/1904.02639/) (2019)
- [Self-labelling via simultaneous clustering and representation learning](https://mlsanity.com/paper/1911.05371/) (2019)
- [ReAct: Out-of-distribution Detection With Rectified Activations](https://mlsanity.com/paper/2111.12797/) (2021)

## Built on by (most cited first, 30 of 43)

- [Out-of-Distribution Detection: A Task-Oriented Survey of Recent Advances](https://mlsanity.com/paper/2409.11884/) (2024)
- [Gradient-Regularized Out-of-Distribution Detection](https://mlsanity.com/paper/2404.12368/) (2024)
- [SeTAR: Out-of-Distribution Detection with Selective Low-Rank Approximation](https://mlsanity.com/paper/2406.12629/) (2024)
- [Compositional Generalization from Learned Skills via CoT Training: A Theoretical and Structural Analysis for Reasoning](https://mlsanity.com/paper/2502.04667/) (2025)
- [Energy-based Hopfield Boosting for Out-of-Distribution Detection](https://mlsanity.com/paper/2405.08766/) (2024)
- [CADRef: Robust Out-of-Distribution Detection via Class-Aware Decoupled Relative Feature Leveraging](https://mlsanity.com/paper/2503.00325/) (2025)
- [GDeR: Safeguarding Efficiency, Balancing, and Robustness via Prototypical Graph Pruning](https://mlsanity.com/paper/2410.13761/) (2024)
- [Memory-efficient Continual Learning with Neural Collapse Contrastive](https://mlsanity.com/paper/2412.02865/) (2024)
- [On the Discrimination and Consistency for Exemplar-Free Class Incremental Learning](https://mlsanity.com/paper/2501.15454/) (2025)
- [Adaptive Multi-prompt Contrastive Network for Few-shot Out-of-distribution Detection](https://mlsanity.com/paper/2506.17633/) (2025)
- [AdaSCALE: Adaptive Scaling for OOD Detection](https://mlsanity.com/paper/2503.08023/) (2025)
- [Continual Learning on CLIP via Incremental Prompt Tuning with Intrinsic Textual Anchors](https://mlsanity.com/paper/2505.20680/) (2025)
- [From Open Vocabulary to Open World: Teaching Vision Language Models to Detect Novel Objects](https://mlsanity.com/paper/2411.18207/) (2024)
- [Outlier Synthesis via Hamiltonian Monte Carlo for Out-of-Distribution Detection](https://mlsanity.com/paper/2501.16718/) (2025)
- [TIF: Learning Temporal Invariance in Android Malware Detectors](https://mlsanity.com/paper/2502.05098/) (2025)
- [Hierarchical Point-Patch Fusion with Adaptive Patch Codebook for 3D Shape Anomaly Detection](https://mlsanity.com/paper/2604.03972/) (2026)
- [Out-of-Distribution Detection with Attention Head Masking for Multimodal Document Classification](https://mlsanity.com/paper/2408.11237/) (2024)
- [Spurious-Aware Prototype Refinement for Reliable Out-of-Distribution Detection](https://mlsanity.com/paper/2506.23881/) (2025)
- [Activation Subspaces for Out-of-Distribution Detection](https://mlsanity.com/paper/2508.21695/) (2025)
- [Hypercone Assisted Contour Generation for Out-of-Distribution Detection](https://mlsanity.com/paper/2501.10209/) (2025)
- [Balanced Hyperbolic Embeddings Are Natural Out-of-Distribution Detectors](https://mlsanity.com/paper/2506.10146/) (2025)
- [An Empirical Analysis of VLM-based OOD Detection: Mechanisms, Advantages, and Sensitivity](https://mlsanity.com/paper/2509.13375/) (2025)
- [AP-OOD: Attention Pooling for Out-of-Distribution Detection](https://mlsanity.com/paper/2602.06031/) (2026)
- [MARVEL: Margin-Aware Robust von Mises-Fischer Expert Learning for Long-Tailed Out-of-Distribution Detection](https://mlsanity.com/paper/2607.02435/) (2026)
- [Probabilistic Contrastive Learning with Explicit Concentration on the Hypersphere](https://mlsanity.com/paper/2405.16460/) (2024)
- [Improving Explainability of Softmax Classifiers Using a Prototype-Based Joint Embedding Method](https://mlsanity.com/paper/2407.02271/) (2024)
- [Semantic or Covariate? A Study on the Intractable Case of Out-of-Distribution Detection](https://mlsanity.com/paper/2411.11254/) (2024)
- [Brain-inspired analogical mixture prototypes for few-shot class-incremental learning](https://mlsanity.com/paper/2502.18923/) (2025)
- [DIsoN: Decentralized Isolation Networks for Out-of-Distribution Detection in Medical Imaging](https://mlsanity.com/paper/2506.09024/) (2025)
- [Learning local and global prototypes with optimal transport for unsupervised anomaly detection and localization](https://mlsanity.com/paper/2508.12927/) (2025)

## Abstract (arXiv)

Out-of-distribution (OOD) detection aims to detect testing samples far away from the in-distribution (ID) training data, which is crucial for the safe deployment of machine learning models in the real world. Distance-based OOD detection methods have emerged with enhanced deep representation learning. They identify unseen OOD samples by measuring their distances from ID class centroids or prototypes. However, existing approaches learn the representation relying on oversimplified data assumptions, e.g, modeling ID data of each class with one centroid class prototype or using loss functions not designed for OOD detection, which overlook the natural diversities within the data. Naively enforcing data samples of each class to be compact around only one prototype leads to inadequate modeling of realistic data and limited performance. To tackle these issues, we propose PrototypicAl Learning with a Mixture of prototypes (PALM) which models each class with multiple prototypes to capture the sample diversities, and learns more faithful and compact samples embeddings to enhance OOD detection. Our method automatically identifies and dynamically updates prototypes, assigning each sample to a subset of prototypes via reciprocal neighbor soft assignment weights. PALM optimizes a maximum likelihood estimation (MLE) loss to encourage the sample embeddings to be compact around the associated prototypes, as well as a contrastive loss on all prototypes to enhance intra-class compactness and inter-class discrimination at the prototype level. Moreover, the automatic estimation of prototypes enables our approach to be extended to the challenging OOD detection task with unlabelled ID data. Extensive experiments demonstrate the superiority of PALM, achieving state-of-the-art average AUROC performance of 93.82 on the challenging CIFAR-100 benchmark. Code is available at https://github.com/jeff024/PALM.