# Learning with Adaptive Prototype Manifolds for Out-of-Distribution Detection

arXiv: https://arxiv.org/abs/2602.05349 · HTML: https://mlsanity.com/paper/2602.05349/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 31 of its 45 references that are in the map.
- First posted on arXiv 5 Feb 2026.

## Builds on (most cited first, 30 of 31)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Prototypical Networks for Few-shot Learning](https://mlsanity.com/paper/1703.05175/) (2017)
- [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)
- [Describing Textures in the Wild](https://mlsanity.com/paper/1311.3618/) (2013)
- [Concrete Problems in AI Safety](https://mlsanity.com/paper/1606.06565/) (2016)
- [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)
- [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)
- [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)
- [Your Classifier is Secretly an Energy Based Model and You Should Treat it Like One](https://mlsanity.com/paper/1912.03263/) (2019)
- [ViM: Out-Of-Distribution with Virtual-logit Matching](https://mlsanity.com/paper/2203.10807/) (2022)
- [Understanding the Behaviour of Contrastive Loss](https://mlsanity.com/paper/2012.09740/) (2020)
- [On the Importance of Gradients for Detecting Distributional Shifts in the Wild](https://mlsanity.com/paper/2110.00218/) (2021)
- [Why ReLU networks yield high-confidence predictions far away from the training data and how to mitigate the problem](https://mlsanity.com/paper/1812.05720/) (2018)
- [SSD: A Unified Framework for Self-Supervised Outlier Detection](https://mlsanity.com/paper/2103.12051/) (2021)
- [TurkerGaze: Crowdsourcing Saliency with Webcam based Eye Tracking](https://mlsanity.com/paper/1504.06755/) (2015)
- [Non-Parametric Outlier Synthesis](https://mlsanity.com/paper/2303.02966/) (2023)
- [How to Exploit Hyperspherical Embeddings for Out-of-Distribution Detection?](https://mlsanity.com/paper/2203.04450/) (2022)
- [Energy-Based Open-World Uncertainty Modeling for Confidence Calibration](https://mlsanity.com/paper/2107.12628/) (2021)
- [Raising the Bar in Graph OOD Generalization: Invariant Learning Beyond Explicit Environment Modeling](https://mlsanity.com/paper/2502.10706/) (2025)
- [Out-of-Distribution Detection with Prototypical Outlier Proxy](https://mlsanity.com/paper/2412.16884/) (2024)

## Abstract (arXiv)

Out-of-distribution (OOD) detection is a critical task for the safe deployment of machine learning models in the real world. Existing prototype-based representation learning methods have demonstrated exceptional performance. Specifically, we identify two fundamental flaws that universally constrain these methods: the Static Homogeneity Assumption (fixed representational resources for all classes) and the Learning-Inference Disconnect (discarding rich prototype quality knowledge at inference). These flaws fundamentally limit the model's capacity and performance. To address these issues, we propose APEX (Adaptive Prototype for eXtensive OOD Detection), a novel OOD detection framework designed via a Two-Stage Repair process to optimize the learned feature manifold. APEX introduces two key innovations to address these respective flaws: (1) an Adaptive Prototype Manifold (APM), which leverages the Minimum Description Length (MDL) principle to automatically determine the optimal prototype complexity Kc^* for each class, thereby fundamentally resolving prototype collision; and (2) a Posterior-Aware OOD Scoring (PAOS) mechanism, which quantifies prototype quality (cohesion and separation) to bridge the learning-inference disconnect. Comprehensive experiments on benchmarks such as CIFAR-100 validate the superiority of our method, where APEX achieves new state-of-the-art performance.