# Your Classifier Can Be Secretly a Likelihood-Based OOD Detector

arXiv: https://arxiv.org/abs/2408.04851 · HTML: https://mlsanity.com/paper/2408.04851/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 73 of its 94 references that are in the map.
- First posted on arXiv 9 Aug 2024.

## Builds on (most cited first, 30 of 73)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Supervised Contrastive Learning](https://mlsanity.com/paper/2004.11362/) (2020)
- [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)
- [Concrete Problems in AI Safety](https://mlsanity.com/paper/1606.06565/) (2016)
- [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)
- [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)
- [Deep Anomaly Detection with Outlier Exposure](https://mlsanity.com/paper/1812.04606/) (2018)
- [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)
- [Predictive Uncertainty Estimation via Prior Networks](https://mlsanity.com/paper/1802.10501/) (2018)
- [ReAct: Out-of-distribution Detection With Rectified Activations](https://mlsanity.com/paper/2111.12797/) (2021)
- [Likelihood Ratios for Out-of-Distribution Detection](https://mlsanity.com/paper/1906.02845/) (2019)
- [Do Deep Generative Models Know What They Don't Know?](https://mlsanity.com/paper/1810.09136/) (2018)
- [CSI: Novelty Detection via Contrastive Learning on Distributionally Shifted Instances](https://mlsanity.com/paper/2007.08176/) (2020)
- [ViM: Out-Of-Distribution with Virtual-logit Matching](https://mlsanity.com/paper/2203.10807/) (2022)
- [Training Confidence-calibrated Classifiers for Detecting Out-of-Distribution Samples](https://mlsanity.com/paper/1711.09325/) (2017)
- [Open-Set Recognition: a Good Closed-Set Classifier is All You Need?](https://mlsanity.com/paper/2110.06207/) (2021)
- [SelectiveNet: A Deep Neural Network with an Integrated Reject Option](https://mlsanity.com/paper/1901.09192/) (2019)
- [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)
- [VOS: Learning What You Don't Know by Virtual Outlier Synthesis](https://mlsanity.com/paper/2202.01197/) (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)
- [Why Normalizing Flows Fail to Detect Out-of-Distribution Data](https://mlsanity.com/paper/2006.08545/) (2020)
- [Delving into Out-of-Distribution Detection with Vision-Language Representations](https://mlsanity.com/paper/2211.13445/) (2022)

## Built on by (most cited first, 4 of 4)

- [Process Reward Model with Q-Value Rankings](https://mlsanity.com/paper/2410.11287/) (2024)
- [Enhancing Out-of-Distribution Detection with Extended Logit Normalization](https://mlsanity.com/paper/2504.11434/) (2025)
- [Energy-Guided Decoding for Object Hallucination Mitigation](https://mlsanity.com/paper/2507.07731/) (2025)
- [Learning Hyperspherical Time-Frequency Representations for Time-Series Out-of-Distribution Detection](https://mlsanity.com/paper/2605.31155/) (2026)

## Abstract (arXiv)

The ability to detect out-of-distribution (OOD) inputs is critical to guarantee the reliability of classification models deployed in an open environment. A fundamental challenge in OOD detection is that a discriminative classifier is typically trained to estimate the posterior probability p(y|z) for class y given an input z, but lacks the explicit likelihood estimation of p(z) ideally needed for OOD detection. While numerous OOD scoring functions have been proposed for classification models, these estimate scores are often heuristic-driven and cannot be rigorously interpreted as likelihood. To bridge the gap, we propose Intrinsic Likelihood (INK), which offers rigorous likelihood interpretation to modern discriminative-based classifiers. Specifically, our proposed INK score operates on the constrained latent embeddings of a discriminative classifier, which are modeled as a mixture of hyperspherical embeddings with constant norm. We draw a novel connection between the hyperspherical distribution and the intrinsic likelihood, which can be effectively optimized in modern neural networks. Extensive experiments on the OpenOOD benchmark empirically demonstrate that INK establishes a new state-of-the-art in a variety of OOD detection setups, including both far-OOD and near-OOD. Code is available at https://github.com/deeplearning-wisc/ink.