# Improving Out-of-Distribution Detection with Markov Logic Networks

arXiv: https://arxiv.org/abs/2506.04241 · HTML: https://mlsanity.com/paper/2506.04241/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 37 references that are in the map.
- First posted on arXiv 28 May 2025.

## Builds on (most cited first, 27 of 27)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [A ConvNet for the 2020s](https://mlsanity.com/paper/2201.03545/) (2022)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [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)
- [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)
- [Deep Neural Networks are Easily Fooled: High Confidence Predictions for Unrecognizable Images](https://mlsanity.com/paper/1412.1897/) (2014)
- [Deep Learning in Neural Networks: An Overview](https://mlsanity.com/paper/1404.7828/) (2014)
- [ReAct: Out-of-distribution Detection With Rectified Activations](https://mlsanity.com/paper/2111.12797/) (2021)
- [Scaling Out-of-Distribution Detection for Real-World Settings](https://mlsanity.com/paper/1911.11132/) (2019)
- [ViM: Out-Of-Distribution with Virtual-logit Matching](https://mlsanity.com/paper/2203.10807/) (2022)
- [Extremely Simple Activation Shaping for Out-of-Distribution Detection](https://mlsanity.com/paper/2209.09858/) (2022)
- [Neural-Symbolic Learning and Reasoning: A Survey and Interpretation](https://mlsanity.com/paper/1711.03902/) (2017)
- [Reducing Network Agnostophobia](https://mlsanity.com/paper/1811.04110/) (2018)
- [Nondeterminism and Instability in Neural Network Optimization](https://mlsanity.com/paper/2103.04514/) (2021)
- [Out-of-Distribution Detection: A Task-Oriented Survey of Recent Advances](https://mlsanity.com/paper/2409.11884/) (2024)

## Abstract (arXiv)

Out-of-distribution (OOD) detection is essential for ensuring the reliability of deep learning models operating in open-world scenarios. Current OOD detectors mainly rely on statistical models to identify unusual patterns in the latent representations of a deep neural network. This work proposes to augment existing OOD detectors with probabilistic reasoning, utilizing Markov logic networks (MLNs). MLNs connect first-order logic with probabilistic reasoning to assign probabilities to inputs based on weighted logical constraints defined over human-understandable concepts, which offers improved explainability. Through extensive experiments on multiple datasets, we demonstrate that MLNs can significantly enhance the performance of a wide range of existing OOD detectors while maintaining computational efficiency. Furthermore, we introduce a simple algorithm for learning logical constraints for OOD detection from a dataset and showcase its effectiveness.