# iDECODe: In-distribution Equivariance for Conformal Out-of-distribution Detection

arXiv: https://arxiv.org/abs/2201.02331 · HTML: https://mlsanity.com/paper/2201.02331/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- Builds on 43 of its 74 references that are in the map.
- First posted on arXiv 7 Jan 2022.

## Builds on (most cited first, 30 of 43)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [Adversarial examples in the physical world](https://mlsanity.com/paper/1607.02533/) (2016)
- [Unsupervised Representation Learning by Predicting Image Rotations](https://mlsanity.com/paper/1803.07728/) (2018)
- [A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks](https://mlsanity.com/paper/1807.03888/) (2018)
- [SpecAugment: A Simple Data Augmentation Method for Automatic Speech Recognition](https://mlsanity.com/paper/1904.08779/) (2019)
- [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)
- [DeepFool: a simple and accurate method to fool deep neural networks](https://mlsanity.com/paper/1511.04599/) (2015)
- [Energy-based Out-of-distribution Detection](https://mlsanity.com/paper/2010.03759/) (2020)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [End to End Learning for Self-Driving Cars](https://mlsanity.com/paper/1604.07316/) (2016)
- [Deep Anomaly Detection with Outlier Exposure](https://mlsanity.com/paper/1812.04606/) (2018)
- [Dynamic Routing Between Capsules](https://mlsanity.com/paper/1710.09829/) (2017)
- [Adversarial Examples Are Not Easily Detected: Bypassing Ten Detection Methods](https://mlsanity.com/paper/1705.07263/) (2017)
- [Using Self-Supervised Learning Can Improve Model Robustness and Uncertainty](https://mlsanity.com/paper/1906.12340/) (2019)
- [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)
- [Training Confidence-calibrated Classifiers for Detecting Out-of-Distribution Samples](https://mlsanity.com/paper/1711.09325/) (2017)
- [Deep Speech: Scaling up end-to-end speech recognition](https://mlsanity.com/paper/1412.5567/) (2014)
- [Characterizing Adversarial Subspaces Using Local Intrinsic Dimensionality](https://mlsanity.com/paper/1801.02613/) (2018)
- [Deep Anomaly Detection Using Geometric Transformations](https://mlsanity.com/paper/1805.10917/) (2018)
- [Detecting Adversarial Samples from Artifacts](https://mlsanity.com/paper/1703.00410/) (2017)
- [Classification-Based Anomaly Detection for General Data](https://mlsanity.com/paper/2005.02359/) (2020)
- [Deep k-Nearest Neighbors: Towards Confident, Interpretable and Robust Deep Learning](https://mlsanity.com/paper/1803.04765/) (2018)
- [To Trust Or Not To Trust A Classifier](https://mlsanity.com/paper/1805.11783/) (2018)
- [Testing for Outliers with Conformal p-values](https://mlsanity.com/paper/2104.08279/) (2021)
- [The Odds are Odd: A Statistical Test for Detecting Adversarial Examples](https://mlsanity.com/paper/1902.04818/) (2019)
- [Triplet-Center Loss for Multi-View 3D Object Retrieval](https://mlsanity.com/paper/1803.06189/) (2018)

## Built on by (most cited first, 27 of 27)

- [Conformal Prediction Under Feedback Covariate Shift for Biomolecular Design](https://mlsanity.com/paper/2202.03613/) (2022)
- [Conformal Prediction Regions for Time Series using Linear Complementarity Programming](https://mlsanity.com/paper/2304.01075/) (2023)
- [Addressing Uncertainty in LLMs to Enhance Reliability in Generative AI](https://mlsanity.com/paper/2411.02381/) (2024)
- [Memory-Consistent Neural Networks for Imitation Learning](https://mlsanity.com/paper/2310.06171/) (2023)
- [Conformal Inference under High-Dimensional Covariate Shifts via Likelihood-Ratio Regularization](https://mlsanity.com/paper/2502.13030/) (2025)
- [Targeted Adversarial Attacks against Neural Network Trajectory Predictors](https://mlsanity.com/paper/2212.04138/) (2022)
- [PAC-Wrap: Semi-Supervised PAC Anomaly Detection](https://mlsanity.com/paper/2205.10798/) (2022)
- [In What Ways Are Deep Neural Networks Invariant and How Should We Measure This?](https://mlsanity.com/paper/2210.03773/) (2022)
- [Certainty in Uncertainty: Reasoning over Uncertain Knowledge Graphs with Statistical Guarantees](https://mlsanity.com/paper/2510.24754/) (2025)
- [Adaptive Hierarchical Graph Cut for Multi-granularity Out-of-distribution Detection](https://mlsanity.com/paper/2412.15668/) (2024)
- [Boosting Out-of-Distribution Detection with Multiple Pre-trained Models](https://mlsanity.com/paper/2212.12720/) (2022)
- [Out-of-Distribution Detection Should Use Conformal Prediction (and Vice-versa?)](https://mlsanity.com/paper/2403.11532/) (2024)
- [Taming False Positives in Out-of-Distribution Detection with Human Feedback](https://mlsanity.com/paper/2404.16954/) (2024)
- [Conformal Information Pursuit for Interactively Guiding Large Language Models](https://mlsanity.com/paper/2507.03279/) (2025)
- [Neuro Symbolic Reasoning for Planning: Counterexample Guided Inductive Synthesis using Large Language Models and Satisfiability Solving](https://mlsanity.com/paper/2309.16436/) (2023)
- [Out-of-Distribution Data: An Acquaintance of Adversarial Examples -- A Survey](https://mlsanity.com/paper/2404.05219/) (2024)
- [Unilaterally Aggregated Contrastive Learning with Hierarchical Augmentation for Anomaly Detection](https://mlsanity.com/paper/2308.10155/) (2023)
- [Multi-Modal Conformal Prediction Regions with Simple Structures by Optimizing Convex Shape Templates](https://mlsanity.com/paper/2312.07434/) (2023)
- [Safety Monitoring for Learning-Enabled Cyber-Physical Systems in Out-of-Distribution Scenarios](https://mlsanity.com/paper/2504.13478/) (2025)
- [EquiReg: Equivariance Regularized Diffusion for Inverse Problems](https://mlsanity.com/paper/2505.22973/) (2025)
- [From Actions to Understanding: Conformal Interpretability of Temporal Concepts in LLM Agents](https://mlsanity.com/paper/2604.19775/) (2026)
- [Multiple Testing Framework for Out-of-Distribution Detection](https://mlsanity.com/paper/2206.09522/) (2022)
- [CODiT: Conformal Out-of-Distribution Detection in Time-Series Data](https://mlsanity.com/paper/2207.11769/) (2022)
- [Removing Geometric Bias in One-Class Anomaly Detection with Adaptive Feature Perturbation](https://mlsanity.com/paper/2503.05520/) (2025)
- [Detection of Adversarial Physical Attacks in Time-Series Image Data](https://mlsanity.com/paper/2304.13919/) (2023)
- [Neural Stochastic Differential Equations for Robust and Explainable Analysis of Electromagnetic Unintended Radiated Emissions](https://mlsanity.com/paper/2309.15386/) (2023)
- [Monitor and Recover: A Paradigm for Future Research on Distribution Shift in Learning-Enabled Cyber-Physical Systems](https://mlsanity.com/paper/2504.13484/) (2025)

## Abstract (arXiv)

Machine learning methods such as deep neural networks (DNNs), despite their success across different domains, are known to often generate incorrect predictions with high confidence on inputs outside their training distribution. The deployment of DNNs in safety-critical domains requires detection of out-of-distribution (OOD) data so that DNNs can abstain from making predictions on those. A number of methods have been recently developed for OOD detection, but there is still room for improvement. We propose the new method iDECODe, leveraging in-distribution equivariance for conformal OOD detection. It relies on a novel base non-conformity measure and a new aggregation method, used in the inductive conformal anomaly detection framework, thereby guaranteeing a bounded false detection rate. We demonstrate the efficacy of iDECODe by experiments on image and audio datasets, obtaining state-of-the-art results. We also show that iDECODe can detect adversarial examples.