# Efficient Out-of-Distribution Detection Using Latent Space of β-VAE for Cyber-Physical Systems

arXiv: https://arxiv.org/abs/2108.11800 · HTML: https://mlsanity.com/paper/2108.11800/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 85 references that are in the map.
- First posted on arXiv 26 Aug 2021.

## Builds on (most cited first, 30 of 37)

- [nuScenes: A multimodal dataset for autonomous driving](https://mlsanity.com/paper/1903.11027/) (2019)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [CARLA: An Open Urban Driving Simulator](https://mlsanity.com/paper/1711.03938/) (2017)
- [Learning Transferable Features with Deep Adaptation Networks](https://mlsanity.com/paper/1502.02791/) (2015)
- [End to End Learning for Self-Driving Cars](https://mlsanity.com/paper/1604.07316/) (2016)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [Disentangling by Factorising](https://mlsanity.com/paper/1802.05983/) (2018)
- [Generative Adversarial Networks: An Overview](https://mlsanity.com/paper/1710.07035/) (2017)
- [Generalizing to Unseen Domains via Adversarial Data Augmentation](https://mlsanity.com/paper/1805.12018/) (2018)
- [GANomaly: Semi-Supervised Anomaly Detection via Adversarial Training](https://mlsanity.com/paper/1805.06725/) (2018)
- [Adversarial Autoencoders](https://mlsanity.com/paper/1511.05644/) (2015)
- [DeepXplore: Automated Whitebox Testing of Deep Learning Systems](https://mlsanity.com/paper/1705.06640/) (2017)
- [DeepTest: Automated Testing of Deep-Neural-Network-driven Autonomous Cars](https://mlsanity.com/paper/1708.08559/) (2017)
- [Learning Confidence for Out-of-Distribution Detection in Neural Networks](https://mlsanity.com/paper/1802.04865/) (2018)
- [Characterizing and Avoiding Negative Transfer](https://mlsanity.com/paper/1811.09751/) (2018)
- [Efficient GAN-Based Anomaly Detection](https://mlsanity.com/paper/1802.06222/) (2018)
- [Learning to Decompose and Disentangle Representations for Video Prediction](https://mlsanity.com/paper/1806.04166/) (2018)
- [Bias-Reduced Uncertainty Estimation for Deep Neural Classifiers](https://mlsanity.com/paper/1805.08206/) (2018)
- [Adversarial Variational Bayes: Unifying Variational Autoencoders and Generative Adversarial Networks](https://mlsanity.com/paper/1701.04722/) (2017)
- [Scenic: A Language for Scenario Specification and Scene Generation](https://mlsanity.com/paper/1809.09310/) (2018)
- [Improving Reconstruction Autoencoder Out-of-distribution Detection with Mahalanobis Distance](https://mlsanity.com/paper/1812.02765/) (2018)
- [Learning Latent Subspaces in Variational Autoencoders](https://mlsanity.com/paper/1812.06190/) (2018)
- [Real-time Out-of-distribution Detection in Learning-Enabled Cyber-Physical Systems](https://mlsanity.com/paper/2001.10494/) (2020)
- [Robust Anomaly Detection in Images using Adversarial Autoencoders](https://mlsanity.com/paper/1901.06355/) (2019)
- [q-Space Novelty Detection with Variational Autoencoders](https://mlsanity.com/paper/1806.02997/) (2018)
- [Reconstruction-Based Disentanglement for Pose-invariant Face Recognition](https://mlsanity.com/paper/1702.03041/) (2017)
- [Anomaly Detection with Adversarial Dual Autoencoders](https://mlsanity.com/paper/1902.06924/) (2019)

## Built on by (most cited first, 19 of 19)

- [Out-of-Distribution Generalization in Time Series: A Survey](https://mlsanity.com/paper/2503.13868/) (2025)
- [Risk-Aware Scene Sampling for Dynamic Assurance of Autonomous Systems](https://mlsanity.com/paper/2202.13510/) (2022)
- [Design Methodology for Deep Out-of-Distribution Detectors in Real-Time Cyber-Physical Systems](https://mlsanity.com/paper/2207.14694/) (2022)
- [Out-of-Distribution Detection for Neurosymbolic Autonomous Cyber Agents](https://mlsanity.com/paper/2412.02875/) (2024)
- [Safety Monitoring for Learning-Enabled Cyber-Physical Systems in Out-of-Distribution Scenarios](https://mlsanity.com/paper/2504.13478/) (2025)
- [CODiT: Conformal Out-of-Distribution Detection in Time-Series Data](https://mlsanity.com/paper/2207.11769/) (2022)
- [Out of Distribution Reasoning by Weakly-Supervised Disentangled Logic Variational Autoencoder](https://mlsanity.com/paper/2210.09959/) (2022)
- [Edge Case Detection in Automated Driving: Methods, Challenges, and Future Directions](https://mlsanity.com/paper/2410.08491/) (2024)
- [Out-of-Distribution Detection for Safety Assurance of AI and Autonomous Systems](https://mlsanity.com/paper/2510.21254/) (2025)
- [nuScenes Revisited: Progress and Challenges in Autonomous Driving](https://mlsanity.com/paper/2512.02448/) (2025)
- [PAC-Based Formal Verification for Out-of-Distribution Data Detection](https://mlsanity.com/paper/2304.01592/) (2023)
- [Co-Design of Out-of-Distribution Detectors for Autonomous Emergency Braking Systems](https://mlsanity.com/paper/2307.13419/) (2023)
- [Improving the Resilience of Quadrotors in Underground Environments by Combining Learning-based and Safety Controllers](https://mlsanity.com/paper/2509.02808/) (2025)
- [Compressing VAE-Based Out-of-Distribution Detectors for Embedded Deployment](https://mlsanity.com/paper/2409.00880/) (2024)
- [Out of Distribution Detection for Efficient Continual Learning in Quality Prediction for Arc Welding](https://mlsanity.com/paper/2508.16832/) (2025)
- [On Uniformly Scaling Flows: A Density-Aligned Approach to Deep One-Class Classification](https://mlsanity.com/paper/2510.09452/) (2025)
- [Disentangled and Distilled Encoder for Out-of-Distribution Reasoning with Rademacher Guarantees](https://mlsanity.com/paper/2512.10522/) (2025)
- [Unsupervised Anomaly Detection in NSL-KDD Using β-VAE: A Latent Space and Reconstruction Error Approach](https://mlsanity.com/paper/2602.19785/) (2026)
- [An Information Theoretic Framework for Graph Novelty Generation via Latent Mixture Modeling](https://mlsanity.com/paper/2606.19770/) (2026)

## Abstract (arXiv)

Deep Neural Networks are actively being used in the design of autonomous Cyber-Physical Systems (CPSs). The advantage of these models is their ability to handle high-dimensional state-space and learn compact surrogate representations of the operational state spaces. However, the problem is that the sampled observations used for training the model may never cover the entire state space of the physical environment, and as a result, the system will likely operate in conditions that do not belong to the training distribution. These conditions that do not belong to training distribution are referred to as Out-of-Distribution (OOD). Detecting OOD conditions at runtime is critical for the safety of CPS. In addition, it is also desirable to identify the context or the feature(s) that are the source of OOD to select an appropriate control action to mitigate the consequences that may arise because of the OOD condition. In this paper, we study this problem as a multi-labeled time series OOD detection problem over images, where the OOD is defined both sequentially across short time windows (change points) as well as across the training data distribution. A common approach to solving this problem is the use of multi-chained one-class classifiers. However, this approach is expensive for CPSs that have limited computational resources and require short inference times. Our contribution is an approach to design and train a single β-Variational Autoencoder detector with a partially disentangled latent space sensitive to variations in image features. We use the feature sensitive latent variables in the latent space to detect OOD images and identify the most likely feature(s) responsible for the OOD. We demonstrate our approach using an Autonomous Vehicle in the CARLA simulator and a real-world automotive dataset called nuImages.