# Out-of-distribution Detection and Generation using Soft Brownian Offset Sampling and Autoencoders

arXiv: https://arxiv.org/abs/2105.02965 · HTML: https://mlsanity.com/paper/2105.02965/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 45 references that are in the map.
- First posted on arXiv 4 May 2021.

## Builds on (most cited first, 22 of 22)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Concrete Problems in AI Safety](https://mlsanity.com/paper/1606.06565/) (2016)
- [Enhancing The Reliability of Out-of-distribution Image Detection in Neural Networks](https://mlsanity.com/paper/1706.02690/) (2017)
- [Deep Anomaly Detection with Outlier Exposure](https://mlsanity.com/paper/1812.04606/) (2018)
- [Predictive Uncertainty Estimation via Prior Networks](https://mlsanity.com/paper/1802.10501/) (2018)
- [Likelihood Ratios for Out-of-Distribution Detection](https://mlsanity.com/paper/1906.02845/) (2019)
- [Training Confidence-calibrated Classifiers for Detecting Out-of-Distribution Samples](https://mlsanity.com/paper/1711.09325/) (2017)
- [Reverse KL-Divergence Training of Prior Networks: Improved Uncertainty and Adversarial Robustness](https://mlsanity.com/paper/1905.13472/) (2019)
- [Robust Out-of-distribution Detection for Neural Networks](https://mlsanity.com/paper/2003.09711/) (2020)
- [Out-of-distribution Detection in Classifiers via Generation](https://mlsanity.com/paper/1910.04241/) (2019)
- [Inspect, Understand, Overcome: A Survey of Practical Methods for AI Safety](https://mlsanity.com/paper/2104.14235/) (2021)
- [Learning Flat Latent Manifolds with VAEs](https://mlsanity.com/paper/2002.04881/) (2020)
- [An Application-Driven Conceptualization of Corner Cases for Perception in Highly Automated Driving](https://mlsanity.com/paper/2103.03678/) (2021)
- [Building robust classifiers through generation of confident out of distribution examples](https://mlsanity.com/paper/1812.00239/) (2018)
- [Detecting Intentions of Vulnerable Road Users Based on Collective Intelligence](https://mlsanity.com/paper/1809.03916/) (2018)
- [Relation between the Kantorovich-Wasserstein metric and the Kullback-Leibler divergence](https://mlsanity.com/paper/1908.09211/) (2019)
- [A Joint Model for IT Operation Series Prediction and Anomaly Detection](https://mlsanity.com/paper/1910.03818/) (2019)

## Built on by (most cited first, 8 of 8)

- [Description of Corner Cases in Automated Driving: Goals and Challenges](https://mlsanity.com/paper/2109.09607/) (2021)
- [Out-of-Distribution Generalization in Time Series: A Survey](https://mlsanity.com/paper/2503.13868/) (2025)
- [Image Background Serves as Good Proxy for Out-of-distribution Data](https://mlsanity.com/paper/2307.00519/) (2023)
- [Delay-SDE-net: A deep learning approach for time series modelling with memory and uncertainty estimates](https://mlsanity.com/paper/2303.08587/) (2023)
- [Contrastive Novelty-Augmented Learning: Anticipating Outliers with Large Language Models](https://mlsanity.com/paper/2211.15718/) (2022)
- [Free Lunch for Generating Effective Outlier Supervision](https://mlsanity.com/paper/2301.06657/) (2023)
- [A Priori Uncertainty Quantification of Reacting Turbulence Closure Models using Bayesian Neural Networks](https://mlsanity.com/paper/2402.18729/) (2024)
- [Cross-Machine Anomaly Detection Leveraging Pre-trained Time-series Model](https://mlsanity.com/paper/2604.05335/) (2026)

## Abstract (arXiv)

Deep neural networks often suffer from overconfidence which can be partly remedied by improved out-of-distribution detection. For this purpose, we propose a novel approach that allows for the generation of out-of-distribution datasets based on a given in-distribution dataset. This new dataset can then be used to improve out-of-distribution detection for the given dataset and machine learning task at hand. The samples in this dataset are with respect to the feature space close to the in-distribution dataset and therefore realistic and plausible. Hence, this dataset can also be used to safeguard neural networks, i.e., to validate the generalization performance. Our approach first generates suitable representations of an in-distribution dataset using an autoencoder and then transforms them using our novel proposed Soft Brownian Offset method. After transformation, the decoder part of the autoencoder allows for the generation of these implicit out-of-distribution samples. This newly generated dataset then allows for mixing with other datasets and thus improved training of an out-of-distribution classifier, increasing its performance. Experimentally, we show that our approach is promising for time series using synthetic data. Using our new method, we also show in a quantitative case study that we can improve the out-of-distribution detection for the MNIST dataset. Finally, we provide another case study on the synthetic generation of out-of-distribution trajectories, which can be used to validate trajectory prediction algorithms for automated driving.