# Beyond Empirical Support: Structured Outlier Generation via Sinkhorn Optimal Transport

arXiv: https://arxiv.org/abs/2609.31470 · HTML: https://mlsanity.com/paper/2609.31470/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 51 of its 73 references that are in the map.
- First posted on arXiv 25 Sep 2026.

## Builds on (most cited first, 30 of 51)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Describing Textures in the Wild](https://mlsanity.com/paper/1311.3618/) (2013)
- [LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loop](https://mlsanity.com/paper/1506.03365/) (2015)
- [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)
- [Prevalence of Neural Collapse during the terminal phase of deep learning training](https://mlsanity.com/paper/2008.08186/) (2020)
- [TS2Vec: Towards Universal Representation of Time Series](https://mlsanity.com/paper/2106.10466/) (2021)
- [Detecting Spacecraft Anomalies Using LSTMs and Nonparametric Dynamic Thresholding](https://mlsanity.com/paper/1802.04431/) (2018)
- [Anomaly Transformer: Time Series Anomaly Detection with Association Discrepancy](https://mlsanity.com/paper/2110.02642/) (2021)
- [Training Confidence-calibrated Classifiers for Detecting Out-of-Distribution Samples](https://mlsanity.com/paper/1711.09325/) (2017)
- [Certifying Some Distributional Robustness with Principled Adversarial Training](https://mlsanity.com/paper/1710.10571/) (2017)
- [Learning Models with Uniform Performance via Distributionally Robust Optimization](https://mlsanity.com/paper/1810.08750/) (2018)
- [Deep Semi-Supervised Anomaly Detection](https://mlsanity.com/paper/1906.02694/) (2019)
- [MOS: Towards Scaling Out-of-distribution Detection for Large Semantic Space](https://mlsanity.com/paper/2105.01879/) (2021)
- [TranAD: Deep Transformer Networks for Anomaly Detection in Multivariate Time Series Data](https://mlsanity.com/paper/2201.07284/) (2022)
- [TurkerGaze: Crowdsourcing Saliency with Webcam based Eye Tracking](https://mlsanity.com/paper/1504.06755/) (2015)
- [Deep Anomaly Detection with Deviation Networks](https://mlsanity.com/paper/1911.08623/) (2019)
- [On Feature Learning in the Presence of Spurious Correlations](https://mlsanity.com/paper/2210.11369/) (2022)
- [Deep Learning for Time Series Anomaly Detection: A Survey](https://mlsanity.com/paper/2211.05244/) (2022)
- [Non-Parametric Outlier Synthesis](https://mlsanity.com/paper/2303.02966/) (2023)
- [DCdetector: Dual Attention Contrastive Representation Learning for Time Series Anomaly Detection](https://mlsanity.com/paper/2306.10347/) (2023)
- [Towards a Rigorous Evaluation of Time-series Anomaly Detection](https://mlsanity.com/paper/2109.05257/) (2021)
- [CATCH: Channel-Aware multivariate Time Series Anomaly Detection via Frequency Patching](https://mlsanity.com/paper/2410.12261/) (2024)
- [Regularization via Mass Transportation](https://mlsanity.com/paper/1710.10016/) (2017)
- [Dream the Impossible: Outlier Imagination with Diffusion Models](https://mlsanity.com/paper/2309.13415/) (2023)
- [An Evaluation of Anomaly Detection and Diagnosis in Multivariate Time Series](https://mlsanity.com/paper/2109.11428/) (2021)
- [Examining and Combating Spurious Features under Distribution Shift](https://mlsanity.com/paper/2106.07171/) (2021)
- [Neural Contextual Anomaly Detection for Time Series](https://mlsanity.com/paper/2107.07702/) (2021)
- [Calibrated One-class Classification for Unsupervised Time Series Anomaly Detection](https://mlsanity.com/paper/2207.12201/) (2022)

## Abstract (arXiv)

Outliers are essential for evaluating and improving the robustness of machine learning systems, especially when future distributions may differ significantly from historical training data. In high-stakes applications, robustness often depends on rare cases that finite datasets fail to capture, making simple resampling or perturbation insufficient for stress scenario generation. Existing outlier synthesis methods typically rely on sparse neighborhoods, low support latent regions, or classifier boundary crossings, which can be heuristic, unstable, and tied to specific modalities or architectures. We therefore propose Sinkhorn Boundary Outlier Generation (SBOG), a structured framework for latent-space outlier generation that couples Sinkhorn optimal transport geometry with distributionally robust boundary modeling. The resulting Sinkhorn-induced support cost guides the sampler toward weakly supported boundary regions, while semantic constraints prevent uncontrolled drift from the intended context, yielding controlled deviations from the in-distribution reference measure rather than arbitrary sparse-region samples. Experiments on time series anomaly generation and image outlier synthesis show that our framework produces informative, semantically controlled outliers and improves downstream robustness evaluation across modalities, providing a foundation for stress scenario generation beyond empirical support.