# Boundary of Distribution Support Generator (BDSG): Sample Generation on the Boundary

arXiv: https://arxiv.org/abs/2107.09950 · HTML: https://mlsanity.com/paper/2107.09950/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 24 references that are in the map.
- First posted on arXiv 21 Jul 2021.

## Builds on (most cited first, 16 of 16)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [Deep Anomaly Detection with Outlier Exposure](https://mlsanity.com/paper/1812.04606/) (2018)
- [Unsupervised Anomaly Detection with Generative Adversarial Networks to Guide Marker Discovery](https://mlsanity.com/paper/1703.05921/) (2017)
- [Memorizing Normality to Detect Anomaly: Memory-augmented Deep Autoencoder for Unsupervised Anomaly Detection](https://mlsanity.com/paper/1904.02639/) (2019)
- [Do Deep Generative Models Know What They Don't Know?](https://mlsanity.com/paper/1810.09136/) (2018)
- [Invertible Residual Networks](https://mlsanity.com/paper/1811.00995/) (2018)
- [Residual Flows for Invertible Generative Modeling](https://mlsanity.com/paper/1906.02735/) (2019)
- [Efficient GAN-Based Anomaly Detection](https://mlsanity.com/paper/1802.06222/) (2018)
- [Skip-GANomaly: Skip Connected and Adversarially Trained Encoder-Decoder Anomaly Detection](https://mlsanity.com/paper/1901.08954/) (2019)
- [Fence GAN: Towards Better Anomaly Detection](https://mlsanity.com/paper/1904.01209/) (2019)
- [Boundary-Seeking Generative Adversarial Networks](https://mlsanity.com/paper/1702.08431/) (2017)
- [Anomaly Detection via Minimum Likelihood Generative Adversarial Networks](https://mlsanity.com/paper/1808.00200/) (2018)
- [Fictitious GAN: Training GANs with Historical Models](https://mlsanity.com/paper/1803.08647/) (2018)
- [Anomaly detection with Wasserstein GAN](https://mlsanity.com/paper/1812.02463/) (2018)
- [Anomaly Detection for imbalanced datasets with Deep Generative Models](https://mlsanity.com/paper/1811.00986/) (2018)

## Built on by (most cited first, 6 of 6)

- [Video Anomaly Detection via Spatio-Temporal Pseudo-Anomaly Generation : A Unified Approach](https://mlsanity.com/paper/2311.16514/) (2023)
- [Tail of Distribution GAN (TailGAN): Generative-Adversarial-Network-Based Boundary Formation](https://mlsanity.com/paper/2107.11658/) (2021)
- [OMASGAN: Out-of-Distribution Minimum Anomaly Score GAN for Sample Generation on the Boundary](https://mlsanity.com/paper/2110.15273/) (2021)
- [FROB: Few-shot ROBust Model for Classification and Out-of-Distribution Detection](https://mlsanity.com/paper/2111.15487/) (2021)
- [Targeted Augmented Data for Audio Deepfake Detection](https://mlsanity.com/paper/2407.07598/) (2024)
- [CARE: Confidence-Aware Regression Estimation of building density fine-tuning EO Foundation Models](https://mlsanity.com/paper/2502.13734/) (2025)

## Abstract (arXiv)

Generative models, such as Generative Adversarial Networks (GANs), have been used for unsupervised anomaly detection. While performance keeps improving, several limitations exist particularly attributed to difficulties at capturing multimodal supports and to the ability to approximate the underlying distribution closer to the tails, i.e. the boundary of the distribution's support. This paper proposes an approach that attempts to alleviate such shortcomings. We propose an invertible-residual-network-based model, the Boundary of Distribution Support Generator (BDSG). GANs generally do not guarantee the existence of a probability distribution and here, we use the recently developed Invertible Residual Network (IResNet) and Residual Flow (ResFlow), for density estimation. These models have not yet been used for anomaly detection. We leverage IResNet and ResFlow for Out-of-Distribution (OoD) sample detection and for sample generation on the boundary using a compound loss function that forces the samples to lie on the boundary. The BDSG addresses non-convex support, disjoint components, and multimodal distributions. Results on synthetic data and data from multimodal distributions, such as MNIST and CIFAR-10, demonstrate competitive performance compared to methods from the literature.