# Adversarially Robust Out-of-Distribution Detection Using Lyapunov-Stabilized Embeddings

arXiv: https://arxiv.org/abs/2410.10744 · HTML: https://mlsanity.com/paper/2410.10744/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 88 of its 118 references that are in the map.
- First posted on arXiv 14 Oct 2024.

## Builds on (most cited first, 30 of 88)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Towards Evaluating the Robustness of Neural Networks](https://mlsanity.com/paper/1608.04644/) (2016)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [Describing Textures in the Wild](https://mlsanity.com/paper/1311.3618/) (2013)
- [Theoretically Principled Trade-off between Robustness and Accuracy](https://mlsanity.com/paper/1901.08573/) (2019)
- [A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks](https://mlsanity.com/paper/1807.03888/) (2018)
- [Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attacks](https://mlsanity.com/paper/2003.01690/) (2020)
- [LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loop](https://mlsanity.com/paper/1506.03365/) (2015)
- [Deep Anomaly Detection with Outlier Exposure](https://mlsanity.com/paper/1812.04606/) (2018)
- [Robustness May Be at Odds with Accuracy](https://mlsanity.com/paper/1805.12152/) (2018)
- [Ensemble Adversarial Training: Attacks and Defenses](https://mlsanity.com/paper/1705.07204/) (2017)
- [Generalized Out-of-Distribution Detection: A Survey](https://mlsanity.com/paper/2110.11334/) (2021)
- [The Limitations of Deep Learning in Adversarial Settings](https://mlsanity.com/paper/1511.07528/) (2015)
- [Square Attack: a query-efficient black-box adversarial attack via random search](https://mlsanity.com/paper/1912.00049/) (2019)
- [FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models](https://mlsanity.com/paper/1810.01367/) (2018)
- [Towards Open Set Deep Networks](https://mlsanity.com/paper/1511.06233/) (2015)
- [Diffusion Models for Adversarial Purification](https://mlsanity.com/paper/2205.07460/) (2022)
- [CSI: Novelty Detection via Contrastive Learning on Distributionally Shifted Instances](https://mlsanity.com/paper/2007.08176/) (2020)
- [Input Convex Neural Networks](https://mlsanity.com/paper/1609.07152/) (2016)
- [Augmented Neural ODEs](https://mlsanity.com/paper/1904.01681/) (2019)
- [Open-Set Recognition: a Good Closed-Set Classifier is All You Need?](https://mlsanity.com/paper/2110.06207/) (2021)
- [Minimally distorted Adversarial Examples with a Fast Adaptive Boundary Attack](https://mlsanity.com/paper/1907.02044/) (2019)

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

- [RODEO: Robust Outlier Detection via Exposing Adaptive Out-of-Distribution Samples](https://mlsanity.com/paper/2501.16971/) (2025)
- [Adaptive Intelligence: leveraging insights from adaptive behavior in animals to build flexible AI systems](https://mlsanity.com/paper/2411.15234/) (2024)
- [Killing it with Zero-Shot: Adversarially Robust Novelty Detection](https://mlsanity.com/paper/2501.15271/) (2025)
- [DISTIL: Data-Free Inversion of Suspicious Trojan Inputs via Latent Diffusion](https://mlsanity.com/paper/2507.22813/) (2025)
- [With Argus Eyes: Assessing Retrieval Gaps via Uncertainty Scoring to Detect and Remedy Retrieval Blind Spots](https://mlsanity.com/paper/2602.09616/) (2026)
- [Adversarially Robust Few-Shot Anomaly Detection with Vision Foundation Models](https://mlsanity.com/paper/2510.13643/) (2025)

## Abstract (arXiv)

Despite significant advancements in out-of-distribution (OOD) detection, existing methods still struggle to maintain robustness against adversarial attacks, compromising their reliability in critical real-world applications. Previous studies have attempted to address this challenge by exposing detectors to auxiliary OOD datasets alongside adversarial training. However, the increased data complexity inherent in adversarial training, and the myriad of ways that OOD samples can arise during testing, often prevent these approaches from establishing robust decision boundaries. To address these limitations, we propose AROS, a novel approach leveraging neural ordinary differential equations (NODEs) with Lyapunov stability theorem in order to obtain robust embeddings for OOD detection. By incorporating a tailored loss function, we apply Lyapunov stability theory to ensure that both in-distribution (ID) and OOD data converge to stable equilibrium points within the dynamical system. This approach encourages any perturbed input to return to its stable equilibrium, thereby enhancing the model's robustness against adversarial perturbations. To not use additional data, we generate fake OOD embeddings by sampling from low-likelihood regions of the ID data feature space, approximating the boundaries where OOD data are likely to reside. To then further enhance robustness, we propose the use of an orthogonal binary layer following the stable feature space, which maximizes the separation between the equilibrium points of ID and OOD samples. We validate our method through extensive experiments across several benchmarks, demonstrating superior performance, particularly under adversarial attacks. Notably, our approach improves robust detection performance from 37.8% to 80.1% on CIFAR-10 vs. CIFAR-100 and from 29.0% to 67.0% on CIFAR-100 vs. CIFAR-10.