# Fortifying Time Series: DTW-Certified Robust Anomaly Detection

arXiv: https://arxiv.org/abs/2605.07690 · HTML: https://mlsanity.com/paper/2605.07690/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 70 references that are in the map.
- First posted on arXiv 8 May 2026.

## Builds on (most cited first, 30 of 36)

- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Towards Evaluating the Robustness of Neural Networks](https://mlsanity.com/paper/1608.04644/) (2016)
- [Certified Adversarial Robustness via Randomized Smoothing](https://mlsanity.com/paper/1902.02918/) (2019)
- [TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis](https://mlsanity.com/paper/2210.02186/) (2022)
- [Distillation as a Defense to Adversarial Perturbations against Deep Neural Networks](https://mlsanity.com/paper/1511.04508/) (2015)
- [Certified Robustness to Adversarial Examples with Differential Privacy](https://mlsanity.com/paper/1802.03471/) (2018)
- [Threat of Adversarial Attacks on Deep Learning in Computer Vision: A Survey](https://mlsanity.com/paper/1801.00553/) (2018)
- [On Evaluating Adversarial Robustness](https://mlsanity.com/paper/1902.06705/) (2019)
- [Detecting Spacecraft Anomalies Using LSTMs and Nonparametric Dynamic Thresholding](https://mlsanity.com/paper/1802.04431/) (2018)
- [Provably Robust Deep Learning via Adversarially Trained Smoothed Classifiers](https://mlsanity.com/paper/1906.04584/) (2019)
- [Multitask learning and benchmarking with clinical time series data](https://mlsanity.com/paper/1703.07771/) (2017)
- [Scalable and accurate deep learning for electronic health records](https://mlsanity.com/paper/1801.07860/) (2018)
- [Adversarial Attacks and Defences: A Survey](https://mlsanity.com/paper/1810.00069/) (2018)
- [Certified Adversarial Robustness with Additive Noise](https://mlsanity.com/paper/1809.03113/) (2018)
- [Time-Series Anomaly Detection Service at Microsoft](https://mlsanity.com/paper/1906.03821/) (2019)
- [Are Labels Required for Improving Adversarial Robustness?](https://mlsanity.com/paper/1905.13725/) (2019)
- [Current Time Series Anomaly Detection Benchmarks are Flawed and are Creating the Illusion of Progress](https://mlsanity.com/paper/2009.13807/) (2020)
- [Randomized Smoothing of All Shapes and Sizes](https://mlsanity.com/paper/2002.08118/) (2020)
- [Perceptual Adversarial Robustness: Defense Against Unseen Threat Models](https://mlsanity.com/paper/2006.12655/) (2020)
- [Advances in adversarial attacks and defenses in computer vision: A survey](https://mlsanity.com/paper/2108.00401/) (2021)
- [Adversarial Distributional Training for Robust Deep Learning](https://mlsanity.com/paper/2002.05999/) (2020)
- [Detection as Regression: Certified Object Detection by Median Smoothing](https://mlsanity.com/paper/2007.03730/) (2020)
- [Boosting Randomized Smoothing with Variance Reduced Classifiers](https://mlsanity.com/paper/2106.06946/) (2021)
- [A Survey of Robust Adversarial Training in Pattern Recognition: Fundamental, Theory, and Methodologies](https://mlsanity.com/paper/2203.14046/) (2022)
- [Calibrated One-class Classification for Unsupervised Time Series Anomaly Detection](https://mlsanity.com/paper/2207.12201/) (2022)
- [Optimism in the Face of Adversity: Understanding and Improving Deep Learning through Adversarial Robustness](https://mlsanity.com/paper/2010.09624/) (2020)
- [Automated Discovery of Adaptive Attacks on Adversarial Defenses](https://mlsanity.com/paper/2102.11860/) (2021)
- [Defenses in Adversarial Machine Learning: A Survey](https://mlsanity.com/paper/2312.08890/) (2023)
- [Adversarial Examples in Constrained Domains](https://mlsanity.com/paper/2011.01183/) (2020)
- [Denoised Smoothing: A Provable Defense for Pretrained Classifiers](https://mlsanity.com/paper/2003.01908/) (2020)

## Built on by (most cited first, 1 of 1)

- [Physics-Constrained Digital Twins for Sensor Integrity in Urban Pedestrian Flow: Detecting Stealthy False Data Injection with Conformal Guarantees](https://mlsanity.com/paper/2609.17635/) (2026)

## Abstract (arXiv)

Time-series anomaly detection is critical for ensuring safety in high-stakes applications, where robustness is a fundamental requirement rather than a mere performance metric. Addressing the vulnerability of these systems to adversarial manipulation is therefore essential. Existing defenses are largely heuristic or provide certified robustness only under ℓp-norm constraints, which are incompatible with time-series data. In particular, ℓp-norm fails to capture the intrinsic temporal structure in time series, causing small temporal distortions to significantly alter the ℓp-norm measures. Instead, the similarity metric Dynamic Time Warping (DTW) is more suitable and widely adopted in the time-series domain, as DTW accounts for temporal alignment and remains robust to temporal variations. To date, however, there has been no certifiable robustness result in this metric that provides guarantees. In this work, we introduce the first DTW-certified robust defense in time-series anomaly detection by adapting the randomized smoothing paradigm. We develop this certificate by bridging the ℓp-norm to DTW distance through a lower-bound transformation. Extensive experiments across various datasets and models validate the effectiveness and practicality of our theoretical approach. Results demonstrate significantly improved performance, e.g., up to 18.7% in F1-score under DTW-based adversarial attacks compared to traditional certified models.