# VACE: Learning Geometrically Structured Representations for Time Series Anomaly Detection

arXiv: https://arxiv.org/abs/2605.23504 · HTML: https://mlsanity.com/paper/2605.23504/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 30 of its 52 references that are in the map.
- First posted on arXiv 22 May 2026.

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

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks](https://mlsanity.com/paper/1807.03888/) (2018)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis](https://mlsanity.com/paper/2210.02186/) (2022)
- [Towards Total Recall in Industrial Anomaly Detection](https://mlsanity.com/paper/2106.08265/) (2021)
- [Chronos: Learning the Language of Time Series](https://mlsanity.com/paper/2403.07815/) (2024)
- [A decoder-only foundation model for time-series forecasting](https://mlsanity.com/paper/2310.10688/) (2023)
- [Self-supervised Visual Feature Learning with Deep Neural Networks: A Survey](https://mlsanity.com/paper/1902.06162/) (2019)
- [MOMENT: A Family of Open Time-series Foundation Models](https://mlsanity.com/paper/2402.03885/) (2024)
- [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)
- [Understanding Dimensional Collapse in Contrastive Self-supervised Learning](https://mlsanity.com/paper/2110.09348/) (2021)
- [xLSTM: Extended Long Short-Term Memory](https://mlsanity.com/paper/2405.04517/) (2024)
- [A review on outlier/anomaly detection in time series data](https://mlsanity.com/paper/2002.04236/) (2020)
- [RankMe: Assessing the downstream performance of pretrained self-supervised representations by their rank](https://mlsanity.com/paper/2210.02885/) (2022)
- [Deep Learning for Time Series Anomaly Detection: A Survey](https://mlsanity.com/paper/2211.05244/) (2022)
- [DCdetector: Dual Attention Contrastive Representation Learning for Time Series Anomaly Detection](https://mlsanity.com/paper/2306.10347/) (2023)
- [Understanding Contrastive Learning Requires Incorporating Inductive Biases](https://mlsanity.com/paper/2202.14037/) (2022)
- [CATCH: Channel-Aware multivariate Time Series Anomaly Detection via Frequency Patching](https://mlsanity.com/paper/2410.12261/) (2024)
- [Local Evaluation of Time Series Anomaly Detection Algorithms](https://mlsanity.com/paper/2206.13167/) (2022)
- [Precision and Recall for Time Series](https://mlsanity.com/paper/1803.03639/) (2018)
- [Towards a General Time Series Anomaly Detector with Adaptive Bottlenecks and Dual Adversarial Decoders](https://mlsanity.com/paper/2405.15273/) (2024)
- [KAN-AD: Time Series Anomaly Detection with Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2411.00278/) (2024)
- [TSPulse: Tiny Pre-Trained Models with Disentangled Representations for Rapid Time-Series Analysis](https://mlsanity.com/paper/2505.13033/) (2025)
- [CrossAD: Time Series Anomaly Detection with Cross-scale Associations and Cross-window Modeling](https://mlsanity.com/paper/2510.12489/) (2025)
- [PaAno: Patch-Based Representation Learning for Time-Series Anomaly Detection](https://mlsanity.com/paper/2602.01359/) (2026)
- [xLSTMAD: A Powerful xLSTM-based Method for Anomaly Detection](https://mlsanity.com/paper/2506.22837/) (2025)

## Abstract (arXiv)

Anomaly detection in multivariate time series is a critical task across a wide range of real-world applications, where abnormal behaviour is rare, labels are unavailable, and the cost of a miss is high. The central challenge is learning a characterisation of normality precise enough to flag deviations. Representation self-supervised learning, typically through contrastive approaches, addresses this by embedding temporal patches into a latent space where normality occupies a well-defined region, with anomalies detected by geometric deviation. However, contrastive approaches shape this space indirectly through pair-sampling heuristics, providing no explicit control over the geometric structure that distance-based scoring requires. This means how tightly normal representations are grouped, and whether distances are directionally meaningful. We present VACE (Velocity-Aligned Channel Embeddings), a self-supervised anomaly detection method that represents normality as a compact, directionally coherent region in the embedding space. To this end, VACE trains a channel-aware encoder through a velocity-consistency objective, with no negatives and no synthetic anomalies, so that normal trajectories are locally smooth and aligned. At test time, a Mahalanobis positional score and a velocity-bank directional score are combined multiplicatively, flagging points that are simultaneously off-distribution and dynamically atypical. Despite its simplicity, VACE achieves state-of-the-art performance on TSB-AD-M under rigorous evaluation, significantly outperforming more complex methods trained on substantially larger budgets.