# Learning Hyperspherical Time-Frequency Representations for Time-Series Out-of-Distribution Detection

arXiv: https://arxiv.org/abs/2605.31155 · HTML: https://mlsanity.com/paper/2605.31155/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 44 of its 55 references that are in the map.
- First posted on arXiv 29 May 2026.

## Builds on (most cited first, 30 of 44)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Supervised Contrastive Learning](https://mlsanity.com/paper/2004.11362/) (2020)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks](https://mlsanity.com/paper/1807.03888/) (2018)
- [Enhancing The Reliability of Out-of-distribution Image Detection in Neural Networks](https://mlsanity.com/paper/1706.02690/) (2017)
- [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)
- [Out-of-Distribution Detection with Deep Nearest Neighbors](https://mlsanity.com/paper/2204.06507/) (2022)
- [ReAct: Out-of-distribution Detection With Rectified Activations](https://mlsanity.com/paper/2111.12797/) (2021)
- [TS2Vec: Towards Universal Representation of Time Series](https://mlsanity.com/paper/2106.10466/) (2021)
- [Scaling Out-of-Distribution Detection for Real-World Settings](https://mlsanity.com/paper/1911.11132/) (2019)
- [CSI: Novelty Detection via Contrastive Learning on Distributionally Shifted Instances](https://mlsanity.com/paper/2007.08176/) (2020)
- [ViM: Out-Of-Distribution with Virtual-logit Matching](https://mlsanity.com/paper/2203.10807/) (2022)
- [InceptionTime: Finding AlexNet for Time Series Classification](https://mlsanity.com/paper/1909.04939/) (2019)
- [On the Importance of Gradients for Detecting Distributional Shifts in the Wild](https://mlsanity.com/paper/2110.00218/) (2021)
- [OpenOOD: Benchmarking Generalized Out-of-Distribution Detection](https://mlsanity.com/paper/2210.07242/) (2022)
- [SSD: A Unified Framework for Self-Supervised Outlier Detection](https://mlsanity.com/paper/2103.12051/) (2021)
- [Mitigating Neural Network Overconfidence with Logit Normalization](https://mlsanity.com/paper/2205.09310/) (2022)
- [Extremely Simple Activation Shaping for Out-of-Distribution Detection](https://mlsanity.com/paper/2209.09858/) (2022)
- [Contrastive Training for Improved Out-of-Distribution Detection](https://mlsanity.com/paper/2007.05566/) (2020)
- [OpenOOD v1.5: Enhanced Benchmark for Out-of-Distribution Detection](https://mlsanity.com/paper/2306.09301/) (2023)
- [How to Exploit Hyperspherical Embeddings for Out-of-Distribution Detection?](https://mlsanity.com/paper/2203.04450/) (2022)
- [ATOM: Robustifying Out-of-distribution Detection Using Outlier Mining](https://mlsanity.com/paper/2006.15207/) (2020)
- [Unsupervised Out-of-Distribution Detection by Maximum Classifier Discrepancy](https://mlsanity.com/paper/1908.04951/) (2019)
- [POEM: Out-of-Distribution Detection with Posterior Sampling](https://mlsanity.com/paper/2206.13687/) (2022)
- [Mixture Outlier Exposure: Towards Out-of-Distribution Detection in Fine-grained Environments](https://mlsanity.com/paper/2106.03917/) (2021)
- [Nearest Neighbor Guidance for Out-of-Distribution Detection](https://mlsanity.com/paper/2309.14888/) (2023)
- [Rethinking Out-of-distribution (OOD) Detection: Masked Image Modeling is All You Need](https://mlsanity.com/paper/2302.02615/) (2023)
- [Learning with Mixture of Prototypes for Out-of-Distribution Detection](https://mlsanity.com/paper/2402.02653/) (2024)
- [Diversified Outlier Exposure for Out-of-Distribution Detection via Informative Extrapolation](https://mlsanity.com/paper/2310.13923/) (2023)

## Abstract (arXiv)

Out-of-distribution (OOD) detection for time-series data remains comparatively underexplored compared to vision and language, with a limited principled understanding of how supervised time-series representations can be leveraged for reliable detection under distributional shifts. This work formulates time-series OOD detection as representation learning with hyperspherical embeddings, where class-conditional structure is induced by a von Mises-Fisher (vMF) likelihood-based objective on the unit sphere. The learned representation combines time- and frequency-domain views of the input signal via domain-specific encoders, integrating them into a joint embedding space for OOD detection. Detection uses distance-based scores over the learned embeddings, including k-nearest neighbors (k-NN) and Mahalanobis scores. We evaluate the approach at scale on the complete UCR and UEA time-series archives under a cross-dataset protocol. Empirical results show consistent improvements under both k-NN and Mahalanobis scoring over strong contrastive learning and post-hoc baselines in the same setting. Code is available at https://github.com/tiiuae/hypertf-time-series-ood.