---
title: "Learning Hyperspherical Time–Frequency Representations for Time-Series Out-of-Distribution Detection"
authors:
  - "Willian T. Lunardi"
  - "Samridha Shrestha"
  - "Martin Andreoni"
doi: "10.24963/ijcai.2026/321"
url: "https://ijcai.org/proceedings/2026/321"
pdf: "https://ijcai.org/proceedings/2026/0321.pdf"
venue: "Proceedings of the Thirty-Fifth International Joint Conference on Artificial Intelligence"
year: 2026
pages: "2888-2896"
track: "Main Track"
keywords:
  - "Machine Learning: Representation learning"
  - "Data Mining: Anomaly/outlier detection"
  - "Machine Learning: Open-World/Open-Set/OOD Learning"
---

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

Willian T. Lunardi, Samridha Shrestha, Martin Andreoni

*Proceedings of the Thirty-Fifth International Joint Conference on Artificial Intelligence*, pages 2888-2896. DOI: [10.24963/ijcai.2026/321](https://doi.org/10.24963/ijcai.2026/321)

## Abstract

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.