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

2026-05-29

AI Summary

This work addresses the challenge of out-of-distribution (OOD) detection for time series under distribution shift, where effective supervised representations are often lacking. To this end, the authors propose a time–frequency joint representation learning method based on hyperspherical embedding. This approach introduces hyperspherical representations to time series OOD detection for the first time, employing dedicated time- and frequency-domain encoders to construct a unified embedding space and modeling class-conditional structure via the von Mises–Fisher distribution. OOD detection is performed using k-nearest neighbor and Mahalanobis distance scoring in the learned embedding space. Comprehensive cross-dataset experiments on the full UCR and UEA archives demonstrate that the proposed method significantly outperforms existing contrastive learning and post-hoc baselines.

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.

Problem

• time-series
• out-of-distribution detection
• distributional shifts
• representation learning
• hyperspherical embeddings

Innovation

• hyperspherical embeddings
• time-frequency representation
• out-of-distribution detection
• von Mises-Fisher distribution
• time-series representation learning