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

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 within a representation-learning framework based on hyper- spherical embeddings, in which class-conditional structure is induced by a von Mises–Fisher like- lihood–based objective on the unit sphere. The learned representation combines time-domain and frequency-domain representations of the input sig- nal, obtained via distinct domain-specific encoders, and integrates them into a joint embedding space for OOD detection. Detection is performed using distance-based scoring functions defined over the learned embeddings, including k-NN and Maha- lanobis scores. The proposed approach is evaluated at scale on the complete UCR and UEA time-series archives under a cross-dataset protocol. Empirical results demonstrate that the resulting models con- sistently improve OOD detection performance un- der both k-NN and Mahalanobis scoring, compared with strong contrastive-learning and post-hoc base- lines evaluated in the same experimental setting.

Setup

a. Use Docker (Recommended)

bash scripts/build_docker.sh
bash scripts/run_docker.sh  # you will be inside the docker env with all reqs already installed

b. Or, install with pip in a virtualenv / conda env:

python -m venv venv
source venv/bin/activate
pip install -r requirements.txt

Experiment scripts

UCR and UEA datasets are autodownloaded by the training scripts. The training takes a lot of time (6-8 hours) since we run 3 seeds on each configuration across 128 UCR and 30 UEA datasets. To reduce training time, run on a system with a higher number of GPUs and increase parallel GPU runs with --ngpus NGPUS for the experiment scripts.

Main table hypertf results.

# Run HyperTF experiments
# Use --ngpus NGPUS to increase number of parallel GPU experiment runs
python scripts/exp_scripts/main_table/exp_hypertf.py

# Run HyperTF with auxiliary outlier data experiments (Runs both the near & far OOD case)
python scripts/exp_scripts/main_table/exp_hypertf_aux_outlier.py

# Run HyperTF with MixOE experiments (Runs both the near & far OOD case)
python scripts/exp_scripts/main_table/exp_hypertf_mixup_oe.py

# Generate main result table using:
python scripts/postprocess/near_far_ood_method_table_per_OOD_group.py main_table

Ablation table fft results

# Run ablation table FFT experiments, runs three runs on two 2 gpus, GPU runs can be changed inside
python scripts/exp_scripts/ablation/exp_fft.py

# Generate ablation table fft results with
python scripts/postprocess/near_far_ood_method_table_per_OOD_group.py main_table/hyper_tf ablation

Train

# UCR training
python train.py --cfg configs/contrastive/ucr_supcon_hyper.yaml --id ECG200 --dataset ECG200
# UEA training
python train.py --cfg configs/contrastive/uea_supcon_hyper.yaml --id Epilepsy --dataset Epilepsy

# Overrides can be passed with -o
# list overrides passed with [i] indexing
python train.py --cfg configs/contrastive/ucr_supcon_hyper.yaml -o loss.args.losses[0].args.temperature=0.01

Data

The Data is automatically downloaded during training from aeon datasets. The datasets should then be arranged in the data/ folder in the following way:

• 128 UCR datasets should be put into data/UCR/ so that each data file can be located by data/UCR/<dataset_name>/<dataset_name>_*.csv.
• 30 UEA datasets should be put into data/UEA/ so that each data file can be located by data/UEA/<dataset_name>/<dataset_name>_*.arff.

Dev Tests

pip install -r tests/requirements.txt
# Currently tests may not match if python version != 3.11.9
pytest tests
# to regenerate and sync test fixtures for the integrations tests
# WARNING: Only do this if sure the test acc/f1/auroc/fpr results should change
python tests/reset_integration_test_fixtures.py

Citation

If you find this work or code useful for your research, please cite our paper:

@inproceedings{lunardi2026learning,
  title={Learning Hyperspherical Time--Frequency Representations for Time-Series Out-of-Distribution Detection},
  author={Lunardi, Willian T. and Shrestha, Samridha and Andreoni, Martin},
  booktitle={Proceedings of the International Joint Conference on Artificial Intelligence (IJCAI)},
  year={2026}
}