Distribution shift poses a significant challenge in machine learning, particularly in biomedical applications using data collected across different subjects, institutions, and recording devices, such as sleep data. While existing normalization layers, BatchNorm, LayerNorm and InstanceNorm, help mitigate distribution shifts, when applied over the time dimension they ignore the dependencies and auto-correlation inherent to the vector coefficients they normalize. In this paper, we propose PSDNorm that leverages Monge mapping and temporal context to normalize feature maps in deep learning models for signals. Evaluations with architectures based on U-Net or transformer backbones trained on 10K subjects across 10 datasets, show that PSDNorm achieves state-of-the-art performance on unseen left-out datasets while being more robust to data scarcity.
@article{arxiv.2503.04582,
title = {PSDNorm: Test-Time Temporal Normalization for Deep Learning in Sleep Staging},
author = {Théo Gnassounou and Antoine Collas and Rémi Flamary and Alexandre Gramfort},
journal= {arXiv preprint arXiv:2503.04582},
year = {2026}
}