WAVE: Optimal-Transport-based Domain-Incremental Learning and Generalization for Cross-Subject EEG Decoding

Brain activity varies substantially across individuals, causing Electroencephalography (EEG) decoding models to degrade when applied to new subjects. Each individual shifts the signal underlying probability measure, and models trained on a fixed population generalize poorly to unseen subjects. We cast cross-subject adaptation as domain-incremental learning (DIL), treating each subject as a domain and adapting sequentially through a replay memory. We introduce WAVE, a probabilistic approach that represents each subject as a hierarchical probability measure over classes and a replay memory as a measure over subjects, which are natural objects in a Wasserstein over Wasserstein (WoW) space. As such, WAVE learns a replay buffer by minimizing an optimal-transport divergence in WoW space and augments data with virtual subjects generated between stored and incoming domains for smoother adaptation and improved generalization. Because the memory stores compressed, synthetic subjects rather than raw recordings, WAVE also avoids retaining privacy-sensitive EEG data. Applied to EEG foundation models, WAVE improves the stability-plasticity-generalization trade-off and matches strong replay baselines without storing real EEG.