The Riemannian Geometry of User Learning in MI-BCI: a Cybathlon Longitudinal Study

Background: \Ac{mi} \acp{bci} are promising assistive technologies, however, their development is hindered by low \ac{eeg} signal quality and an incomplete understanding of neural modulation during training. Traditional performance-based metrics provide limited insight into the mechanisms of skill acquisition. We hypothesize that Riemannian geometry offers a robust framework for analyzing structural and physiological \ac{eeg} patterns associated with learning. Methods: This study analyzes longitudinal \ac{eeg} data collected during a Cybathlon pilot to investigate how Riemannian features evolve throughout \ac{mi}-\ac{bci} training. Novel metrics are introduced by combining geodesic distances on the Riemannian manifold with cosine similarity between tangent-space vectors, enabling the quantification of neural trajectories during training. Results: The results demonstrate that the proposed Riemannian features capture meaningful changes in neural representations that reflect user learning. Furthermore, we introduce the concept of user learning states, showing that specific subsets of the extracted neural features can be associated with a emergent or with a stable state Conclusions: These findings highlight the value of geometric \ac{eeg} metrics for characterizing cortical adaptation during \ac{mi}-\ac{bci} training and for guiding the development of adaptive training strategies in \ac{mi}-based \ac{bci} systems.