Towards Robust EEG Decoding Based on Riemannian Self-Attention

Brain-Computer Interface (BCI) systems often rely on EEG decoding to translate neural activity into commands. A major challenge in this field is the low signal-to-noise ratio (SNR) of EEG data and the high inter-subject variability. While Riemannian geometry-based methods have shown promise by treating EEG covariance matrices as points on a Symmetric Positive Definite (SPD) manifold, existing approaches often use simple architectures that fail to capture complex local relationships or struggle with numerical instability when dealing with ill-conditioned matrices.

The authors propose a Riemannian self-attention network, GBWAtt, designed to operate directly on the SPD manifold. The framework consists of four main modules: a Spatiotemporal Feature Extraction Module (SFEM) to process raw EEG signals, an SPD Modeling Module (SPDM) to generate SPD representations, an SPD Self-Attention Module (SSAM) that leverages the Bures-Wasserstein metric (BWM) to model geometric relationships, and a Manifold to Euclidean Embedding Mapping (MEEM) layer for final classification. By incorporating the generalized Bures-Wasserstein metric (GBWM) with learnable parameters and matrix power deformation, the model adapts to the underlying geometric structure of the data, providing a more nuanced representation than traditional metrics like the Affine-Invariant Metric (AIM).

The proposed GBWAtt framework demonstrates superior robustness and effectiveness across three EEG benchmarking datasets. By replacing standard Euclidean attention with a Riemannian self-attention mechanism, the model better handles the non-Euclidean nature of EEG-derived covariance matrices. The use of the Bures-Wasserstein metric provides significant advantages in numerical stability, particularly for ill-conditioned SPD matrices, while the learnable geometric parameters allow the network to dynamically adjust to the evolving latent geometry of the EEG signals.