A Multi-Scale Submanifold-Aware SPD Attention Network for EEG Decoding

Riemannian attention has become an effective approach for electroencephalography (EEG) decoding by modeling temporal dependencies among covariance representations on the Symmetric Positive Definite (SPD) manifold. However, existing methods typically perform attention only in a single fixed, full-dimensional SPD space, where redundant covariance directions may dilute discriminative temporal relations. To address this limitation, we propose a multi-scale Submanifold-aware SPD Attention network (SSAtt) that learns compact SPD representations for explicitly capturing temporal interactions. SSAtt projects each temporal covariance descriptor into one or more lower-dimensional SPD spaces through sample-adaptive congruence transformations. Each transformation combines a learnable base transformation with a hypernetwork-generated dynamic component, while Newton-Schulz orthogonalization promotes semi-orthogonal projection matrices and thereby preserves the positive definiteness of the projected representations. Riemannian attention is then performed in parallel on the original SPD manifold and the learned compact SPD spaces, allowing full-dimensional covariance information and compact discriminative structures to be jointly exploited. Extensive experiments on four EEG benchmarks demonstrate the effectiveness of SSAtt.