Geometry-Aware Deep Congruence Networks for Manifold Learning in Cross-Subject Motor Imagery

Abstract: Cross-subject motor-imagery decoding remains a major challenge in EEG-based brain-computer interfaces due to strong subject variability and the curved geometry of covariance matrices on the symmetric positive definite (SPD) manifold. We address the zero-shot cross-subject setting, where no target-subject labels or adaptation are allowed, by introducing novel geometry-aware preprocessing modules and deep congruence networks that operate directly on SPD covariance matrices. Our preprocessing modules, DCR and RiFU, extend Riemannian Alignment by improving action separation while reducing subject-specific distortions. We further propose two manifold classifiers, SPD-DCNet and RiFUNet, which use hierarchical congruence transforms to learn discriminative, subject-invariant covariance representations. On the BCI-IV 2a benchmark, our framework improves cross-subject accuracy by 3-4% over the strongest classical baselines, demonstrating the value of geometry-aware transformations for robust EEG decoding.